Players being "clutch" when targeting 20 wins -- a study

In my previous post, I speculated about the anomaly, discovered by Bill James, that there are more 20-game winners than 19-game winners in the major leagues. That is the only case, between 0 and 30, where a higher-win season happens more frequently than a lower-win season.

Here, once again, are some of the win frequencies. For instance, there were 123 seasons of exactly 19 wins since 1940. (All numbers in this study are 1940-2007.)

16 311
17 221
18 185
19 123
20 144
21 92
22 54

In the previous post, I suggested that the bulge at twenty wins appears to be about 29 "too high". So we'll proceed as if there are an extra 29 twenty-win seasons to be explained.

I did a little digging to see if I could figure out what caused this to happen. I think I have an answer, and it's a bit of a surprise.


1. Extra Starts
The first thing I looked at was whether pitchers with 18 or 19 wins late in the season would be given an extra start near the end of the season to try to hit the 20. So for each group of pitchers, I checked what percentage of their starts came in September or later:

16  win pitchers: 17.53% of starts in September
17  win pitchers: 17.77% of starts in September
18  win pitchers: 18.36% of starts in September
19  win pitchers: 18.49% of starts in September
20  win pitchers: 18.47% of starts in September
21  win pitchers: 18.15% of starts in September
22+ win pitchers: 18.18% of starts in September

So it looks like there's a positive relationship between September starts and eventual wins, and a little bulge that happens in the 18-20 range. Maybe those pitchers are getting extra starts, or, as Greg Spira suggested, perhaps the other pitchers miss a start in favor of a minor-league callup, while the pitchers with a shot at 20 are given all their usual starts. The bulge appears to be about a quarter of a percent.

If we assume that, if not for targeting 20 wins, the 19-20 pitchers would have been 0.25% lower without the special treatment, that's 23 of their 9,229 combined starts. If half those starts led to a 19-game winner becoming a 20-game winner, that's an extra 11 pitchers in the twenty-win column. It seems reasonable – it's less than 29, anyway, which is the number we're trying to explain.


2. Relief Appearances
Greg also suggested, in the previous post, that pitchers with 19-wins may be given an extra late-season relief appearance to try to get their twentieth win. I checked Retrosheet game logs, and Greg is right – there has been some of that going on.

I found all September relief appearances for eventual 20-game winners, where they had at least 18 wins at the time of the relief appearance, and they got a decision (Retrosheet game logs won't list a reliever unless he wins or loses, but that doesn't matter for this study). Here they are:

1951: Early Wynn gets his 18th win [in relief]
1951: Mike Garcia gets his 19th win
1956: Billy Hoeft gets his 20th win
1957: Jim Bunning gets his 20th win
1964: Dean Chance has 19 wins but loses
1966: Chris Short gets his 20th win
1991: John Smiley gets his 19th win
1997: Randy Johnson gets his 20th win

So that accounts for seven 20-game winners who would otherwise have won only 19 games.

But what about 19-game winners? Those guys may get extra relief appearances too. I checked, and there are fewer of them.

1956: Lawrence Brooks (18th win, loss at 19 wins)
1962: Art Mahaffey has 19 wins but loses
1964: Bob Gibson gets his 19th win
1964: Jim Bunning gets his 19th win
1974: Ken Holtzman has 19 wins but loses

(Just out of interest, Bob Gibson's appearance was in the last game of the 1964 season, so he couldn't have been going for 20.)

And here are the late-season relief decisions for the eventual 21-game winners:

1940: Bobo Newsom (20th win)
1940: Rip Sewell (20th win)
1946: Howie Pollet (18th win)
1947: Johnny Sain (21st win)
1959: Sam Jones (18th win, loss at 20 wins)
1960: Warren Spahn (loss at 17 wins)
1960: Ernie Broglio (19th win)
1965: Mudcat Grant (loss at 21 wins)

So it looks like pitchers do get extra relief appearances in pursuit of high win totals (or *did* -- most of these guys were pre-1970). There were four 19-game winners created this way; seven 20-game winners; and six 21-game winners.

The difference between 19 and 20, here, is three players – a lot fewer than I would have thought. But 3 is something, again when there's only 29 to explain.


3. Clutch Pitching
Maybe, when going for their 20th win, a player will bear down and pitch better than usual. I found all starting pitchers with exactly 19 wins, and looked at how they did in the start(s) that would give them their 20th win.

In 490 such starts, they went 227-142 (.655). I couldn't get their ERA or runs allowed from the Retrosheet game logs, but I did get the average number of runs their *team* allowed in those games. It was 3.63.

That doesn't mean much without context. Here are the results for some other win totals:

17 wins: 3.72 runs allowed, .658, 670-348 in 1385 starts
18 wins: 3.54 runs allowed, .652, 487-260 in 982 starts
19 wins: 3.54 runs allowed, .655, 367-193 in 704 starts
20 wins: 3.62 runs allowed, .615, 227-142 in 490 starts
21 wins: 3.53 runs allowed, .676, 138-66 in 273 starts
22 wins: 3.34 runs allowed, .774, 82-24 in 148 starts

Now, we have something: immediately after hitting the 20-win mark, the starters suddenly became a lot less likely to win. Instead of a winning percentage of maybe .660, which you would have expected (remember that the more wins, the better the pitchers, so the winning percentage should increase down the list), they wound up only .615. That's .045 points in 369 decisions, or about 17 wins – almost half the 35 wins we're trying to explain!

By this measure, it looks like this half of the anomaly is not too many 20-game winners relative to 19-game winners, but that poor performance at 20 causes a logjam keeping the 20s from getting to 21.

But: if you look at runs allowed, the performance at 20 wins doesn't seem all that bad. It should be around 3.54, and it's at 3.62. That's .08 runs for each of their 490 starts -- about 40 runs. How did these pitchers win 17 fewer games while allowing only 40 extra runs? Forty runs is 4 games, not 17 games.

The answer: run support. Here's the pitchers' run support for each category:

17 wins: 4.39 run support
18 wins: 4.41 run support
19 wins: 4.45 run support
20 wins: 4.05 run support
21 wins: 4.46 run support
22 wins: 4.48 run support

The 4.05 is not a typo. When starting a game with 20 wins, pitchers got four-tenths of a run less support than they should have. That's huge. Over 490 games, it's almost 200 runs. That wipes out 20 wins, which keeps twenty 20-win pitchers from getting to 21 wins.

I have no idea why this should happen. I suppose it's possible that, seeing how the ace already has 20 wins, the manager might play his bench for this meaningless September game. But how often would that happen? No way it would be enough for 0.4 runs per game, would it?

By the way, it looks like these 20-game winners beat Pythagoras in these starts. They finished only 17 games below expectation, while losing 240 runs (40 pitching, 200 hitting). Assigning blame in proportion over those 17 extra games, we'll say that 3 of the extra losses came from pitching, and 14 from run support.

I find it something of a relief that it was run support, and not (positive) clutch performance on the part of their pitchers, that caused the effect – it wasn't the case that they pitched better when close to a (selfish) goal. Going for their 20th win, pitchers did not appear to do any better or worse than when going for their 18th, 19th, or 22nd wins. And they pitched only marginally better than when going for their 21st.

It's human nature that pitchers want to win 20 for personal reasons, but at least the evidence is that they try just as hard every other game of the year.


4. Concluding
Summarizing these results, we were looking for 29 "extra" 20-game seasons. We got:

-- 11 from extra starts
-- 3 from extra relief appearances
-- 3 from pitchers' own poorer performance in subsequent games
-- 14 from poor run support from their teammates in subsequent games.

That adds up to 31 games, which is close enough to our original estimate of 29.

It's interesting that about half the effect comes from 19-game winners getting extra chances to hit 20, and the other half comes from 20-game winners being unable to rise to 21.

And, to me, the biggest surprise is that almost 40% of the 20-game-winner effect came from that huge hole in run support. In other words, a big part of the surplus of 20-game pitchers is probably just random luck.



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UPDATE (12/2014, almost seven years later): Bill James points out that the results don't quite work.  I've updated the analysis in a new post here.