 The standard “proof beyond a reasonable doubt” is often paired with the Blackstone ratio, the principle that it is better that ten guilty defendants go free rather than even just one innocent be convicted. The exact ratio is in fact a matter of controversy (Volokh 1997). It is tempting to think that, say, the .9 threshold guarantees a 1:9 ratio between false convictions and false acquittals. But this would be hasty for at least two reasons. First, probabilistic thresholds affect the expected rate of mistaken decisions. The actual rate may deviate from its expected value (Kaye 1999). Second, if the threshold is .9, at most 10% of decision against defendants are expected to be mistaken (false convictions) and at most 90% of the decisions in favor of the defendant are expected to be mistaken (false acquittals). The exact ratio will depend on the probabilities assigned to defendants and how they are distributed (Allen 2014). What can be said, in general, is that the threshold that minimizes the expected rate of incorrect decisions overall, no matter the underlying distribution, lies at .5 (see Kaye 1982, 1999; Cheng &amp; Pardo 2015 for a proof).