jason palmer mrktgulrucsdedu rich evaluation period number experiments coin tosses long enough everyone expected poorly ie probability person well much less 1 number people playing anyone well statistically significant case anyone well likely know theyre think probably case warren buffets lifetime earnings statistically significant difficult make simple model stock investing consider mathematically simplistic setting could take coin tossing example suppose someone claims able get heads often half time test claim make person flip coin enough times probability head rate r greater 05 small number heads binomialnp make null hypothesis head rate 05 mean r would 05 variance would 14n n number tosses test using chebyshev inequality pr 051 14n0012 2500n let n 25 billion probability empirical head rate greater 051 given coin fair person special ability 1 million get people making claim say test time number people say n getting head rate greater 051 binomialmp p 25n expected value mp m2500n variance mp1p m2500n using markov inequality number people greater 051 head rate pn 1 mp m2500n fixed make n large enough probability anyone getting head rate greater 051 less epsilon hand number tosses isnt large relatively large number people test good head rate may significant regarding paradox specifically define faith mike degree believe actually well faith mike claimants depend n n small faith everyone low n large faith everyone high could also define faith anyone well achieve greather 05 head rate beat stock market degree believe possible given everyones results faith decrease large enough n always develop considerable degree faith hope helpful best jason original message nhipljlbixengrorstedu mailtonhipljlbixengrorsteduon behalf rich neapolitan sent saturday june 25 2005 417 pm faqeecsoregonstateedu subject uai luck skill preparing talk whether people like warren buffet really better investment analysis simply case thousands people analysis probably well poor simply chance possibly different experiment many people toss coin many times experiment probably throw lot heads thinking conceived following paradox suppose stranger named mike showed office told could pick stocks really well advised year made bundle would suspect knew since chance successful chance alone small suppose instead 10000 guys also showed said could pick stocks well case mike still good results would dismiss success probably due luck since 10000 people likely someone well paradox follows faith mike penalized simply people made claims id interested opinions matter rich wed 06 aug 2008 062622 0700 uai luck skill corrected