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Monday, April 30, 2007
If a pitcher pitches a brilliant game, is he likely a good pitcher?
I’ve always thought and written that when a pitcher pitches a brilliant game, he looks like Cy Young and when that same pitcher throws a stinker of a game, he looks like Sy Epstein (our old family lawyer).
Naturally, I also wondered, when a pitcher does pitch an excellent game, what are the chances that he is a very good pitcher, an average one, a poor one, etc. I did some quick sims to get some idea and here is what I found.
In the major leagues, here is the approximate distribution of true talent levels among starting pitchers. Don’t ask me where I came up with it. O.K., you asked. I simply used the 2007 Pecota pitcher projection database and counted all the average pitchers (according to their projections), the above-average ones, below-average, etc. Here is what I came up with (approx.):
1) average: 28%
2) .5 runs per 9 below average: 22%
3) 1 run below average: 17%
4) .5 runs above average: 21%
5) 1 run above average: 11%
As you can see, it is not a symmetrical normal curve, because there is much more below-average than above-average talent in MLB and in the population from whence MLB pitchers come. If I weighted by playing time, it might look like a symmetrical normal curve. Anyway it doesn’t matter. Actually, it does matter, but for the sake of argument, let’s assume that when a pitcher pitches, the chances that he is among one of these 5 classes is the above percentages.
The next step was to see what the chances were of each of these 5 classes of pitchers throwing a great game. I defined a great game as allowing 2 runs or less (earned or unearned) after 8 innings. Here is what I came up with using my sim. It could have been done theoretically using run distribution tables for the various average number of runs (in each class).
1) 30%
2) 25%
3) 22%
4) 40%
5) 45%
Not much of a spread here. The best pitchers in baseball, those that are around 1 run per 9 innings better than league average (guys like Santana and the old Pedro are probably another .5 runs better than that), are only about twice as likely to throw a great game as the worst pitchers in baseball, those with true talent levels 1 run worse than average (per 9 innings).
So if a random, unknown pitcher throws a great game, as defined above, what are the chances that he belongs to each of these 5 classes? You might be tempted to think that he is probably a very good pitcher. Let’s see.
We use Bayesian probability for this. Going into the game (the “a priori” probabilities), this pitcher is .28 likely to be an average pitcher, .22 likely to be below average, .17 likely to be among the worst, .21 likely to be above average and .11 likely to be among the best. However, after throwing a great game, we have to weight these averages by the chances of each class of pitchers throwing a great game. So now we have .28*.30 or .084, .22*.25 or .055, .17*.22 or .0374, .21*.40 or .084, and .11*.45 or .0495. .084+.055+.0374+.084+.0495 = .3099, which is how often a great game gets thrown. Dividing each class’ chances (their % of the population times their chance of a great game) by this number gives us:
.084/.3099 = .27
.055/.3099 = .18
.0374/.3099 = .12
.084/.3099 = .27
.0495/.3099 = .16
So, there is a 27% likelihood that our pitcher is league average, a 27% likelihood that he is above average, an 18% likelihood that he is below-average, 16% that he is among the best in baseball, and 12% that he is among the worst. In fact, it is 57/43, or better than a 1.3 to 1 ratio, that our pitcher is average or worse! Even if we compare the chances of him being among the worst in baseball to among the best, the latter is only a 16 to 12, or 4 to 3 favorite.