God and .500

¹²³ · Aug 3, 2010

Playing The Percentages In Baseball

By Tangotiger, 01:19 PM

Suppose that God herself came to you and told you that she was going to do something devious: for the 2011 baseball season, every team would have 25 players of identical talent, with all 30 teams being equals. That no player would learn from each plate appearance, and no player would get hurt. That no player will even interact on the most basic level with each other, and if they did, it would be indistinguishable from any other interaction. No player would even age, having been frozen in time. All the games would be played in the same city, at the same time, in 15 identical ballparks, domed, and staffed by identical groundskeepers and HVAC guys. This is the most controlled science experiment ever: nothing can possibly ever change.

And after each team plays 162 games, you will get ten teams winning between 78 and 84 games, with ten winning fewer than 78 and 10 winning more than 84. All that would happen based purely on the only thing that differentiates each of the thirty teams and 750 ballplayers: luck.

We expect the distribution of wins to have one standard deviation equal to 6.4 wins. Imagine, one team will have 91 wins, and another will have 71 wins, and they are identical in all respects! They are identical because god told you. That if they played each other one million times, they’d each have a .500 record. But 162 games is not a million.

***

As it turns out, in reality, you don’t have ten of thirty teams that win outside of those 78 and 84 games. In the 12 seasons between 1998 to 2009, you had an average of ten teams that won less than 75 games, ten teams that won more than 87 games, and ten teams that won between 75 and 87 games. The distribution of actual wins is one standard deviation of 11.8 wins. INCLUDED in that 11.8 wins is the luck portion of 6.4 wins. The difference between the two is (11.8^2-6.4^2)^0.5, or 10.0 wins.

That is, when you look at the won-lost records of baseball teams, 60% of that is the talent and other vagaries of the participants, and 40% of that is luck. If you have a team that wins 91 games (+10 wins above average), that could be because it was +6 because of talent and +4 because of luck, or +12 because of talent and -2 because of bad luck, or -5 because of talent and +15 because of fantastic luck.

We don’t know for any one team, how we can work backwards from the W/L record. All we can do is make a best guess, and have a huge uncertainty level around that guess. Since it’s easy enough to take two identical god-told teams that won 91 games and 71 games and make them both 81 win teams, do you see how hard it would be to take a team that won 86 games and another that won 76 games and say that the 86-win team is in fact better than the 76-win team?

Sports, life actually, is played by unique persons. But luck, timing, good/back breaks plays a huge role in the outcomes. Not everything is luck. But not everything is talent either.
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God and .500

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