Pitchers with lucky and unlucky W-L records

Another nice article in SABR's "Baseball Research Journal 35" figures out which were the luckiest and unluckiest starting pitchers in terms of career wins. It's called "Still Searching for Clutch Pitchers," by Bill Deane ("with statistics by Pete Palmer").

Deane and Palmer figured it this way: first, they counted all the runs the pitcher gave up in all his starts. Then, they figured how many runs his teams scored for him in the games he started, and pro-rated that figure to his innings pitched. They subtract one from the other to come up with a run differential. Finally, they take a .500 record (with the same number of decisions), and add or subtract wins based on that run differential. The result is the pitcher's expected W-L record.

Here are the luckiest pitchers according to Deane and Palmer. Remember, "luck" here does not include any above- or below-normal run support, which has been taken out of the picture.

+20.6 wins: Mickey Welch (307-210 actual, 286-191 projected)
+17.8 wins: Greg Maddux (333-203 actual)
+16.8 wins: Bob Welch (211-146 actual)
+15.2 wins: Clark Griffith (237-146 actual)
+15.1 wins: Christy Mathewson (373-188 actual)
+14.0 wins: Roger Clemens (348-178 actual)

And the unluckiest:

-24.3 wins: Red Ruffing (273-225 actual, 307-201 projected)
-14.7 wins: Jim McCormick (265-214 actual)
-13.7 wins: Dizzy Trout (170-161 actual)
-13.4 wins: Bob Shawkey (195-150 actual)
-13.1 wins: Walter Johnson (417-279 actual)
-12.1 wins: Bert Blyleven (287-250 actual)

The authors note that, over all the pitchers, the distribution of the discrepancies between actual and expected, in terms of standard deviations, is exactly as you would expect from the normal distribution. And so they conclude that the difference between expected wins and actual wins is presumably due to luck.

But they don't explicitly say that they're using the standard deviation of the binomial distribution (that is, the SD of coin tosses). From the article, all we can conclude is that the distribution of the discrepancies is normal, not that it exactly matches what would have resulted if the discrepancies were luck. (For instance, you might find that 2.5% of people have SAT scores more than 2 SDs above normal, just as expected, but that doesn't mean that SAT scores are just luck.)

A couple of other minor quibbles:

How many runs does it take to turn a loss into a win? Palmer uses the formula

Runs per win = 10 * (average runs per inning for both teams)

The article bases "runs per inning for both teams" on the combined scoring of the team and its opponents *when that pitcher starts*. I don't think that's right: you have to base it on the *league* scoring. That's because the runs saved are off the league runs, so you have to start at the average.

Put it this way: suppose Roger Clemens gives up 3.5 runs a start, and the league average is 4.5. The league average of 4.5 means 10 runs per win. Clemens saved 1.0 runs *off the 4.5 level*, so you have to use the 4.5 level (not 3.5) to figure the runs.

Actually, the best way might be to integrate the function, or at least sum a few small slices. For instance:

The first 0.1 runs saved are at the rate of 1 win per 10 runs (using 4.5 + 4.5).
The next 0.1 runs saved are at the rate of 1 win per 9.94 runs (using 4.4 + 4.5).
The next 0.1 runs saved are at the rate of 1 win per 9.89 runs (using 4.3 + 4.5).
...
The last 0.1 runs saved are at the rate of 1 win per 9.49 runs (using 3.6 + 4.5).

The average of all the slices is the number you should use. But the article uses 9.49 runs per win for *all* the runs saved, not just the last slice, and therefore it's probably overestimating the "luck" by just a little bit. And, in fact, I've seen arguments that Palmer's formula doesn't actually work all that well anyway.

But in any case, I don't think it's enough to affect the results much, which is why I call it a quibble.

One more minor point: if ten runs makes up a win for a team, does it necessarily follow that ten runs make up a win for a starter? Maybe due to leverage differences, it takes 12 runs for a starter win, but only 8 runs for a reliever win. Again, I'm not sure that's true, and even if it is true, it's probably minor anyway.

The authors do check the overall results, and find that the average "luck" is one win more than expected. "This could be," they write, "because those who are 'lucky' in the win column are more likely to get 200 decisions [which was the study cutoff]."

Sounds right to me. Overall, I think the results of this study are probably pretty accurate.