A lot of times when evaluating baseball players, people are tempted to think that if a player struggles mightily in the first half (below their career averages), then in the second half, in order to reach those career averages, the player will naturally perform far above the norm. So for example, if a career .300 hitter bats .200 over the first half of the season, it is very tempting to think that he’ll hit .400 over the second half of the season so that it all averages out to .300 over the whole year.
Unfortunately, as the fantasy baseball articles invariably point out every all-star break, that is not what you should expect. It’s a variation of the Gambler’s Fallacy—if you flip a coin and get ten heads in a row, then a lot of people would expect the eleventh flip to be tails because it’s “due.” But it’s easy to see that no matter what’s happened in the past, that eleventh flip is still 50-50. The twelfth flip is still 50-50. You could get 99 heads in a row and the hundredth flip is still 50-50. The past doesn’t affect the future probability at all. In the same way, if a .300 batter bats .200 in the first half, he’s not going to bat .400 in the second half—he’ll bat .300 in the second half.
Mathematically, the principle is sound, but what the fantasy baseball writers ignore is that unlike a coin flip, baseball performance is NOT random. I think one could speculate that a player may indeed exceed his career averages after a period of struggling because his surroundings adapt to that performance. For example, perhaps if a player struggles for a long time, he gets moved down in the order where pitchers are not as careful with him (such as right in front of the pitcher’s batting slot). Or perhaps pitchers are simply not as careful because due to the subpar half-season, he is not perceived as a threat anymore. I don’t have the time or the wherewithal to do a proper analysis, but my impression is that there are so many factors that it is disingenuous to reduce it to a simple Gambler’s Fallacy.
2 comments:
Absolutely true. The reason for this, which you are approaching without actually stating, is that Batting Average is NOT "probability." It's simply a statistic for what has already transpired.
A .300 hitter doesn't mean that he will get a hit 3 out of 10 times, but that he HAS already gotten a hit 3 out of every 10 times. It does not suggest whatsoever that he will continue to do that.
Rather, we assign Batting Average to be "a vague identity that speaks to probability" because some hitters will hit at or around the same BA each year.
Additionally, there are so many other factors --some of which you've identified, such as "how careful a pitcher is"-- that go into BA, including fielding, situational hitting by teammates, psychological factors, conditioning, injuries, etc. etc. etc.
Best you can say is that there is a probability (what probability is anyone's best guess) that a hitter will hit near his batting average.... but which batting average? Lifetime? Certainly that can change year in year out. Last year's? Psh. Three year average? You see how this can go on ad nauseum.
Hugs!
dg
Said even better than I did...
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