Players being "clutch" when targeting 20 wins -- a follow-up

In his 2007 essay, "The Targeting Phenomenon," (subscription required), Bill James discussed how there are more single-season 20-game winners than 19-game winners. That's the only time that happens, that the higher number happens more frequently than the lower number. 

This is obviously a case of pitchers targeting the 20-win milestone, but Bill didn't speculate on the actual mechanisms for how the target gets hit. In 2008, I tried to figure it out. But, this past June, Bill pointed out that my conclusion didn't fit with the evidence:

"... the Birnbaum thesis is that the effect was caused one-half by pitchers with 19 wins getting extra starts, and one-half by poor offensive support by pitchers going for their 21st win, thus leaving them stuck at 20. But that argument doesn't explain the real life data. 

"[If you look closely at the pattern in the numbers,] the bulge in the data is exactly what it should be if 20 is borrowing from 19 -- and is NOT what it should be if 20 is borrowing both from 19 and 21."

(Here's the link.  Scroll down to OldBackstop's comment on 6/6/2014.)

So, I rechecked the data, and rethought the analysis, and ... Bill is right, as usual. The basic data was correct, but I didn't do the adjustments properly.

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My original study covered 1940 to 2007. This study, though, will cover only 1956 to 2000. That's because I couldn't find my original code and data. The "1956" is what I happened to have handy, and I decided to stop at 2000 because Bill did. 

First, here are the raw numbers of seasons with X wins:

17 wins: 159
18 wins: 132
19 wins:  92
20 wins: 113
21 wins:  56
22 wins:  35
23 wins:  20
24 wins:  20

You can see the bulge we're dealing with: there are way too many 20-win pitchers. And it can't be that the excess comes from the 21-win bucket, because, then, the average of 20 and 21 would stay the same, and wouldn't be much lower than 19. That can't be right. And, as Bill pointed out, even if only *half* the excess came from the 21 bucket, 20 would still be too big relative to 19.

So, let me try fixing the problem.

In the other study, I checked four ways in which 20 wins could get targeted:

1. Extra starts for pitchers getting close
2. Starters left in the game longer when getting close
3. Extra relief apparances for pitchers getting close
4. Better performance or luck when shooting for 20 than when shooting for 21.

I'll take those one at a time.

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1. Extra starts

The old study found that pitchers who eventually wound up at 19 or 20 wins did, in fact, get more late-season starts than others -- about 23 more overall. In this smaller study (1956-2000 instead of 1940-2007), that translates down to maybe 18 extra starts. 

That's about 9 extra wins. Let's allocate four of them to pitchers who wound up at 19 instead of 18, and the other five to pitchers who wound up at 20 instead of 19. If we back that out of the actual data, we get:

18 wins: 132 136
19 wins:  92  93
20 wins: 113 108
21 wins:  56  56

(If you're reading this on a newsfeed that doesn't support font variations: the first column is the old values, which should be struck out.)

What happens is: the 18 bucket gets back the four pitchers who won 19 instead. The 19 bucket loses those four pitchers, but gains back the five pitchers who won 20 instead of 19. The 20 bucket loses those five pitchers.

(In the other study, I didn't bother doing this, backing out the effects when I found them, so I wound up taking some of them from the wrong place, which caused the problem Bill found.)

So, we've closed the gap from 21 down to 15.

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2. Starters left in the game longer

After I had posted the original study, Dan Rosenheck commented,

"You didn't look at innings per start. I bet managers leave guys with 19 W's in longer if they are tied or trailing in the hope that the lineup will get them a lead before they depart."

I checked, and Dan was right. In a subsequent comment, I figured Dan's explanation accounted for about 10 extra twenty-game winners. Those are all taken from the 19-game bucket, because the effect occurred only for starters currently pitching with 19 wins.

For this smaller dataset, I'll reduce the effect from 10 seasons to 7. 

So:

18 wins: 136 136
19 wins:  93 100
20 wins: 108 101
21 wins:  56  56

Now, the bulge is down to 1.  We still have a ways to go, if the 19 is to be significantly higher than the 20, but we're getting there.

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3. Extra Relief Apparances

The other study listed every pitcher who got a win in relief while nearing 20 wins. Counting only the ones from 1956 to 2000, we get:

3 pitchers winding up at 19
5 pitchers winding up at 20
2 pitchers winding up at 21

Backing those out:

18 wins: 136 139
19 wins: 100 102
20 wins: 101  98
21 wins:  56  54

The gap now goes the proper direction, but only slightly.

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4. Luck

This was the most surprising finding, and the one responsible for the "getting stuck at 20" phenomenon. Pitchers who already had 20 wins were unusually unlikely to get to 21 in a subsequent start. Not because they pitched any worse, but because they got poor run support from their offense.

When Bill pointed out the problem, I wondered if the run-support finding was just a programming mistake. It wasn't -- or, at least, when I rewrote the program, from scratch, I got the same result.

For every current starter win level, here are the pitchers' W-L records in those starts, along with the team's average runs scored and allowed:

17 wins:   483-311 .557   4.30-3.61
18 wins:   350-250 .608   4.30-3.61
19 wins:   260-182 .588   4.24-3.56
20 wins:   150-136 .524   3.81-3.54
21 wins:    94- 61 .606   4.49-3.44
22 wins:    59- 23 .720   4.26-2.80

The run support numbers are remarkably consistent -- except at 20 wins. Absent any other explanation, I assume that's just a random fluke.

If we assume that the 20-win starters "should have" gone 171-115 (.598) instead of 150-136 (.524), that makes a difference of 21 wins.

The mistake I made in the previous study was to assume that those wins were all stolen from the "21-win" bucket. Some were, but not all. Some of the unlucky pitchers eventually got past the 20-win mark; a few, for instance, went on to post 23 wins. In their case, it becomes the 23-win bucket stealing a player from the 24-win bucket.

I checked the breakdown. For every starter who tried for his 21st win but didn't achieve it that game, I calculated where he eventually finished the season. From there, I scaled the totals down to 21, the number of wins lost to bad luck. The result:

20  wins:  9 pitchers
21  wins:  5 pitchers
22  wins:  3 pitchers
23  wins:  1 pitcher
24  wins:  2 pitchers
25+ wins:  less than 1 pitcher

So: the 20-win bucket stole 9 pitchers from the 21-win bucket. The 21-win bucket stole 5 pitchers from the 22-win bucket. And so on. 

Adjusting the overall numbers gives this:

18 wins: 139 139
19 wins: 102 102
20 wins:  98  89
21 wins:  54  50
22 wins:  35  33

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And that's where we wind up. It's still not quite enough, to judge by Bill's formula and even just the eyeball test. It still looks like there's a little bulge at 20, by maybe five pitchers. If 20 could steal five more pitchers from 19, we'd be at 107/84, which would look about right.

But, we've done OK. We started with a difference of +21 -- that is, 21 more twenty-game winners than nineteen-game winners -- and finished with a difference of -13. That means we found an explanation for 34 games, out of what looks like a 39-game discrepancy.

Where would the other five come from? I don't know. It could be luck and rounding errors. It could also be that the years 1956-2000 aren't a representative sample of the original study, so we lost a bit of accuracy when I scaled down.  Or, it could be some fifth real factor I haven't thought of.

In any case, here's the final breakdown of the number of "excess" 20-game winners:

-- 5 from getting extra starts;
-- 7 from being left in games longer than usual;
-- 3 from getting extra relief appearances;
-- 9 from bad run support getting them stuck at 20;
-- 5 from luck/rounding/sources unknown.

By the way, one important finding still stands through both studies. Starters didn't seem to pitch any better than normal with their 20th win on the line, so you can't accuse them of trying harder in the service of a selfish personal goal.