Comments on The Marlins and their Hitting Streak: What are the Odds?TypePad2009-08-19T16:37:13ZMiami Heraldhttp://miamiherald.typepad.com/fish_bytes/tag:typepad.com,2003:http://miamiherald.typepad.com/fish_bytes/2009/08/the-marlins-and-their-hitting-streak-what-are-the-odds/comments/atom.xml/jason s commented on 'The Marlins and their Hitting Streak: What are the Odds?'tag:typepad.com,2003:6a00d83451b26169e20120a512bbe7970b2009-08-23T07:46:38Z2009-08-23T07:46:38Zjason swith some small simplifying assumptions, we can make a direct calculation. ok, here goes some math. (skip to the bottom...<p>with some small simplifying assumptions, we can make a direct calculation.<br />
ok, here goes some math. (skip to the bottom for the result.)<br />
first we have to figure out the probability of a team getting 10+ hits in one game. using the team avg of .267, i figured out the probability of getting 0,1,2...,9 hits, then subtracted from 1. ( for example, the probability of getting 1 hit is .267*(1-.267)^27*C(28,1) i assumed they always have 27 outs, and ignored DP, CS, etc.) that probability works out to .3785 Thus the probability of a 14-game streak is .3785^14, or .0000012 Then we have to figure out the probability that this occurs anytime during the season, for any team. there are 149 different games in which the streak could start, and 30 teams. so the probability any team has such a streak in one season is .0000012*30*149, or .0055. thus, you would expect such a streak once every 180 seasons.<br />
but wait! it turns out that this calculation is very sensitive to the batting average. for a batting average of .270, you expect one such streak every 88 seasons. and for a batting average of .275, you expect such a streak once every 29 seasons.<br />
so when you consider the batting averages of the 1930s, its no surprise that was last time a streak like this occurred.</p>