text:
\section{Introduction}

From a high energy physics perspective, General Relativity is a low-energy Effective Field Theory (EFT) of the gravitational sector. Its UV completions generically include additional degrees of freedom whose low-energy signatures are captured by higher-derivative corrections.  For macroscopically large black holes, these additional operators perturbatively alter the familiar relationships between the quantities which specify the black hole state and derived properties such as the Hawking temperature, entropy, and extremality bounds.

In this note, we derive a universal relation between the leading corrections to the extremality bound and entropy of generic black holes. Consider a gravitational theory permitting black holes characterized by mass $M$ and additional quantities $\vec{\Q}$.  Associated to these solutions are an entropy $S_{0}(M,\vec{\Q})$ and temperature $T_{0}(M,\vec{\Q})$.  States of fixed $\vec{\Q}$ generically have a minimum mass set by an extremality bound of the form $M>M_{\rm ext}^{0}(\vec{\Q})$.

Now consider perturbatively changing the theory in a manner controlled by a parameter $\epsilon$, defined precisely later in \eqref{GenericFreeEnergy}.  The extremality bound and entropy then become $\epsilon$-dependent and are changed to the form $M>M_{\rm ext}(\vec{\Q},\epsilon)$ and $S(M,\vec{\Q},\epsilon)$, where $M_{\rm ext}(\vec{\Q},0)=M_{\rm ext}^{0}(\vec{\Q})$ and $S(M,\vec{\Q},0)=S_{0}(M,\vec{\Q})$.  In this note, we prove the following, exact result under mild assumptions:
\begin{align}
\mkern-9mu \frac{\partial M_{\rm ext}(\vec{\Q},\epsilon)}{\partial \epsilon}=\lim_{M\to M_{\rm ext}(\vec{\Q},\epsilon)}\mkern-9mu-T\left (\frac{\partial S(M,\vec{\Q},\epsilon)}{\partial \epsilon}\right )_{M,\vec{\Q}}\ ,\label{ExactRelationIntroduction}
\end{align}
where $T=T(M,\vec{\Q},\epsilon)$ is the corrected temperature.

Using the above, we then derive further, approximate relations which hold at leading order in a perturbative expansion.  For instance, \eqref{ExactRelationIntroduction} implies a leading-order expression of the form
  \begin{align}
\Delta M_{\rm ext}(\vec{\Q})
&\approx-T_{0}(M,\vec{\Q})\Delta S(M,\vec{\Q} )\Big|_{M\approx M^{0}_{\rm ext}(\vec{\Q})}\ ,\label{ApproxRelation2Introduction}
  \end{align}
where $\Delta S(M,\vec{\Q} )$ and $\Delta M_{\rm ext}(\vec{\Q})$ are the leading corrections to the entropy of a state with fixed $M,\vec{\Q}$ and to the extremality bound, respectively.  The meaning of $M\approx M^{0}_{\rm ext}(\vec{\Q})$ and the assumptions under which \eqref{ApproxRelation2Introduction} is valid are discussed in detail below. As thermodynamic quantities do not generically admit analytic expansions in $\epsilon$ near extremality, the conditions under which \eqref{ExactRelationIntroduction} follows from \eqref{ApproxRelation2Introduction} are not entirely trivial.

Our results are intimately connected to the Weak Gravity Conjecture (WGC) \cite{ArkaniHamed:2006dz}. One facet of the WGC is that the $U(1)$ charge-to-mass ratio  of extremally charged black holes should be larger than unity in any gravitational EFT which admits a consistent UV completion.   In particular, the WGC posits that black holes support $Q/M\ge 1$ at extremality for generic masses and the bound is expected to only approach the classical Einstein-Maxwell extremality result $Q/M=1$ in the $M\to \infty$ limit.    See \cite{Cheung:2014ega,Bellazzini:2019xts,Hamada:2018dde} for previous EFT-based arguments supporting this version of the conjecture.

The connection between \eqref{ApproxRelation2Introduction} and the WGC is due to the work of \cite{Cheung:2018cwt,Cheung:2019cwi}.  The authors demonstrate  that, under certain assumptions, higher-derivative corrections generate $\Delta S (M,\vec{\Q}) >0$ for thermodynamically stable black holes. A similar idea was also suggested in \cite{Kats:2006xp}.  This line of reasoning was applied to the case of a single $U(1)$ charge $Q$ in \cite{Cheung:2018cwt}, where higher-derivative corrections to the entropy and extremality bound were computed explicitly and found to obey
\begin{align}
\Delta M_{\rm ext}(Q)\propto \Delta S(M,Q)\Big|_{M\approx Q}\ \label{CheungRemmenRelation}
\end{align}
with a negative constant of proportionality.  If $\Delta S>0$, then the single $U(1)$ form of the WGC follows immediately.

The result \eqref{ApproxRelation2Introduction} is a generalization of \eqref{CheungRemmenRelation} and it follows that a generic perturbed extremal black hole is less massive than its unperturbed counterpart with the same quantum numbers, if $\Delta S>0$. This statement is the generalization of having an increased $Q/M$ ratio in the case of multiple non-trivial quantum numbers.  Hence, if the $\Delta S>0$ conjecture of \cite{Cheung:2018cwt} is correct, \eqref{ApproxRelation2Introduction} proves that the extremality curves of a wide class of black hole systems display WGC-like behavior.  Conversely, assuming the WGC is correct, \eqref{ApproxRelation2Introduction} demonstrates that the conjecture also implies a preferred sign for shifts to the entropy of near extremal black holes.

We have confirmed that \eqref{ApproxRelation2Introduction} is consistent with the results in \cite{Cheung:2018cwt,Cheung:2019cwi,Reall:2019sah,Cano:2019oma,Cano:2019ycn} and in the final section of this note we explicitly verify \eqref{ExactRelationIntroduction} and \eqref{ApproxRelation2Introduction} in the case of charged, asymptotically anti-de Sitter, four-dimensional black holes.

The derivation of \eqref{ExactRelationIntroduction} is purely thermodynamic and is not specific to black holes.  Relatedly, the proof has no explicit dependence on such details as the spacetime dimensionality or the matter content of the theory. In a general context, \eqref{ExactRelationIntroduction} is a relation between the change in the energy of a system at zero temperature and the change in the entropy at fixed extensive variables due to an alteration of the underlying dynamics.    While \eqref{ExactRelationIntroduction} and its approximate descendants may therefore find interesting applications beyond the regime of black hole physics, in this note we remain focused on gravitational systems.

\noindent \textbf{Conventions}: We work in Euclidean signature and our curvature conventions are $R^{\rho}{}_{\sigma\mu\nu}=\partial_{\mu}\Gamma^{\rho}_{\nu\sigma}+\ldots$ and $R_{\sigma\nu}=R^{\rho}{}_{\sigma\rho\nu}$.  Natural units are used throughout: $G_{N}=k_{B}=\hbar=c=1$.

\noindent \textbf{Note Added}: The central derivation in this letter has been improved. The original letter only contained the approximate relation \eqref{ApproxRelation2Introduction} which was derived for $M\approx M_{\rm ext}^{0}(\vec{\Q})$, whereas the current version proves the exact result \eqref{ExactRelationIntroduction}, from which \eqref{ApproxRelation2Introduction} follows.  The relation \eqref{ExactRelationIntroduction} explains subtleties which can arise in the strict $M=M_{\rm ext}^{0}(\vec{\Q})$ limit and is consistent with  \cite{Loges:2019jzs,Cano:2019oma,Cano:2019ycn} which probe this regime.  References \cite{Cano:2019oma,Cano:2019ycn} appeared after the initial version of this letter.

\section{General Argument}

The argument for \eqref{ExactRelationIntroduction} follows from considering the effects of perturbative corrections to the free energy of generic thermodynamic systems.  This problem was addressed in \cite{Reall:2019sah} for the case of spinning, four-dimensional black holes.

Consider a thermodynamic system characterized by the entropy $S$ and the collection of additional extensive variables $\vec{\Q}$ such that the energy of the system is $M(S,\vec{\Q})$.  The first law is then of the form
\begin{align}
  {\rm d} M=T{\rm d} S+\vec{\mu}\cdot{\rm d} \vec{\Q}\ , \label{FirstLaw}
  \end{align}
  with $\vec{\mu}$ a set of generalized chemical potentials.  In a black hole context, $\vec{\Q}$ may contain conserved quantities, such as various angular momenta and $U(1)$ charges, as well terms not associated to any conservation law, like the ``volume" of the black hole \cite{Kastor:2009wy} and the value of moduli fields at infinity \cite{Gibbons:1996af} in scenarios where variations of these latter parameters are considered.

  Let us work in the ensemble where all of the quantum numbers $\vec{\Q}$ are allowed to fluctuate.  The following argument also generalizes to cases where an arbitrary subsets of $\vec{\Q}$ fluctuates; we only focus on the present ensemble for clarity of presentation.  The associated thermodynamic potential $G(T,\vec{\mu})$ arises from Legendre transforming $M(S,\vec{\Q})$ over $S$ and $\vec{\Q}$ in the usual manner. We will simply refer to $G$ as the ``free energy" in the following.

We assume that the above free energy consists of a dominant, zeroth order piece, $G_{0}(T,\vec{\mu})$, plus a perturbative correction $\Delta G(T,\vec{\mu})$.  In this note, unperturbed quantities will carry a $0$ subscript or superscript and will often be referred to as being ``classical."  Following \cite{Reall:2019sah}, we insert a convenient counting parameter $\epsilon$ in front of $\Delta G$ such that $G(T,\vec{\mu})\longrightarrow G(T,\vec{\mu},\epsilon)$ where
\begin{align}
G(T,\vec{\mu},\epsilon)&\equiv G_{0}(T,\vec{\mu})+\epsilon\Delta G(T,\vec{\mu})\ .\label{GenericFreeEnergy}
\end{align}
The quantities $S$, $\vec{\Q}$, and $M$ are given by:
\begin{align}
S(T,\vec{\mu},\epsilon)&=-\left (\frac{\partial G}{\partial T}\right )_{\vec{\mu},\epsilon} \nonumber\\
\mathcal{Q}_{i}(T,\vec{\mu},\epsilon)&=-\left (\frac{\partial G}{\partial \mu_{i}}\right )_{T,\mu_{j\neq i},\epsilon} \nonumber\\
M(T,\vec{\mu},\epsilon)&= G(T,\vec{\mu},\epsilon)+TS+\vec{\mu}\cdot\vec{\Q}\ ,
\label{BasicThermoRelations}
\end{align}
which are the standard thermodynamic relations.

When the microscopic dynamics of the system are described by an action of the form $I=I_{0}+\epsilon\Delta I$, with $I_{0}$ the leading term and $\Delta I$ a perturbative correction, $\Delta G$ is directly determined by $\Delta I$, at leading order in $\epsilon$.  In the specific case of black holes, $G(T,\vec{\mu})$ is given by~\cite{Gibbons:1976ue}
\begin{align}
\beta\, G(T,\vec{\mu})&=I[g_{\mu\nu}(T,\vec{\mu}),\ldots]\ ,\label{EuclideanAction}
\end{align}
where $\beta=1/T$ is the inverse Hawking temperature, $I$ is the Euclidean action, $g_{\mu\nu}=g_{\mu\nu}(T,\vec{\mu})$ is the Euclideanized metric solution parameterized in terms of $T$ and $\vec{\mu}$, the ellipses represent other possible fields, and the corresponding entropy $S$ in \eqref{BasicThermoRelations} is the Wald entropy \cite{Wald:1993nt}.  A subtraction prescription is typically required to render \eqref{EuclideanAction} finite \cite{Gibbons:1976ue,Emparan:1999pm,Balasubramanian:1999re}. For gravitational systems, the unperturbed action $I_{0}$ might be Einstein-Hilbert, Einstein-Maxwell, etc.~and $\Delta I$ could represent higher-derivative corrections, extra matter fields, or lower derivative terms such as a cosmological constant, for example. We only require that the effects of $\Delta I$ are appropriately small.
The Euclidean solution is also corrected due to the change in the theory, such that $g_{\mu\nu}=g^{0}_{\mu\nu}+\epsilon\Delta g_{\mu\nu}$, with $g^{0}_{\mu\nu}$ a solution of $I_{0}$.  The terms in \eqref{GenericFreeEnergy} are, at leading order,
 \begin{align}
 \beta G_{0}&=I_{0}[g^{0}_{\mu\nu},\ldots] \nonumber\\
  \epsilon\beta \Delta G&=\epsilon\Delta I[g^{0}_{\mu\nu},\ldots] \nonumber\\
  &\quad +I_{0}[g^{0}_{\mu\nu}+\epsilon\Delta g_{\mu\nu},\ldots]-I_{0}[g^{0}_{\mu\nu},\ldots]\ .\label{G0DeltaGForGravitationalSystems}
 \end{align}
 Up to $\mathcal{O}(\epsilon)$, the final line above can only receive a contribution from boundary terms and is expected to vanish if these (and any necessary subtraction prescriptions) are chosen to respect the proper variational principle, essentially by definition, in which case $\Delta g_{\mu\nu}$ is not required and $\Delta G\propto\Delta I$.  This fact was explicitly demonstrated in \cite{Reall:2019sah}, for the case of asymptotically flat spacetimes and also occurs in the example of the following section.

We can derive a universal relation from \eqref{GenericFreeEnergy} by assuming that we can invert \eqref{BasicThermoRelations} to switch amongst the variables $T$, $\vec{\mu}$, $M$, and $\vec{\Q}$ and that the perturbative corrections to the entropy respect the condition
 \begin{align}
	\lim_{T\to 0} T \left (\frac{\partial S(T,\vec{\Q},\epsilon)}{\partial \epsilon}\right )_{T,\vec{\Q}} = 0 \ , \label{ThirdLawAssumption}
\end{align}
which can be interpreted as a version of the third law.

We begin by considering the perturbed extremality bound, which is now $M>M_{\rm ext}(\vec{\Q},\epsilon)$ where
\begin{align}
M_{\rm ext}(\vec{\Q},\epsilon)&\equiv \lim_{T\to 0}M(T,\vec{\Q},\epsilon)\ .
  \end{align}
  Let us characterize the effect of the perturbative corrections by computing the $\epsilon$-derivative of $M$ at fixed $T,\vec{\Q}$.  Using \eqref{BasicThermoRelations} and the chain rule, one finds
  \begin{align}
  \left (\frac{\partial M}{\partial \epsilon}\right )_{T,\vec{\Q}}&=\left (\frac{\partial}{\partial\epsilon}\left (G+TS+\vec{\mu}\cdot\vec{\Q}\right )\right )_{T,\vec{\Q}} \nonumber\\
  &=\left (\frac{\partial  G }{\partial \vec{\mu}}\right )_{T,\epsilon}\! \!\cdot\left (\frac{\partial  \vec{\mu} }{\partial \epsilon}\right )_{T,\vec{\Q}}
  +\left (\frac{\partial  G }{\partial \epsilon}\right )_{T,\vec{\mu}} \nonumber\\
  &\quad
  +T\left (\frac{\partial  S }{\partial \epsilon}\right )_{T,\vec{\Q}}
  +\vec{\Q}\cdot\left (\frac{\partial  \vec{\mu} }{\partial \epsilon}\right )_{T,\vec{\Q}}\ ,
  \end{align}
  where we considered $G$ as a function of $(T,\vec{\mu},\epsilon)$ while $S$ and $\vec{\mu}$ were treated as functions of $(T,\vec{\Q},\epsilon)$.  Due to \eqref{BasicThermoRelations}, the first and final terms above cancel and we are left with
  \begin{align}
  \left (\frac{\partial M}{\partial \epsilon}\right )_{T,\vec{\Q}}=\Delta G(T,\vec{\mu}(T,\vec{\Q},\epsilon))+T\left (\frac{\partial  S }{\partial \epsilon}\right )_{T,\vec{\Q}}\ ,\label{dMdepsilon}
  \end{align}
   where we used that $\left (\frac{\partial G}{\partial \epsilon}\right )_{T,\vec{\mu}}=\Delta G(T,\vec{\mu})$, by definition. Finally, if we take the $T\to 0$ limit and use the third law assumption \eqref{ThirdLawAssumption}, we find
     \begin{align}
  \lim_{T\to 0}\left (\frac{\partial M}{\partial \epsilon}\right )_{T,\vec{\Q}}=\lim_{T\to 0}\Delta G(T,\vec{\mu}(T,\vec{\Q},\epsilon))\ .\label{dMdepsilonT0}
  \end{align}

   Next, the change in the entropy at fixed $M,\vec{\Q}$ is characterized by $\left (\frac{\partial S}{\partial \epsilon}\right )_{M,\vec{\Q}}$.  A straightforward generalization of the argument in \cite{Reall:2019sah} (see \cite{Loges:2019jzs}, also) yields the result
   \begin{align}
    -T\left (\frac{\partial S}{\partial \epsilon}\right )_{M,\vec{\Q}}&=\Delta G\left (T(M,\vec{\Q},\epsilon),\vec{\mu}(M,\vec{\Q},\epsilon)\right )\ .\label{dSdepsilon}
    \end{align}  The proof is similar to the derivation of \eqref{dMdepsilon}: it is a straightforward exercise in the chain rule and the use of thermodynamic identities, including the first law \eqref{FirstLaw}.

 It is then evident that \eqref{dMdepsilonT0} and \eqref{dSdepsilon} coincide if the latter is evaluated at the extremal point $M=M_{\rm ext}(\vec{\Q},\epsilon)$ corresponding to $T=0$ in the perturbed theory:
 \begin{align}
\mkern-10mu  \lim_{T\to 0}\left (\frac{\partial M}{\partial \epsilon}\right )_{T,\vec{\Q}}\mkern-7mu &=\mkern-7mu \lim_{M\to M_{\rm ext}(\vec{\Q},\epsilon)}\mkern-20mu -T(M,\vec{\Q},\epsilon)\left (\frac{\partial S}{\partial \epsilon}\right )_{M,\vec{\Q}} .\label{ExactRelation}
 \end{align}
 As argued below, we expect the left side of \eqref{ExactRelation} to be finite, in which case $\left (\partial S/\partial\epsilon\right )_{M,\vec{\Q}}$ must diverge as $\sim T^{-1}$ as $M\to M_{\rm ext}(\vec{\Q},\epsilon)$, though $S(M,\vec{\Q},\epsilon)$ itself need not diverge in this limit. The above is an exact identity for any system of the form \eqref{GenericFreeEnergy}, irrespective of whether $\Delta G$ is small in any sense.  However, we anticipate that in applications the role of $\epsilon$ will be played by a combination of EFT coefficients and the free energy will only take the form \eqref{GenericFreeEnergy} in a leading-order expansion, in which case \eqref{ExactRelation} is exact only for the truncated system.

The result \eqref{ExactRelation} relates properties of corrected states in the perturbed theory.  Through suitable approximations, it is also possible to interpret \eqref{ExactRelation} as a comparison between states in the classical and corrected theories, but there are subtleties in this analysis.  In particular, the right side of the relation is suggestive of a comparison of entropies of states with fixed $M,\vec{\Q}$, but cannot immediately be understood as such if $M_{\rm ext}(\vec{\Q},\epsilon)<M_{\rm ext}^{0}(\vec{\Q})$.  This is due to the fact that the derivative is evaluated at $M_{\rm ext}(\vec{\Q},\epsilon)$ and there was no state carrying mass $M_{\rm ext}(\vec{\Q},\epsilon)$ and quantum numbers $\vec{\Q}$ in the unperturbed theory, in this scenario.

 In the aforementioned case, we can instead evaluate right side of \eqref{ExactRelation} at the unperturbed extremal point $M_{\rm ext}^{0}(\vec{\Q})$, rather than $M_{\rm ext}(\vec{\Q},\epsilon)$.  This corresponds to a valid comparison between states in the classical and perturbed theories, as such a state exists in both cases, by assumption. The result is the approximate relation
 \begin{align}
\mkern-10mu  \lim_{T\to 0}\left (\frac{\partial M}{\partial \epsilon}\right )_{T,\vec{\Q}}\mkern-7mu &\approx\mkern-7mu \lim_{M\to M_{\rm ext}^{0}(\vec{\Q})}\mkern-20mu -T(M,\vec{\Q},\epsilon)\left (\frac{\partial S}{\partial \epsilon}\right )_{M,\vec{\Q}} \ ,\label{ApproxRelation1}
 \end{align}
 with the error controlled by $\epsilon$.

 In this regime, the temperature  must also be proportional to a power of $\epsilon$.  Moreover, one expects the power to be fractional, in the generic case, due to the fact that the unperturbed extremal state will typically only continue to exist in the corrected theory for one sign of $\epsilon$ (an imaginary temperature indicating the erasure of the state).  Similar consideration apply to $S(M,\vec{\Q},\epsilon)$.  For instance, possible expansions for $S$ and $T$ which are consistent with results in the literature \cite{Cano:2019ycn,Loges:2019jzs} are
 \begin{align}
  S(M_{\rm ext}^{0}(\vec{\Q}),\vec{\Q},\epsilon)&\approx S_{\rm ext}^{0}(\vec{\Q})+\epsilon^{\lambda}\Delta S(M_{\rm ext}^{0}(\vec{\Q}),\vec{\Q}) \nonumber\\
  T(M_{\rm ext}^{0}(\vec{\Q}),\vec{\Q},\epsilon)&\approx \epsilon^{1-\lambda}\Delta T(M_{\rm ext}^{0}(\vec{\Q}),\vec{\Q})\ ,\label{TSExpansionNonanalytic}
 \end{align}
 where $0<\lambda<1$.   In contrast, we expect the mass to have an analytic expansion in $\epsilon$ about $T=0$,
  \begin{align}
 \lim_{T\to 0}M(T,\vec{\Q},\epsilon)&\approx M_{\rm ext}^{0}(\vec{\Q})+\epsilon \Delta M_{\rm ext}(\vec{\Q})\ ,\label{MEpsilonExpansion}
 \end{align}
 since, on physical grounds, zero temperature states of fixed $\vec{\Q}$ should exist in both the classical and unperturbed theories for generic perturbations, and hence for either sign of $\epsilon$, unlike those of fixed $(M,\vec{\Q})$ with $M$ near extremality.  Plugging \eqref{TSExpansionNonanalytic} and \eqref{MEpsilonExpansion} into \eqref{ApproxRelation1}, we are then left with the leading-order result
  \begin{align}
 \Delta M_{\rm ext}(\vec{\Q})\! &=-\lambda\Delta T(M,\vec{\Q})\Delta S(M,\vec{\Q})\Big|_{M=M_{\rm ext}^{0}(\vec{\Q})}\ ,\label{ApproxRelation1Example}
 \end{align}
 in this example. Behavior such as \eqref{TSExpansionNonanalytic} where the temperature is dominated by the $\epsilon$-dependent corrections was interpreted in \cite{Cheung:2018cwt} as a breakdown of the perturbative calculation, but \eqref{ApproxRelation1} remains valid in this regime as long as the higher-order corrections in $\epsilon$ are small.

 Finally, by further modifying \eqref{ExactRelation} we can derive an approximate relation which is applicable regardless of whether $M_{\rm ext}(\vec{\Q},\epsilon)$ is larger or smaller than $M_{\rm ext}^{0}(\vec{\Q})$.  Specifically, we evaluate the right side of \eqref{ExactRelation} a mass range slightly above  $M_{\rm ext}^{0}(\vec{\Q})$ where corrections to the temperature are additionally small, i.e., where we satisfy
\begin{align}
\mkern-8mu\frac{M-M_{\rm ext}^{0}(\vec{\Q})}{M_{\rm ext}^{0}(\vec{\Q})}\ll 1\ , \frac{T(M,\vec{\Q},\epsilon)-T_{0}(M,\vec{\Q})}{T_{0}(M,\vec{\Q})}\ll 1\ .\label{RequirementsGenericBound}
\end{align}
 The latter condition further indicates that $M>M_{\rm ext}(\vec{\Q},\epsilon)$, meaning that states in this mass range exist in the perturbed theory for either sign of $\epsilon$.  Hence, we expect that both $T$ and $S$ will admit analytic expansions in $\epsilon$ of the form
 \begin{align}
 T(M,\vec{\Q},\epsilon)&\approx T_{0}(M,\vec{\Q})+\epsilon \Delta T(M,\vec{\Q}) \nonumber\\
 S(M,\vec{\Q},\epsilon)&\approx S_{0}(M,\vec{\Q})+\epsilon \Delta S(M,\vec{\Q})\ .\label{TSExpansionAnalytic}
 \end{align}
 with $T_{0}\gg \epsilon\Delta T$, $S_{0}\gg \epsilon\Delta S$.    In practice, we access this region by working at $M=M_{\rm ext}^{0}(\vec{\Q})\times (1+\delta)$ with $\delta \ll 1$, as required by the first half of \eqref{RequirementsGenericBound}, and with $\delta$ generically bounded non-trivially from below by the second half of \eqref{RequirementsGenericBound}.  As in \eqref{ApproxRelation2Introduction}, we refer to this part of parameter space as $M\approx M_{\rm ext}^{0}(\vec{\Q})$ and evaluating the right side of \eqref{ExactRelation} here gives
  \begin{align}
\mkern-10mu  \lim_{T\to 0}\left (\frac{\partial M}{\partial \epsilon}\right )_{T,\vec{\Q}}\mkern-15mu &\approx\mkern-3mu  -T(M,\vec{\Q},\epsilon)\left (\frac{\partial S}{\partial \epsilon}\right )_{M,\vec{\Q}}\Big|_{M\approx M_{\rm ext}^{0}(\vec{\Q})}\mkern-10mu \label{ApproxRelation2}
 \end{align} with the error now controlled both by $\epsilon$ and $\delta$.  Inserting \eqref{TSExpansionAnalytic} into \eqref{ApproxRelation2} results in the claimed, leading-order relation \eqref{ApproxRelation2Introduction}.

 We conclude this section by commenting on related work.  The relation \eqref{ApproxRelation2Introduction} valid for $M\approx M_{\rm ext}^{0}(\vec{\Q})$ has been confirmed to be in agreement with the results in \cite{Cheung:2018cwt,Cheung:2019cwi,Reall:2019sah,Cano:2019ycn}.  A near-horizon metric based explanation for why the shifts to the black hole extremality bound and entropy are related was given in Sec.~6.3 of \cite{Cheung:2018cwt}, which gives a complementary argument for \eqref{ApproxRelation2Introduction} in the restricted case of gravitational systems.  The relation valid in the strict $M=M_{\rm ext}(\vec{\Q})$ limit \eqref{ApproxRelation1} has been checked against \cite{Loges:2019jzs,Cano:2019oma,Cano:2019ycn} and, again, exact agreement is found.  In particular, \cite{Loges:2019jzs,Cano:2019ycn} have results of the form \eqref{ApproxRelation1Example} with $\lambda=1/2$ while in \cite{Cano:2019oma} it was demonstrated that there are cases where \eqref{ApproxRelation1} trivializes with $\Delta M_{\rm ext}=T=0$, but $\Delta S\neq 0$.  We expect such degenerate cases to be highly non-generic.

 \section{Example: Charged Black Holes in ${\bf AdS_{4}}$}

 In this section, we explicitly confirm the relations \eqref{ExactRelationIntroduction} and \eqref{ApproxRelation2Introduction} for the case of extremally charged black holes in a four-dimensional, asymptotically anti-de Sitter (\textit{AdS}) spacetime.  First, we treat the scenario where cosmological constant plays the role of the perturbing parameter, in which case we confirm the exact result \eqref{ExactRelationIntroduction}.  Then, additional higher-derivative operators are included in the action and we verify the approximate $M\approx M_{\rm ext}(\vec{\Q})$ result \eqref{ApproxRelation2Introduction} for large, extremal black holes.

 The classical Euclidean action we consider is
\begin{align}
I_{0}[g,A]&=-\frac{1}{16\pi}\int_{\mathcal{M}}{\rm d}^{4}x\,\sqrt{g}\, \left (R-F^{2}+\frac{6}{\ell^{2}}\right ) \nonumber\\
&\quad-\frac{1}{8\pi}\int_{\partial\mathcal{M}}{\rm d}^{3}x\, \sqrt{h}\, K\ ,\label{AdSEMAction}
\end{align}
with $\mathcal{M}$ the spacetime manifold and $\partial\mathcal{M}$ its boundary.
Above, $F^{2}=F_{\mu\nu}F^{\mu\nu}$, $\ell$ is the AdS radius, $h_{ij}$ is the metric induced on $\partial \mathcal{M}$, and $K$ is the trace of extrinsic curvature of $\partial\mathcal{M}$.

The action \eqref{AdSEMAction} is divergent when evaluated on a solution and we will regulate these divergence as in \cite{Gibbons:2004ai} by subtracting off the action of empty \textit{AdS}.  The divergence could alternatively be treated using holographic counterterms along the lines of \cite{Emparan:1999pm,Balasubramanian:1999re}, for instance, but we do not pursue this direction here.

The black hole solution of \eqref{AdSEMAction} with charge $Q$ and mass $M$ has a background metric and vector potential, $g^{0}_{\mu\nu}{\rm d} x^{\mu}{\rm d} x^{\nu}\equiv{\rm d} s^{2}_{0}$ and $A^{0}_{\mu}$, given by:
\begin{align}
{\rm d} s_{0}^{2}&=\Sigma(r){\rm d} t^{2}+\Sigma(r)^{-1}{\rm d} r^{2} +r^{2}{\rm d}\Omega^{2}_{2} \nonumber\\
\Sigma(r)&\equiv 1-\frac{2M}{r}+\frac{Q^{2}}{r^{2}}+\frac{r^{2}}{\ell^{2}} \nonumber\\
A^{0}_{\mu}{\rm d} x^{\mu}&=\frac{iQ}{r}{\rm d} t\ ,\label{BackgroundSoln}
\end{align}
where ${\rm d}\Omega^{2}_{2}$ is the standard line element on a two-sphere. There are, of course, more general solutions with non-trivial angular momentum and magnetic charge; see \cite{Caldarelli:1999xj}, for instance, for a study of \textit{AdS} Kerr-Newman thermodynamics in a more general setting.

We begin by confirming the exact result \eqref{ExactRelationIntroduction} for the above system, with $1/\ell^{2}$ playing the role of the perturbing parameter.  In order to make this explicit, we rescale $\ell\to \ell/\sqrt{\epsilon}$ in the following.  It is a standard exercise to derive the thermodynamic quantities associated to \eqref{BackgroundSoln} and the resulting mass and temperature of the system can be expressed via the exact relations
\begin{align}
M(S,Q,\epsilon)&=\frac{S+\pi Q^{2}}{2\sqrt{\pi S}}+\frac{\epsilon S^{3/2}}{2\pi^{3/2}\ell^{2}} \nonumber\\
T(S,Q,\epsilon)&=\frac{S-\pi Q^{2}}{4\sqrt{\pi}S^{3/2}}+\frac{3\epsilon\sqrt{S}}{4\pi^{3/2}\ell^{2}}\ .\label{AdSRNRelations}
\end{align}
The fact that the mass can naturally be written in the exact form $M=M_{0}(S,Q)+\epsilon \Delta M(S,Q)$ implies that \eqref{ExactRelationIntroduction} will in fact hold to all orders in $\epsilon$ for this system, as follows from the microcanonical ensemble version of the proof from the preceding section.  That is, we do not need to restrict to small black hole states which are only perturbatively corrected by $\ell$.

A derivative of \eqref{AdSRNRelations} determines $\left (\partial S/\partial \epsilon\right )_{M,Q}$ to be
\begin{align}
-T\left (\frac{\partial S}{\partial\epsilon}\right )_{M,Q}&=\frac{S^{3/2}}{2\pi^{3/2}\ell^{2}}\ .
\end{align}
The extremal value of $S$ is found by solving \eqref{AdSRNRelations} at $T=0$. Plugging the result into the above gives the extremal value of the derivative, denoted here as:
\begin{align}
-T\left (\frac{\partial S}{\partial\epsilon}\right )_{M,Q}\Big|_{\rm ext.}&=\frac{\ell\left (-1+\sqrt{1+\frac{12 Q^{2}\epsilon}{\ell^{2}}}\right )^{3/2}}{12\sqrt{6}\, \epsilon^{3/2}}\ .\label{NegTdSAdSRNAtExtremality}
\end{align}
On the other hand, inserting this value of $S$ into the first relation in \eqref{AdSRNRelations} gives the extremality bound:
\begin{align}
M_{\rm ext}(Q,\epsilon)&=\frac{12Q^{2}+\ell^{2}\left (-1+\sqrt{1+12Q^{2}\epsilon/\ell^{2}}\right )}{3\sqrt{6\epsilon}\,\ell\sqrt{-1+\sqrt{1+12Q^{2}\epsilon/\ell^{2}}}}\ .\label{AdSRNClassicalExtremality}
\end{align}
Taking the derivative of the \eqref{AdSRNClassicalExtremality} and simplifying demonstrates that $\left (\partial M_{\rm ext}/\partial \epsilon\right )_{Q}$ precisely coincides with \eqref{NegTdSAdSRNAtExtremality}, confirming the exact relation \eqref{ExactRelationIntroduction}.

Next, we verify the approximate $M\approx M_{\rm ext}(\vec{\Q})$ relation \eqref{ApproxRelation2Introduction} by adding the following higher-derivative operators to the system:
\begin{align}
\Delta I&=\frac{\ell^{2}}{16\pi}\int_{\mathcal{M}}{\rm d}^{4}x\, \sqrt{g}\Big (\alpha_{1}F^{4}\!+\!\alpha_{2} \ell^{2}F^{6}\!+\!\alpha_{3}\ell^{4}F^{8}\Big)\ ,\label{HigherDerivativeAction}
\end{align}
where the factors of $\ell$ were introduced for convenience. If tracking powers of $\epsilon$, each $\alpha_{i}$ would be accompanied by an $\epsilon$, but we omit these factors in what follows.  We have focused on a small set of higher-derivative matter operators chosen such that that empty \textit{AdS} with radius $\ell$ remains a solution of the corrected action and such that no additional boundary terms are required to render the action well-posed, choices made for simplicity.  Analyses involving curvature-dependent operators whose results are compatible with our relations can be found in \cite{Cheung:2018cwt,Cheung:2019cwi,Reall:2019sah,Cano:2019oma,Cano:2019ycn}, for instance.

The operators in \eqref{HigherDerivativeAction} change both the metric and vector potential, but neither correction is needed for the verification of \eqref{ApproxRelation2Introduction}.  The correction to the vector potential produced by \eqref{HigherDerivativeAction} changes the action by a boundary term which vanishes as $\partial\mathcal{M}$ is taken to infinity.  The correction to the metric also only changes the action by a boundary term and after regulating the result as described above, the result is again trivial as $\partial \mathcal{M}$ is taken to infinity, in direct analogy to what was found in \cite{Reall:2019sah}.

The free energy corresponding to the classical action \eqref{AdSEMAction} in the small-$T$ limit is
\begin{align}
G_{0}(T,\mu)&=-\frac{\ell\left (-1+\mu^{2}\right )^{3/2}}{\sqrt{3}}+\mathcal{O}(T\ell)\ ,\label{G0AdS}
\end{align}
as determined by a standard calculation. The leading correction to the free-energy then arises from simply evaluating \eqref{HigherDerivativeAction} on the zeroth order solution \eqref{BackgroundSoln} expressed as a function of $\mu$ and $T$ using the zeroth order relations between $(M,Q)$ and $(\mu,T)$.  The calculation is straightforward and gives
\begin{align}
\Delta G(T,\mu)&=\alpha_{1}\frac{\sqrt{3}\ell\mu^{4}}{5\sqrt{\mu^{2}-1}}-\alpha_{2}\frac{2\mu^{6}\ell}{\sqrt{3}(\mu^{2}-1)^{3/2}} \nonumber\\
&\quad+\alpha_{3}\frac{36\sqrt{3}\ell\mu^{8}}{13(\mu^{2}-1)^{5/2}}+\mathcal{O}(T\ell)\ .\label{DeltaGAdS}
\end{align}

We use \eqref{G0AdS} and \eqref{DeltaGAdS} to study large, $Q\gg \ell$ extremal black holes for the remainder of this letter, with the limit taken for simplicity.  In the classical theory \eqref{AdSEMAction}, the extremality bound in this limit is \eqref{AdSRNClassicalExtremality}
\begin{align}
M^{0}_{\rm ext}(Q)=\frac{2Q^{3/2}}{27^{1/4}\ell^{1/2}}\left (1+\mathcal{O}\left (\frac{\ell}{Q}\right )\right )\ .\label{MextLargeAdS}
\end{align}
In order to find $\Delta M_{\rm ext}(Q)$, we evaluate $\Delta G(T,\mu)$ \eqref{DeltaGAdS} on the classical expression for $\mu(Q)$ in the $T\to 0$ limit, with the result
\begin{align}
\Delta M_{\rm ext}(Q)&=\lim_{T\to 0}\Delta G(T,\mu_0(Q,T)) \nonumber\\
&=\frac{3^{1/4}Q^{3/2}}{65\ell^{1/2}}\Big (39\alpha_{1}-130\alpha_{2}+540\alpha_{3}\Big )\ ,\label{DeltaMLargeAdS}
\end{align}
valid at leading order in a $\ell/Q$ expansion.  By computing the free energy to higher orders in $T$, one can also determine $T(M,Q)$ near extremality.  Evaluating the result at $M=\frac{2Q^{3/2}}{27^{1/4}\ell^{1/2}}\times(1+\delta)$, the leading-order result is
\begin{align}
 T\approx\frac{12^{1/4}}{\pi}\frac{Q^{1/2}}{ \ell^{3/2}}\sqrt{\delta\!-\!\frac{3}{130}\left (39\alpha_{1}\!-\!130\alpha_{2}\!+\!540\alpha_{3}\right )}\ ,\label{TLargeAdS}
\end{align}
which is consistent with \eqref{DeltaMLargeAdS}. The result \eqref{TLargeAdS} also demonstrates that satisfying the requirements in \eqref{RequirementsGenericBound} demands
\begin{align}
1\gg\delta \gg \alpha_{1},\alpha_{2},\alpha_{3}\ .\label{LargeAdSdeltaRange}
\end{align}
There is no difficulty in satisfying the above for any natural values of the $\alpha_{i}$.

Finally, we compute $-T(M,Q)\Delta S(M,Q)$  by again retaining higher order terms in the free energy and using \eqref{BasicThermoRelations}.  This straightforward exercise gives
\begin{align}
-T\Delta S\approx  \frac{3^{1/4}Q^{3/2}}{65\ell^{1/2}}\Big (39\alpha_{1}-130\alpha_{2}+540\alpha_{3}\Big )\ ,\label{NegTdSLargeAdS}
\end{align}
when evaluated in the range \eqref{LargeAdSdeltaRange}, up to relative $\mathcal{O}(\delta^{1/2}, \alpha_{i}/\delta,\ell/Q)$ corrections.  Comparing \eqref{DeltaMLargeAdS} and \eqref{NegTdSLargeAdS}, we see that \eqref{ApproxRelation2Introduction} is confirmed. We have also verified that the system defined by \eqref{G0AdS} and \eqref{DeltaGAdS} obeys the third law condition \eqref{ThirdLawAssumption} at leading order in $\alpha_{i}$.

\textbf{Acknowledgements}: We thank Cliff Cheung, Junyu Liu, Harvey Reall, Grant Remmen, Ira Rothstein, and  Jorge Santos for helpful discussions.  We also thank Brando Bellazzini, Yuta Hamada, Toshifumi Noumi, and Gary Shiu for comments made on the original version of this letter after its initial appearance.  The Mathematica package \texttt{xAct} \cite{[][``xAct: Efficient tensor computer algebra for the Wolfram Language" www.xact.es]xAct} was used extensively in the course of this work. The work of GG and RP is  partially supported by the National Science Foundation under Grant No. PHY-1915611.

\bibliographystyle{apsrev4-1}

redpajama_set_name: RedPajamaArXiv


text:
GALLERY: Crews searching for missing 13-year-old Tulsa boy
Tulsa County Sheriff's Office is looking for a 13-year-old boy last seen in the Arkansas River overnight. Authorities are looking for Rylan Harris, who is one of five boys who ran away from the Tulsa Boys Home on Monday night, deputies said. CLICK HERE for full story.
Photo by: Scott Marion, KJRH Crews searching for missing 13-year-old boy swept away by riverPhoto by: Tulsa Co. Sheriff's Office Photo by: Scott Marion, KJRH Photo by: Scott Marion, KJRH Crews searching for missing 13-year-old boy swept away by riverPhoto by: Tulsa Co. Sheriff's Office Crews searching for missing 13-year-old boy swept away by riverPhoto by: Tulsa Co. Sheriff's Office
Scott Marion, KJRH
Crews searching for missing 13-year-old boy swept away by riverTulsa Co. Sheriff's Office
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redpajama_set_name: RedPajamaCommonCrawl


text:
Carlos García Vallejo (25 de enero de 1892 - 3 de febrero de 1949) fue un militar español que participó en la Guerra civil española. Tras el estallido de la contienda se mantuvo fiel a la República y mandó varias unidades militares de forma destacada.

Biografía

Carrera militar
Nació en Madrid en 1892. Ingresó en el Ejército en 1906, licenciándose tres años después. En septiembre de 1914 ya ostentaba el rango de capitán por méritos de guerra. Posteriormente estuvo destinado en el Norte de África, en el Grupo de Fuerzas Regulares Indígenas de Larache (1918). Regresaría a la península, donde estuvo destinado en el Regimiento de Infantería Tetuán n.º 45 entre 1918 y 1928. Entre 1931 y 1932 estuvo destinado en la Guinea Española, siendo el segundo jefe de la Guardia Colonial. En 1933 fue destinado a León, al Regimiento de Infantería n.º 36; al año siguiente intervino en las operaciones militares en Asturias, tras el estallido de la revolución asturiana. En 1935 fue puesto al mando de un batallón de ametralladoras y destinado a la Ciudadela de Menorca.

Guerra Civil
Al comienzo de la Guerra civil se encontraba destinado en Castellón de la Plana, en el Batallón de Ametralladoras n.º 3. Algunos autores han considerado que García Vallejo fue en realidad un «leal geográfico», es decir, que se mantuvo leal a la República por haber quedado en zona republicana. No obstante, durante la contienda mandó importantes unidades militares y se mantuvo fiel a la República. Poco después del comienzo de la contienda fue enviado con su unidad hacia Andalucía. A finales de agosto, durante la Ofensiva de Córdoba su columna permaneció en reserva en la retaguardia, con la misión de apoyar el avance de la Columna Balibrea en Puente Mocho.

En octubre fue nombrado jefe del Subsector de Andújar, al frente del cual logró resistir la posterior ofensiva franquista de finales año. Como jefe del subsector también tuvo a su cargo el Asedio del Santuario de Nuestra Señora de la Cabeza. En marzo de 1937 fue nombrado comandante de la 92.ª Brigada Mixta, que se formó a partir de las antiguas fuerzas que habían estado a su mando. El 3 de abril se produjo una importante reorganización en el seno del Ejército Republicano y García Vallejo se hizo cargo de la 20.ª División, formada con las brigadas mixtas 52.ª, 89.ª y 92.ª, y con su cuartel general en Andújar. Para entonces ya ostentaba el rango de Teniente coronel. Las operaciones contra el Santuario se prolongaron hasta mayo de 1937, debiendo destinar para su asalto a las brigadas mixtas 16.ª, 82.ª, 91.ª y 115.ª; después de sostener fuertes combates con los defensores, los republicanos lograron rendir el Santuario el 1 de mayo.

El 3 de junio fue nombrado comandante del IX Cuerpo de Ejército, con su cuartel general en Úbeda. A finales de año se trasladó a Castellón, por enfermedad. En la primavera de 1938, encontrándose en Levante, se le encargó el establecimiento de una línea defensiva cerca de Albocácer. En ese momento las fuerzas franquistas habían lanzado una potente ofensiva que pretendía conquistar Valencia. El 5 de mayo de 1938 fue nombrado comandante del nuevo del nuevo XVII Cuerpo de Ejército, tomando parte activa en el eje defensivo republicano frente a la ofensiva franquista. A finales de junio la presión franquista le obligó a retirarse a la línea XYZ, donde logró resistir numerosos asaltos enemigos hasta finales de julio. En agosto el XVII Cuerpo pasó a la reserva, quedando situado en el área de Utiel-Requena.

El 26 de noviembre de 1938 fue ascendido al rango de coronel. En otoño García Vallejo y su XVII Cuerpo de Ejército fueron enviados al frente de Andalucía, donde quedaron situados en la reserva. A comienzos de 1939 fue enviado a la zona de Hinojosa del Duque, desde la cual intervino en la Ofensiva de Valsequillo-Peñarroya, sin mucho éxito.

Posguerra
Al final de la contienda fue hecho prisionero por las fuerzas franquistas e internado en el Campo de Concentración de Santa María de Huerta (Soria). Posteriormente pasaría por varias prisiones militares. En 1942 fue juzgado en consejo de guerra, durante el cual el fiscal pidió la pena de muerte para García Vallejo. Finalmente fue condenado a treinta años de prisión por el delito de «adhesión a la rebelión» y fue expulsado del Ejército. El 16 de enero de 1946 fue indultado y puesto en libertad unos días después.

Falleció en 1949.

Familia
Contrajo matrimonio con Carmen Gil Montaner.

Notas

Referencias

Bibliografía

Enlaces externos
 Ricardo Pardo Camacho - Coronel Carlos García Vallejo, un militar leal

Militares de España en la guerra del Rif
Militares de la guerra civil española leales a la República
Víctimas de la represión durante la dictadura franquista
Nacidos en Madrid

redpajama_set_name: RedPajamaWikipedia


text:
Jicchak Chofi (, 25. ledna 1927, Tel Aviv – 15. září 2014) byl v letech 1974 až 1982 ředitel izraelské zpravodajské služby Mosad. Během jeho působení v této pozici proběhla řada mimořádně úspěšných operací, na nichž se zpravodajská služba podílela, včetně záchrany izraelských rukojmí během operace Entebbe, likvidace představitelů palestinské teroristické organizace Černé září, majících podíl na masakru izraelských olympioniků na LOH v Mnichově, či zničení iráckého jaderného reaktoru Osirak. Předtím sloužil jako generál izraelské armády v pozici velitele severního velitelství.

Biografie
Narodil se v Tel Avivu ještě za dob britské mandátní Palestiny. V roce 1944 se v sedmnácti letech stal příslušníkem úderných jednotek Palmach židovské podzemní vojenské organizace Hagana. O čtyři roky později během války za nezávislost velel jedné z rot brigády Jiftach. Později sloužil jako operační důstojník jižního velitelství Izraelských obranných sil. Když se Ariel Šaron stal velitelem výsadkářské brigády, nastoupil jako jeho zástupce. V této funkci jej posléze nahradil a zastával ji během šestidenní války v roce 1967. Podle Ezera Weizmana, který během války sloužil jako velitel operací Generálního štábu, sehrál Chofi klíčovou roli na izraelském úspěchu.

Do roku 1972 sloužil jako zástupce velitele operačního ředitelství armády. Poté byl jmenován velitelem severního velitelství, v jehož čele stál v letech 1972 až 1974, tedy i během jomkipurské války v roce 1973. Jako jeden z mála důstojníků varoval před možností překvapivého arabského útoku, k němuž nakonec během této války došlo.

V roce 1974 byl jmenován ředitelem zpravodajské služby Mosad, v jejímž čele nahradil Cvi Zamira. Během jeho funkčního období se podařilo zlikvidovat několik představitelů palestinské teroristické organizace Černé září zodpovědné za masakr izraelských olympioniků na LOH v Mnichově. V červenci 1976 se zasazoval za akci, která měla zachránit izraelské pasažéry uneseného letadla Air France v ugandské Entebbe. Při přípravě této akce, později známé jako operace Entebbe nařídil Chofi kacům umístěným v Ugandě provést podrobný průzkum letiště, na kterém unesené letadlo stálo a využil kontakty v etiopských tajných službách k tomu, že izraelská letadla, která operaci provedla, mohla dotankovat na zpáteční cestu do Izraele v Nairobi. V roce 1981 dohlížel na izraelský útok na irácký jaderný reaktor u Bagdádu.

Po odchodu z čela Mosadu v roce 1982 jej v této pozici nahradil Nachum Admoni. Následně stanul na ředitelském postu hlavní izraelské energetické společnosti Israel Electric Corporation. Zemřel v roce 2014 ve věku 87 let.

Reference

Externí odkazy

Ředitelé Mosadu
Izraelští generálové
Židovští válečníci
Příslušníci Hagany
Izraelští Židé
Sabrové
Židé v Britském mandátu Palestina
Narození v roce 1927
Úmrtí v roce 2014
Muži
Narození 25. ledna
Úmrtí 14. září
Narození v Tel Avivu
Úmrtí v Izraeli
Osobnosti jomkipurské války


This tool allows you to see your twitch chat on top of games as long as it doesn't run in full screen. it has a bunch of customizable styles and features. I'll be adding more features soon like notifications for follows and subs and subtle popups that notifies you if you forget to change games.


text:
Chat: Mike Gianella
Welcome to Baseball Prospectus' Wednesday February 27, 2013 8:00 PM ET chat session with Mike Gianella.
Mike checks in for his inaugural fantasy chat.
Mike Gianella: How you all doing tonight? Only about a month or so away from baseball season starting, can't wait. Let's get going.
NightmareRec0n (Boston): How do you handle "extra" spots? For example, in my league we have 4 OF spots, and extra IF spot, and 2 ULT spots. Does this mean you always draft the best offensive player regardless of position if you have an open spot for them? Or do you save your extra spots?
Mike Gianella: At the top, I don't think it matters too much and I'd draft the best players possible. Once you get into the middle rounds, though, you probably want to adjust your rankings to reflect your league's unusual position requirements. OF is pretty thick in a standard mixed; the last thing you want to do is load up on 6 OF (including the UT slots) and watch as your opponents get quality OF later because you simply went for the best players on the board.
Matt (Rhode Island): Is there a way to analyze "drop off" for a draft strategy to identify value? For example the drop off between Tier 1 1st basement and Tier 2 1st basemen is less then Tier 1 2nd basemen and Tier 2 Second Basemen, so you'd be better off with a Tier 1 2nd basemen and a Tier 2 1st basemen.
Mike Gianella: Hi Matt. You probably want to start by looking at a solid valuation system (like Baseball Prospectus's own PFM), entering your league's parameters, and seeing where the fall-offs are from a valuation perspective. The shallower the league, the more likely that the "tiers" you identify exist. I'm not exactly certain where the "tiers" necessarily begin and end, but as a general rule I'd agree that two top tier 2B along with a quality 2nd tier 1B are going to help you a little bit more.
TheCoupons (FL): My current keepers are Pujols, Granderson, Wright, Teixeria, Hamilton and Machado in a 12 team H2H 6 man keeper league. Should I be looking to get younger, perhaps targeting a Bryce Harper or Giancarlo Stanton? Or am I safe playing with these players on the wrong side of 30?
Mike Gianella: Cory Schwartz of MLB Network coined a saying I emphatically agree with: "Flags Fly Forever". Your goal - first and foremost - is to win. Obviously, if you can get a Harper or a Stanton via trade, I like them better than anyone you have an your squad...with the possible exception of Pujols depending on your format. However, that's a pretty strong core that you have in a six-man keeper. Play to win now.
Dylan (Portland,ME): Assuming Cabrera, Trout, and Braun are off the board, who would you take fourth in a OPS league with 4 outfielders and a extra IF slot? Votto? Cano? Pujols? or even reach on Stanton?
Mike Gianella: Hi Dylan. PFM says Albert Pujols, but I'm really high on Joey Votto this year and in an OPS league while I wouldn't go as far to say he's a no brainer he's a strong choice for me. Unlike some of my fantasy colleagues at BP, I think Giancarlo Stanton is a reach here. The BB last year weren't high, and while he may get a few more free passes, the eye doesn't speak to a significant increase in walks.
ttt (Manhattan): In a keeper league, I have Norichika Aoki and Michael Brantley as my 3rd OF & top bench player (1B & DH spots are taken by Prince & Morneau). I have an offer to trade either one of them to upgrade my pitching staff (same trade, they're interchangeable). PECOTA prefers Aoki, but I'm worried he will regress heavily in 2013, do you have any thoughts?
Mike Gianella: Howdy, Triple-T. I'm with PECOTA here. I do see some regression for Aoki, but I don't think it will be heavy. The speed looks legitimate, and while I think he might slip in HR a little bit, the numbers overall should be similar. Brantley is the guy I'd move. The Indians offense is loaded, and while Baseball Prospectus's own Jason Martinez has Brantley and Drew Stubbs both starting, I wouldn't be surprised to see Brantley not play quite as much as he did last year. Plus, Brantley doesn't really do any one thing especially well. I think this is a no brainer. I don't know what your offer is, but I'd move Brantley.
ball four (seattle): What is Paul Sporer really like?
Mike Gianella: We've never met, unless you count talking to Paul five minutes before the two podcasts I've been on as meeting. If I get to Ron Shandler's First Pitch in Arizona in November I'll meet Paul, but hopefully our paths will cross before then.
Robert (Puerto Rico): Which 5 or 10 players you think cantop the list of the 2014 Rookie list for Fantasy, also other than Buxton and Boagarts can be an impact back.
Mike Gianella: Bret Sayre is our prospect guy on the fantasy side, but I'll try to help. The tough thing with questions like this is that players who have 2014 ETAs who excel tend to defy the timetables and wind up contributing in 2013. My five guys for 2014 would be: Jose Fernandez, Xander Bogaerts, Javier Baez, Taijuan Walker, Jameson Taillon, in that order. Baez has the best chance of the potential 2014 crop to be an impact bat.
MarcoVillaCards (New York): Any news out of camp on Trevor Crowe?
Mike Gianella: Hi Marco. Crowe signed a minor league deal with the Astros. It's doubtful he'll break camp with the club, though it doesn't take a lot of imagination to see him beating Rick Ankiel out for a spot. Crowe is organizational depth, though, and unless you're in a super deep AL-only Ultra league, I'd cross his name off of your list.
Shawnykid23 (CT): Thanks for the chat Mike! Dynasty League- looking to improve my pitching. Would you take Niese, Estrada, Lynn who could help this year, or someone like Skaggs or Gausman who could be up later in the year, but be better next year?
Mike Gianella: Hi Shawny. It depends on your chances this year, but if you think you have any kind of chance, I'd go with Niese or Lynn, in that order. I like Skaggs and Gausman a lot long-term, but rookie pitchers typically have their ups and downs. Take the guy who can help you win now if you can. Even in dynasty, pitching finds on the wire are somewhat easier to find than hitting prospects that come out of nowhere.
Alex (Anaheim): Is Teixeira a potential buy low candidate in drafts this year, or is he too big a name to get overlooked?
Mike Gianella: Hi Alex. It depends on your league, but I suspect Tex isn't going to be much of a bargain. His NFDC ADP right now is 63rd overall, and 8th among first basemen. That's not too pricey by my lights, but it's not a bargain either. My concern with Tex is that even if he's healthy and the power is there, the AVG/OBP trend has been pointing in the wrong direction for the last couple of years. If Tex is "only" hitting .260, there are a lot of first basemen in his class and he isn't anything particularly special.
Fred L (Houston): It seems like Austin Jackson is flying under radar. Do you think he can build on last year's breakout season?
Mike Gianella: Yes. I think Jackson took some real steps forward last year. The BB%/K% both improved and the ISO has jumped every year since his rookie campaign. Jackson reminds me a bit of someone like Adam Jones: a player who might never be a superstar but could be the next notch right below. A $30 season at Jackson's peak wouldn't surprise me.
Grady Sizemore (Cleveland): Is my career over?
Mike Gianella: I'm no doctor, but probably. In any event, you're not a guy who should be on anyone's fantasy radar right now, unless you're in one of those M*A*S*H leagues.
Donnie (Running Errands): Auction Draft, Dynasty League. Do you go stars/scrubs, or do you try for balance? A prospect draft will follow the MLB draft.
Mike Gianella: In a league with a long reserve list, I generally prefer stars and scrubs. You're not going to find players for your reserve list who can do what a Ryan Braun or a Miguel Cabrera can do, but you might find players who can do what Freddie Freeman and Dexter Fowler can do. Maximize the top slots on your roster; if you do a good job picking up prospects and have a deep farm system, the playing time at the bottom of your roster will come.
AJ (Phoenix): Jose Fernandez v. Taijuan Walker. Both Top 10 prospects according to BP. Which one do you like? How close is it?
Mike Gianella: I like Fernandez better. Despite the fact that Fernandez's numbers were much better in 2012, it's pretty close for me. Fernandez dominated but hasn't pitched at the higher levels of the minors yet and faced what John Sickels calls the "Double-A acid test." Walker has and didn't fare especially well, but I don't think that knocks him out of the running for ace status long-term. If you're looking for a higher ceiling guy it's Fernandez, but it's hard to see how you can go wrong with either.
cedis81 (the internets): In a 16 team 6x6 keeper league (5x5 with OPS for hitters, BB for pitchers), I can keep three players. Already sold on keeping 2 stud pitchers for really cheap 1 year deals, but want to balance that out with bats for longer contracts. The other options for my third and final keeper are Wil Myers at $1 for 2 years (2013 and 2014) and Will Middlebrooks at $1 for 2 years. Am I crazy to lean towards Myers even though he's likely to miss at least April, and possibly all of May? I like Middlebrooks a lot, but his contact issues and plate discipline do worry me a little. What are your thoughts? Thanks
Mike Gianella: For me it's Myers, and this is even before the Middlebrooks injury tonight. I think Myers is going to be up sooner rather than later and even in 5/6th of a season can earn as much as Middlebrooks. Myers has a chance to be an impact player while I think Middlebrooks is going to be more of a complimentary - albeit solid - player. I'd take Myers here.
Ed (Left Coast): Hey Mike, My keeper deadline is tomorrow, and I've got to decide between keeinng a $6 Shelby Miller for 3 years, or a $25 Yu for 3 years. What do you recommend? I would be left with either $134 or $153 of a $260 budget for 14 postitions? Thanks for the chat!
Mike Gianella: Hi Ed on the Left Coast. It depends on your league's inflation factor, but I think I'd lean Miller. Unless you're in one of those old school 4x4 leagues, Yu Darvish at $25 isn't any kind of great bargain. Miller could be and perhaps more importantly could turn into a dump chip for you mid-season. You've got a better chance of turning a profit out of Miller and a better chance of grabbing a potential ace like Darvish at auction.
Chopper (Indy): Welcome, Mike! What are your offensive expectations for Aaron Hill this year, and how about an approximate MLB ETA for Jorge Soler? Thanks!
Mike Gianella: Thanks Chopper. I think Hill is going to slip somewhat this year on the AVG side, though I think the power will be there. A reasonable expectation would be something between his 2011 and his 2012 leaning toward 2012. I think we'll see Soler sometime in mid-2014, at the earliest, though as I said earlier, predicting what prospect timetables is a fool's errand.
Randy (Boston): H2H dynasty points league, no points taken away for K's or CS, would you rather Ben Revere or Carlos Gomez? Thanks
Mike Gianella: If you're not being penalized for K/CS, I'd rather have Gomez. I'm really high on him for fantasy purposes this year and unless he hits .210 he's going to play every day. Revere is a one-trick pony. I'm not convinced any discernible power is coming so he'd have to hit .320 to even be in this discussion.
dangor (New York): In a straight draft, what's your thoughts this year on waiting until at least Round 7 for your first pitcher. Can you win with a staff of second tier starters with proper streaming?
Mike Gianella: Hey dangor. I'm not doctrinaire about when I take pitchers, but I think that can work just fine. Once you get into the middle to later rounds, everyone has different opinions about which pitchers are better than others. In a standard mixer, you can aggressively pitch-or-ditch all season long and still find a way to win. The streaming strategy does work a little better in H2H formats.
Sean T (Bethesda): Thanks for chatting. What are your expectations for Carlos Gomez going into this year in a points league? Any chance he builds on last years performance?
Mike Gianella: I'm in the minority, but I like Gomez a lot this year. He's a fundamentally flawed player and I don't think he's going to build on this year's performance, but I do see him getting a full season's worth of at bats. As a result, his value will jump accordingly even if he only produces 85-90% of what he did in 2012.
Kai John (Santa Barbara): In a Dynasty league, is trading Hosmer for Bogaerts + a high draft pick a good idea if I'm making a trade for AGonzalez as well?
Mike Gianella: Hi Kai. It obviously depends on what the trade for Gonzalez entails. I'm fine with trading Hosmer for Bogaerts and that pick in dynasty though. I think Hosmer is going to bounce back, but Bogaerts plus a presumably second blue chipper is hard to pass up in that kind of deal.
The Squid (200 West): Some tough calls in a 5x5 11-team mixed auction keeper league ($260 cap). Need to decide on contracts for E Hosmer, D Jennings, M Moore, T Bauer. Each year adds $3 to the AAV of the contract (from a base of $1). Can also non-tender and keep the player for the year at $1. Leaning towards signing each for 4yrs ($13), except for Bauer for 2yrs ($7). Thoughts? Please help!
Mike Gianella: I think that sounds right for Hosmer and Jennings. For pitchers I tend to be more conservative, and in a mixed I don't see a huge need to give guys super long deals who haven't pitched at or near an elite level yet. I'd give Moore $7 and Bauer $4.
Mikey (Near Milwaukee): If u could only choose 1 prospect for a dynasty league of T Walker, Gausman, Zimmer, A Sanchez, or Guerreiri??
Mike Gianella: Walker, though Gausman isn't a bad choice either.
Ricky (Chicago): What do you make of Cespedes this year? Is he a .290 hitter or is he more like .260? Also, how many homers/steals are we getting from this guy?
Mike Gianella: I like Yoenis Cespedes a lot. I think he builds off of last year and think that the batting average is going to stay where it was or maybe even get a little better. I'm looking at a ceiling of 30/20 for Cespedes, though I'd ink him in for less if I were projecting my team totals.
Ratcatcher (Gormenghast): Brandon Phillips - $27 stud to build a team around in a 4x4 10 team NL auction league, or chum to be thrown back into the pool to soak up other people's dollars?
Mike Gianella: Neither...he's a keep in a league with any kind of inflation but certainly not a guy I'd build my team around either.
Mike (France): Why the big love in the industry for Starlin Castro? He looks way overvalued on his ADP especially in comparison to Ian Desmond who's going way later.
Mike Gianella: He's 23 years old and has shown gradual improvement in his ISO the last three years. He's never going to be a 30 HR guy, but a 25/25 peak isn't out of the question. Desmond is solid, but his HR/FB% was really high and his AVG isn't supported by his BABIP. Desmond is OK but I expect some regression. FWIW, not EVERYONE in the industry hates Desmond; he went for $28 to Nando Di Fino of CBS Sports in yesterday's CBS Sports NL-only Analyst league auction...or the same price as Castro.
Ernie (Baltimore): Mike, Your thoughts on Jason Hammel becoming the ace that the O's really need or is he just a #2/#3 starter ? Hard for me to tell with all his years in Colorado. Your thoughts ?
Mike Gianella: I think Hammel's solid but I wouldn't call him an ace. He seems more to me like a mid-tier starter. Colorado definitely masked some of his value and I think Hammel can be a bottom end guy in a standard mixer. But I don't see him going further than that.
fatbeast (Troutville, VA): Is bryce harper worthy of a top-35 selection in H2H?
Mike Gianella: I don't think he's quite there yet. Harper could take a big step forward this year, but it's also possible that he stagnates and doesn't do more at the tender age of 20. In a keepr league, he's probably a no brainer there, but in a one-and-done I'd temper my expectations.
Craigster (KC): What kind of year do you think Jeremy Guthrie will have ? Kind of teased us Royal fans at the end of last year.
Mike Gianella: I like Guthrie. Colorado was clearly a bad fit, and while those numbers he put up for KC won't be there again, he is pitching in a positive environment for a fly ball pitcher for the first time in his career. A 3.85 ERA and a 1.26 WHIP with about 120-130 Ks are what I expect.
DanDaMan (SeaCliff): I finally get a night time chat after years of suggesting them and ironically I was off today- I'm blocked from the site at work so I can never participate live. Anyway, look forward to more pm chats. Mike- looking forward to the final position rankings. When do you think we can expect to see those? Thanks, Dan
Mike Gianella: Mine or the Baseball Prospectus' team? My dollar ranking updates will be available every Monday from now until the Monday of Opening Day. Right now the team is working on the second half of the outfielders and that should be published shortly. I'm not sure what the schedule is for starting pitchers and relief pitchers.
Guy (TX): Can Saltalamacchia raise his OBP this year? Would you rather have Rob Brantley?
Mike Gianella: It's hard to see a big leap in Jarrod Saltalamacchia's OBP given his incredibly high strikeout percentages. I'd still take Salty over Rob Brantly. We know what we'll get with Salty. Brantly - who I do like long-term - seems like a complete unknown.
Chris (California): In a dynasty league, who should I target with the #1 prospect pick? (2012 draft guys)... thinking about Zunino or Russell
Mike Gianella: Mike Zunino is probably going to be a better real life player but I'd go with Addison Russell. Catchers tend to have a longer learning curve with the bat, and I don't like sitting through 2-3 years of a catcher growth curve.
Joe (Chicago): How long would you wait on a catcher after Buster Posey is gone?
Mike Gianella: I'd probably wait until the fourth or fifth round. I don't see a particularly big impact guy after Posey, and there is a little more depth at the position than I have seen in the past. Don't reach and cheat yourself out of stats at another position.
Freddy (Fremont): I am a little newer to auction drafting. How do I go about tiering my players for my NL only draft?
Mike Gianella: Hey Freddy from Fremont. I'm not a believer in using tiers for auction formats. I like to assign bid limits to every player and use that as a starting point. The bids that I'm providing to Baseball Prospectus this year to their subscribers should give you a leg up at your auction. Thinking in the tiered mentality can lock you out of bargains at your auction if you think that you can "only" buy one player in a certain price range.
Bo (PA): Can you name some players being drafted in the first couple of rounds who you think could end up relative busts?
Mike Gianella: I don't see any busts per se, but I always look at Evan Longoria and shake my head a little bit. He's only earned over $30 once in his career and even if you take his injured seasons and prorate his AB, he still isn't a $30 player. People keep treating him like an elite, but he has almost never shown it on the field. I don't think he'll be a bust, but he's not going to live up to the stats of a first or second round pick in my mind.
Bob (St Louis): As a Philly guy, are you buying into Dom Brown's hand adjustment and RAJ finally giving him a legit chance?
Mike Gianella: Bob, I'm actually a North Jersey Mets fan transplant into this "hostile" Philly environment. I'd like to see Brown in some real live action before buying into the adjustment or - failing that - action in the last week of Spring Training when a lot of the minor league chaff isn't out there. That being said, I do think that Brown is a legitimate talent and he could be a bargain in deeper formats. He'll get at least half a season this year to prove himself in my view.
Freddy (Fremont): I am in an NL only league that is transitioning from a 4x4 to a 5x5. Is there a good way to determine how many runs and k's I need to plan on to stay top three in those categories? Do that devalue saves and steals?
Mike Gianella: I'm not sure what your format is, but I posted an article last Friday with category averages in mixed, AL, and NL-only formats http://www.baseballprospectus.com/article.php?articleid=19686. Saves and steals are both devalued in 5x5, but saves are devalued significantly more. Fernando Rodney earned $51 in 4x4 last year (according to my own valuation system) but "only" $32 in 5x5.
Donnie (Running Errands): I have 3 CF in a dynasty league that uses (LF,CF,RF), I can only play two. Out of Andrew McCutchen, Adam Jones, and Billy Hamilton, which would you keep, which would you trade? What's a fair asking price?
Mike Gianella: I'd keep McCutchen and Jones but boy oh boy that's a tough/terrible call to have to make on Hamilton right now. If his bat plays in the Majors, he could be the 10s version of Vince Coleman. I'd want a lot for Hamilton, and I think you'd be able to get it. In dynasty, people are all over his ceiling.
Robert (Puerto Rico ): Is Brian Goodwin an impact bat?
Mike Gianella: Define impact bat. Goodwin sounds like a 15-20 HR guy long term, though his speed is what could make him a solid, all around fantasy player. We're not talking Giancarlo Stanton if that's what you're asking.
Sean T (Bethesda): Josh Johnson - any chance he regains his 2011 form (pre-injury)? What kind of numbers do you expect from him?
Mike Gianella: It's possible that Johnson can bounce back. The talent has always been there and you hit the nail on the head, health is usually the only obstacle. I suppose I'm "expecting" numbers in the 2008-2009 range...but I wouldn't draft/pay for that.
Shawn (CT): What are some of your favorite peripherals for identifying potential break-out players?
Mike Gianella: For pitchers, I like to look at K% and SwStr%. Pitchers that are getting a lot of swings and misses but not necessarily getting results have a chance of taking a step forward. With hitters, I like finding guys with good FB% but low HR/FB%. The home runs often come the following season.
Freddy (Fremont): What process do you go through to determine trade value for your fantasy team in a keeper league? I find the determination of proper value the hardest part. In the end, I feel like I probably give up a little too much.
Mike Gianella: I take a player's raw bid value, calculate that against the inflation rate and determine how undervalued the player is in that context. I tend to take young players and try to grade their performance a little more generously, since in a keeper you want to try to have a couple of young stars or emerging players to dump if you're in contention.
Jason (Philadelphia ): What players to you see suffering a big regression. What players do you think surprise this year?
Mike Gianella: Torii Hunter seems like an obvious regression candidate. The BABIP was extreme and the power and speed are dwindling as he moves into his later 30s. Chris Davis is kind of a one-trick pony and if the power slips even a little his value takes a serious hit. I don't see another 30+ bombs for Davis this year. As far as surprises go, I think Ike Davis shakes off the rust of his Valley Fever and becomes a serious 40 home run threat. Tyler Colvin is a player I really like to find a way into playing time and hit 20 home runs (assuming, of course, he gets to play).
fatbeast (Troutville, VA): Should CC still be drafted as a staff ace/high-2?
Mike Gianella: Low 1 or high 2 sounds about right. He does make me a little nervous, but if he looks fine this spring you can't assume injury.
Scott (LA): Looking at the Rox for some low cost, high upside flyers. Do you like any of the following to exceed expectations? Chris Nelson, Eric Young Jr, Jordan Pacheco? Do you see any of their near ready prospects like Tim Wheeler, Charles Blackmon or Nolen Arenado making an impact this year?
Mike Gianella: Of the three Rockies you mention, I like Nelson the most. I could see a power spike simply from playing a full season in the thin air and think Nelson could be a sneaky, under the radar value play. Of the prospects you mention, I'm not sold on any of them making a significant impact this year. Arenado could be up if everything breaks right, but it's not something I'd count on.
bosox9 (Lake villa Illinois): Rank these 3-SS: Baez, Addison Russell and correa
Mike Gianella: It's Correa, Baez and Russell for me, though I think it's close enough and all three are far enough away that they could theoretically fall out in any permutation.
Mat (Fort Myers): Any underrated guys you would target in an NL Only league?
Mike Gianella: Will Venable is a guy I like. He only went for $9 in CBS but has the potential to earn $15-20 easily. David DeJesus seems like he had a down year last year but earned $14 in NL-only. Daniel Murphy is another guy who didn't do much in HR/SB but more than earned his keep.
stevenst (TX): Would you trade Josh Hamilton (4 yr contract at 30) for Oscar Taveras (10 yr of control, escalating 1-15) straight up if you were the favorite to win your league this year and would have to replace Hamilton with Ryan Ludwick?
Mike Gianella: I would, because I'd think that if I had to I could flip Taveras for more talent than Hamilton in a subsequent trade if that's what it took to win.
stevenst (TX): Is Saltalamacchia a decent catcher in a 16 team mixed league? 16 team AL only league? 16 team Red Sox only League?
Mike Gianella: He's OK in deeper mixed and obviously fine in AL-only. If you're in a 16-team Red Sox only league you're going to run out of players quickly.
Sean T (Bethesda): How long before Jansen starts taking away save opps from League?
Mike Gianella: Tough to say, but even in a best case scenario for Brandon League owners it's not hard to see Kenley Jansen saving 5-10. The simple answer is if League struggles I don't think Don Mattingly will have orders from up above to use League because he has the big contract.
Sean T. (Bethesda): Who are some players that are undervalued by Rotiserie Rankings that may be steals in a Points league draft?
Mike Gianella: For hitters, you're looking for boring vanilla guys that contribute stats across the board. Think Hunter Pence: seemingly vanilla players that contribute something across the board. For pitchers, innings munchers matter a lot. Bruce Chen isn't worth much in a Roto format but because he just keeps churning out innings he provides more value in a points format.
Andy (Chicago): Trevor Bauer worth keeping (2 pitcher keepers, 2 hitter keepers) in a 14 team mixed standard scoring league for $3 even though he's not sure to have a spot in the rotation? Other options at that price would be Skaggs and Strailey. Thanks
Mike Gianella: Of those three pitchers, Dan Straily is the guy I like most in a mixed, though quite honestly all three all borderline in that format even at such a cheap price. There is a lot of fungible talent at the bottom of the pitching pool in mixers.
Mikey (midwest usa): which pair do you prefer: S. Romo + E. Volquez or A. Reed + J. Niese??
Mike Gianella: Reed and Niese. I don't like Volquez much at all. High walk rates are fantasy poison.
SecondHandStore (Under a bunch of snow): Could you rank these guys: Justin Upton, Jason Heyward, Bryce Harper
Mike Gianella: I'd go Heyward, Upton, and Harper though they're really close and I could see flipping the rankings in any direction.
bosox9 (SS ): Bogaerts see action in Boston by end of yer
Mike Gianella: It seems doubtful unless he really has a lights out year in the minors.
Matt (LA): I typically find myself idiotically having money left at the end of auctions due to shying away from spending big on guys. What "safe" high dollar players would you recommend I go after this year as I try to change my ways?
Mike Gianella: I'm not sure what your format is, but what I would recommend is taking the dollar values that I provide for Baseball Prospectus and using those as a starting point in your auction. Try to get players on my list a dollar or two under value. If players are going well over my bid limits then don't worry about spending on a high dollar player: you will wind up building a balanced squad that is well under value.
Sean T (Bethesda): Please rank these closers on ability to keep their jobs all season - League, Janssen, Street, Broxton, Cishek.
Mike Gianella: Street, Janssen, Broxton, Cishek, League, though this obviously depends on Janssen's health and how serious Dusty is about toying with moving Chapman back to the pen.
Mike (Chi-town): Romo & Holland are amongst my keepers this season - do both keep their closer jobs all year?
Mike Gianella: I'd say yes to Sergio Romo in all likelihood... keeping in mind that the Giants aren't afraid to switch roles at the earliest sign of trouble. I think Greg Holland will be OK, but Kelvin Herrera is extremely talented. If you're a believer in the skills versus roles thing, Herrera's a guy you'll want to grab in deeper formats.
mikey (midwest usa): In a deep, 20 team dynasty league. Realized early that everyone likes shiny, new toys and everyone tries to prove their prospect knowledge... boys will be boys. Do you agree with the adage: "a bird in the hand..." unless the birds in the bush is REALLY special?? Do you favor est. players or prospects when building dynasty rosters?? The published flame out rates makes the decision for me, but wonder what you think.
Mike Gianella: I'm more of a Roto guy than a Dynasty guy, but I generally prefer the birds in the hand. If I'm going to go after prospects, I want blue chippers. Top 20 ranked hitters...maybe top 30, and top 10 pitchers...maybe top 20. There is too much that can happen from year to year with prospects.
Lance (Dallas): Hey Mike. Can't decide what to do about my keepers. I'm in a standard Yahoo league (nothing too spectacular about it but the group of guys I'm in it with). I can pick three. Matt Kemp Elvis Andrus Carlos Gonzalez Felix Hernandez Gio Gonzalez I'm leaning towards either Kemp/Andrus/G. Gonzalez or Kemp/G. Gonzalez/Hernandez. What do you think?
Mike Gianella: Kemp, Gonzalez, Hernandez for me. I'm not sure it's particularly close either, unless you're in a really shallow mixed league where OF are a dime a dozen.
PGT (Louisiana): What High OBP guys are your favorite draft picks this year?
Mike Gianella: Joe Mauer is always a guy I like in AVG or OBP formats; he offers a lot of value through those categories at a tough position to fill. If he's healthy, Lance Berkman is a great OBP guy...and he's moving to a great park in a strong line-up. The health is a huge if, of course.
Jonesy (Quebec): which side of this trade you got: Eaton, Alonso and K. Lohse for Butler, Aoki, and Volquez??
Mike Gianella: I like the Butler/Aoki side. Lohse isn't even going to sign in time to pitch a full season and Eaton is an unknown in terms of what he'll do. Seems like you're flipping an unknown in Eaton for a known in Aoki, a much lower ceiling guy in Alonso for a higher ceiling guy in Butler and that even if Lohse does pitch 150 innings this year, the Lohse/Volquez gap doesn't make up for the hitting loss there.
HH (TX): Which Rangers pitcher would you rather have on your Fantasy Team, Harrison or Holland?
Mike Gianella: I'd rather have Harrison. He's boring, but every year all he does is go out and produce value. Holland probably has the higher ceiling but so far he has been a fantasy tease. Go with the certainty here, particularly since Harrison isn't exactly chopped liver.
Brett (MN): Are you buying Justin Morneau as a real bounce-back candidate?
Mike Gianella: I think Morneau will be solid again, but I have a hard time seeing him as the elite hitter that he once was if that's what you mean.
Frank (Singapore): Jose Tabata - any hope for a return to the initial promising career, or is it over?
Mike Gianella: There's probably a chance but it has to be viewed as a long shot at this point. He's buried in Pittsburgh and probably needs a trade.
BOO-URN (parts unknown): Thoughts on Morosi's prediction for PHI to finish ahead of ATL?
Mike Gianella: It seems silly, though last year at this time if you told me the Phillies were going to be a .500 team I would have thought you were huffing chemicals. Realistically, the Phillies would need a lot to go right for this to happen. If Roy Halladay returns to Cy Young form, then maybe the Phillies are an 87 win team. At that point, some combination of a breakout by Dom Brown or Darin Ruf, a full, healthy, and productive season by Ryan Howard or Chase Utley and something resembling a 2-3 win season from Delmon Young or Michael Young could make it happen. But it seems to be asking a lot for all of things to happen in 2013.
jlarsen (Chicago): In an AL-only Dynasty league and I have the 6th and 8th picks, respectively. The 1st round usually consists of new-to-AL players who were in the NL previously and draft picks who CBS didn't add until the offseason. What value do you see me getting out of the 6th pick and should I go for MLB-calibur players in the 1st or a top draftee like Joey Gallo?(Zunino and a few others have already been claimed)
Mike Gianella: Go with the MLB guys. Joey Gallo could go in so many different directions at this point. Blowing a 1st round pick on Gallo seems like buying a lottery ticket to me.
cal guy (cal): Who ends up having the better career, Machado or Bogaerts? Bundy or Cole? Taveras or anyone on this year's BP 101?
Mike Gianella: Bogaerts, Cole, and Taveras for me, though with the first two it's close and there are a lot of different trajectories. Taveras is starting to look like someone really special. I don't think he's going to be quite as good as Bryce Harper, but a number of scouting experts are starting to put them in the same paragraph, which is saying something.
Joe (St Louis): In a dynasty points league, please rank Taveras, Bundy, Myers, Medlen. Thanks Mike.
Mike Gianella: For this year Medlen, Myers, Taveras, Bundy. Long term, Taveras, Myers, Medlen, Bundy.
jlarsen (Chicago): In my AL-only Dynasty Lg, I acquired Mike Moustakas, Addison Reed, Byron Buxton and the 6th overall pick for Justin Verlander & my 10th, 11th and 12th round picks. Was this a good pick-up, considering that I have Matt Moore, Yu Darvish, Derek Holland and Tommy Milone as my top starters
Mike Gianella: Hard to say considering I don't know what those picks would typically fetch in your league. That seems like a lot to give up since it's an AL-only. Your staff looks deep, but this isn't a mixed. I do like Buxton a lot, but I don't like the idea of giving up Verlander without getting a top hitter back. I have been burned in the past dealing an ace pitcher for a package of players rather than one big hitter in return.
Tom (Toronto): Will Moustakas be more like his first half or second half?
Mike Gianella: Unless he makes an adjustment, probably more like his second half. Moustakas swings under a lot of pitches resulting in a very high number of infield flies. Unless he levels his swing, he's probably going to continue to put up poor batting averages with not as much power as you'd expect from a big fly ball guy. He's still young and has time to improve but I don't like what I saw last season.
stewbies (Rochester, NY): Is Lincecum a good bounce back candidate?
Mike Gianella: It depends on what you want him to bounce back to. I can see him putting up a 4.00 ERA or something in that neighborhood but it's hard to expect him to be the Timmah who won back-to-back Cy Young awards. It wasn't talked about to the same degree, but Lincecum's velo drop in 2012 reminded me of Ubaldo Jimenez's in 2011. This isn't a bet I'm going to be making this year.
Adam (Cabo San Lucas): 14 team, keep 4 guys. I have Braun, Cutch and Cano. For #4, do I go Yu, Pedroia or Bruce? it's a snake draft, and I don't have a first round pick (but I do have two 2nd rounders).
Mike Gianella: I think I'd go with Pedroia. Yes, it would give you two second basemen but it's a good position to lock up and play keep away with. I'm not as high on Bruce as others are and while I like Yu I don't like the idea of freezing pitchers in a limited format like this unless you're talking about a bonafide ace.
zissou (naples): Do you think Josh Rutledge can be a strong fantasy player this season?
Mike Gianella: He could be because of that park, but I'm extremely wary of Rutledge and am recommending staying away from him in shallower formats. Rutledge has a poor batting eye and it seems in September that pitchers finally figured this out and started throwing more stuff out of the zone. The result was a huge K% spike and a drop in Rutledge's overall stats. Maybe he figured something out over the winter and turns it around, but I think there's at least moderate risk here.
Mark (Fairbanks, AK): 14 team deep keeper league. Have to keep 15. Young team that won't win for another few years. Already keeping Myers, Taveras, Profar and Bauer. Trying to decide on last keeper: T.Walker J.Gyorko T.d'Arnaud M.Olt
Mike Gianella: Walker, particularly if you're definitely in a position that you're not going anywhere for a few years. Olt would be a better choice if you thought you might even have a snowball's chance in '13.
zissou (naples): Who are some underrated closers to target later in drafts? Do you like Casey Janssen or Jason Grilli?
Mike Gianella: Grill probably falls into the underrated category. There is a lot of noise about Mark Melancon taking Grilli's job, but Grilli's numbers were solid last year and if he's healthy he probably hangs on. Greg Holland's walk rate was high last year, but the other numbers were strong and like Grilli the noise about Holland's set-up might keep the price low. Tom Wilhelmsen is a somewhat low profile but proved himself in 2012. I like Janssen if the health is there but the health gets me nervous. At least at the moment.
Matt (Saranac Lake, NY): In an auction league with these free agent pitchers, what three arms you be apt to target if you were aiming for greatest return on investment - Price, Scherzer, Verlander, Kershaw, Latos, Cobb, Minor, Weaver, Fister, Shields, Archer, Cahill, McCarthy, Greinke, Lincecum, Lester, Sabathia? Thanks!
Mike Gianella: Are we talking raw value or profit? Raw value it would be Verlander, Kershaw and Price. If you're talking about potential bargains though, I think I'd go with Minor, Fister and Cahill. All three have the potential to earn more than their price and seem to be somewhat undervalued in drafts and auctions that I've seen play out.
Johnny T (The Hills): Any of these guys worth a look in an NL only 4x4 standard league? Trevor Rosenthal, Tony Cingrani, Arodys Vizcaino, Christian Garcia, J.J. Hoover, or Sam Lecure.
Mike Gianella: Rosenthal is definitely worth a $2-3 bid in NL-only. His stuff is legitimate and even if he's only a set-up man, his Ks mean that he could put up sneaky $10-12 value.
Chris (California): What do you thing about a Carlos Gonzalez/Alex Gordon for Jason Heyward trade in a 6x6 league? (AVG, R, HR, RBI, SB, OPS)
Mike Gianella: That seems like way too much to give up.
Bill (Trenton): A team in my 15-player keeper league is loaded with Miggy/Kemp/Hanley/Cargo/Cano/Uptons/Felix/CC etc. They've won the last 3. What's the best strategy to try to compete?
Mike Gianella: It almost seems like your league needs to adjust its rules so that situations like this don't happen. I have no idea how a team can wind up being this stacked.
zissou (naples): Do you think Tommy Hanson can get back on track with a new team?
Mike Gianella: I think it's possible, though I have the same concerns everyone else has with the potential for injury. The park can't hurt.
Johnny T (The Hills): Any of these hitters worth a flyer in an NL only standard 4x4 league? DJ LeMahieu, Adeiny Hechavarria, or Jordany Valdespin.
Mike Gianella: All three are worth fliers, we're talking NL-only. Valdespin probably has the highest ceiling if he can get playing time because of the HR/SB combo. Hechavarria should play, but yawn on the stats.
Bob (Boston): Which side of this trade do you like? Kemp/Bogaerts for Granderon/Profar/Middlebrooks (when Granderson was healthy) .. standard keeper lg.
Mike Gianella: You should add "when Middlebrooks was healthy" to that as well. I think that's a pretty fair deal, though since it's a mixer I think I like the superstar or potential superstar in Kemp and that side of the deal better.
zissou (naples): Do you think Yovani Gallardo will finally make the jump into the next tier this season or more of the same (mid-high 3 ERA, 200 Ks)?
Mike Gianella: More of the same for me. I've never been a big Gallardo fan. He's fine, but there is always this contingent that thinks he's going to magically jump into the ace stratosphere. Maybe he will, but nothing in the numbers tells me that.
Bill (Trenton): Is Geater Davis the greatest soul singer of the south?
Mike Gianella: Robert Johnson for me. The first time I heard him, I felt like someone was ripping my heart in half.
zissou (naples): Could you see Aroldis Chapman turning into a legit top fantasy starter this year? If he struggles, is Cinci tied to Broxton at closer with his contract?
Mike Gianella: He has the raw stuff, but I wouldn't bet on it happening just yet. I'm concerned that the high pitch counts are going to keep him from getting past the 6th inning and keep the WHIP up. My colleague Paul Sporer also brought up a good point on our podcast: without a refined tertiary pitch it's worth wondering what Chapman's going to do the 2nd time through the line-up. I think he'll be very good (Chapman, not Sporer). I just don't know if I'd bet on an ace.
zissou (naples): Do you think Jean Segura could be a top 10 fantasy SS? His final month last season has me intrigued.
Mike Gianella: Not this year. I see mostly speed at this point and am thinking Top 15 might be the ceiling.
zissou (naples): Does Joakim Soria have much keeper value left? When do you see him being fantasy viable again?
Mike Gianella: Soria is a 2014 play for when after Joe Nathan leaves, and even that is obviously iffy. So, no, I don't see a lot of keeper value unless you're in a "keep forever" format.
Trent (Phippsburgh, ME): In an auction (with on-base %), which bats would you target as the best value buys - Fielder, Longoria, Andrus, Tulo, Hanley, Kemp, Cargo, Beltre, Miggy, Pujols, Drew, Kinsler, Cano, Kipnis, Pedroia?
Mike Gianella: Value or bargains? Miggy, Fielder, and Pujols clearly jump out. It's hard to know bargains without knowing the format.
zissou (naples): What's your take on Marco Estrada? Last year breakout legit?
Mike Gianella: I think he's going to be a solid starter this year. It's hard to predict he'll be THAT good, but a 3.5 ERA seems like a more than realistic expectation.
Grinder (Boston): Ryan Dempster, returning to his numbers in the NL or is he more likely to resemble the mess he was in Texas ?
Mike Gianella: Closer to what he did in the NL. Texas isn't an easy place to pitch, and I suspect the program they have over there with their pitchers is easier to implement in Spring Training than it is mid-season.
amazin_mess (NY): Who do you like more this year - Adrian Beltre, Prince Fielder or Matt Kemp?
Mike Gianella: Kemp, Beltre, Fielder. This obviously is predicated on Kemp's health. Fielder might be slightly ahead of Beltre without positional concerns, but the fact that Beltre's at third puts him slightly ahead.
Chris (California): Sorry, I mixed up the trade- What do you thing about a Carlos Gonzalez for Jason Heyward/Alex Gordon trade in a 6x6 league? (AVG, R, HR, RBI, SB, OPS)
Mike Gianella: I think that's solid. I'd do it.
Mike Gianella: I'm going to call it a night. Thanks so much for participating.


For the first time, Taipei City, Chinese Taipei, will host the 2017 World Junior Championships. The event begins on March 15 with the men's and pairs short programs.
A total of 184 skaters from 43 International Skating Union (ISU) members will contest the four disciplines. All skaters will compete in the short program segments with the top 24 singles skaters, 16 pairs and 20 ice dance teams moving on to the long programs.
The men's event will be very competitive. Reigning World junior champion Daniel Samohin (ISR) heads into the competition with a season's best of 226.53 points and will be aiming at defending his title. But he will face tough competition from Russia's Dmitri Aliev, the reigning Junior Grand Prix Final champion (seasons best 240.07 points), and Alexander Samarin, the 2016-2017 Junior Grand Prix Final silver medalist (seasons best 236.52 points); Korea's Jun-Hwan Cha, the current Grand Prix Final bronze medalist (seasons best 239.47 points); Canada's Nicolas Nadeau, the 2016 World Junior silver medalist; America's Alexei Krasnozhon and Vincent Zhou and Russia's Alexander Petrov.
In the ladies event, World junior champion Marin Honda from Japan (season's best: 184.11 points) will be out to defend her title, but she will face stiff competition from Russia's Alina Zagitova, the reigning Junior Grand Prix Final champion (season's best: 207.43 points); her teammate, Polina Tsurskaya, who missed the Junior Final due to injury, but won her two Junior Grand Prix events earlier this season, Junior Grand Prix Final bronze medalist Kaori Sakamoto from Japan; Eunsoo Lim from Korea; Russia's Stanislava Konstantinova and Japan's Yuna Shiraiwa.
The pairs event is wide open. Top contenders are Russia's Aleksandra Boikova and Dmitrii Kozlovskii, the Junior Grand Prix Final bronze medalists, Alina Ustimkina and Nikita Volodin and Amina Atakhanova and Ilia Spiridonov, and Australia's Ekaterina Alexandrovskaya and Harley Windsor. Reigning World Junior champions Anna Dušková and Martin Bidař moved into the senior ranks following the Junior Grand Prix Final last December.
All 2016 World Junior ice dance medalists have returned this year. Reigning World Junior champions Lorraine McNamara and Quinn Carpenter from the U.S. hope to defend their title and are aiming at their third consecutive World Junior podium. Their teammates, Rachael Parsons and Michael Parsons, the reigning Junior Grand Prix Final champions and defending World Junior silver medalists will provide tough competition, as will Russia's Alla Loboda and Pavel Drozd, the 2016 World Junior bronze medalists.
The season best total scores are compiled from the Grand Prix events (senior and junior), ISU Championships, the Olympic Winter Games and the Challenger Series only. No other international competitions or national championships are factored in.


Here is a my latest creation powered by Perch 2.4 and the Blog App. The front end uses Bootstrap 3 and Font Awesome.
I hope you like it, and my first post in the new forum. Testing out some of the new forum mark up so fingers crossed I got it correct.
Nice. Did you hand code that site or use a website development app? If it was the latter, may I ask what you used?
Nice and clean i like your design. :) Perhaps more pictures of one item from the gallery..
Thanks. I hand coded the site, I use Panic Coda 2.
That's a clean looking site where the design exactly complements the quality of the product.
So nice to see a CMS site that doesn't follow the same 3 column blog type layout.
One thing I would do is lose the irritating progress bar on the opening page. Serves no useful purpose and takes the eye away from the prize.


After yesterday's armadillo fail, I was eager to get back out on the streets of Victoria and give it another go.
Though I wasn't all that thrilled to go out and retrace many of the same roads that made up yesterday's "almost" armadillo, I was eager and determined to right yesterday's wrongs.
Also it was Friday afternoon, and this provided the perfect excuse to take a break from work and ride my bike in the sunshine.
I'm much happier with this specimen. It's a nine-banded armadillo (Dasypus novemcinctus) – a solitary, nocturnal critter found in North, Central, and South America.
Say, did you know that armadillos harbour Mycobacterium leprae, the bacterium that causes leprosy? So if you should happen upon an armadillo, don't touch it. Or kiss it. Or eat it.
This entry was posted in gps art and tagged armadillo, bicycling, creativity, cycling, garmin, gps, gps art, nine-banded armadillo, strava, strava art, victoria bc. Bookmark the permalink.
I just Googled Armadillos, what curious creatures!
Aren't they? One of my followers on Strava – a fellow from East Java, Indonesia – commented that "in Indonesia we call this animal Trenggiling." I suggest you google Trenggiling – it's a mighty cool looking critter!


text:
The brass behind the gold
How Britain (population: 65m) beat China (population: 1.4 billion) in the Olympics
More cash, ruthlessly funnelled towards winners, explains Britain's medal haul
BRITONS worried about their country's global standing after it opted to leave the European Union in June might take some solace from this summer's Olympic games in Rio de Janeiro. Britain finished second in the medal table (as ranked by the number of golds won), ahead of China, and became the first country ever to increase its medal haul immediately after hosting the games.
Britain's tally of 65 medals in 2012, when London welcomed the world's athletes, was its best in a century. A total of 29 golds was enough to lift Team GB to third in the world, with as many first-place finishes as France, Germany and Japan combined.
Few expected the Brits to repeat that performance in Rio, if only because such a feat was unprecedented. Host nations typically enjoy an "Olympic bounce": over the past three decades, most have gradually increased their medal returns in the run-up to a home games, before peaking on their own turf, and tailing off in ensuing tournaments. This trend can largely be explained by hosts funnelling extra money towards sporting programmes in the hope that their athletes will put on a good show on home soil. Nobody wants to be the loser at their own party.
Spending data are hard to find for many countries, since they are reluctant to give away details about their preparation. But an analysis by the BBC has shown that British Olympic success has correlated strongly with total funding over the past 20 years. Both have grown heftily since the embarrassment of the 1996 games in Atlanta, when Team GB won just one gold medal.
A good indicator of beefed-up Olympic programmes is the number of athletes that a country sends to the games. Host nations do get an easier run in qualification in some sports: they have guaranteed spots in rowing, football and gymnastics, for example, though no special treatment in athletics, track cycling or swimming. But they evidently put more effort into training their sportsmen and women up to Olympic standard too. Yet hosts typically send fewer competitors to subsequent games. This makes Britain's recent success all the more remarkable. The team that arrived in Rio was one-third smaller than the one that took part in London, yet it snaffled 27 gold medals and 67 overall.
Some of that was down to luck. Britain's rugby sevens team, which collected an unexpected silver medal, avoided an early exit after their Argentine opponents squandered a penalty kick for victory; Andy Murray, who won gold in the tennis singles, benefited when his nemesis, Novak Djokovic, crashed out in the first round. Other countries have voiced suspicions about Team GB's rapid improvement in certain disciplines, especially in the velodrome. Britain won no gold medals at the 2015 Track Cycling World Championships, but six of the ten on offer in Rio. (British Cycling, the sport's governing body, has said it is focused on Olympic goals: Britons won seven golds in London's velodrome.)
But the underlying cause of Team GB's success has been an efficient allocation of resources. The £350m ($460m) pot of National Lottery money that was available to British teams in the four years leading up to the Rio games was shared only among those likely to win medals. Cycling, rowing and sailing, which produced 26 gongs in 2012, received a combined stipend of £88m for the Olympic cycle of 2013-17. Athletes in these disciplines have better equipment, facilities, and training regimes than ever before. Weightlifting, fencing and archery, in which Britain won no medals four years ago, were given £8.8m. Such an unforgiving approach to spending allowed Britain to win one gold medal for every 14 athletes competing in Rio, its best ratio in the post-war era.
Occasionally a lesser-funded sport can prove its worth. Britain's struggling gymnasts received just £1.8m ahead of the Beijing games, but beat their medal target in 2012 and were given a budget of £14.6m in 2013. Max Whitlock, a 23-year-old pommel-horse specialist, won two gold medals in Rio—the first Briton ever to win an Olympic gymnastics title. Well-targeted investment, it seems, pays off.
Correction: An earlier version of this article incorrectly stated that host nations get no advantage in qualifying for Olympic events. In fact, they do have guaranteed spots in some sports. This has been corrected.


Motorbikes Glasgow - Welcome to the Glasgow Motorbikes Directory from Tipped.co.uk featuring recommended motorbike showrooms in Glasgow. It lists those who provide motorbikes in Glasgow. It also includes those who offer scooters in Glasgow. Read reviews of Glasgow scooters and write your own review too. If your Glasgow motorbike business isn't listed, then advertise it for FREE today.