Baseball Therapy: The Complete Value of a Complete Game

The complete game has become an increasingly rare beast. In 2013, there were 124 complete games registered by the 4,862 pitchers who started out on the hill, and Adam Wainwright led all of baseball with five. If a pitcher makes it through nine innings, he’s likely having a very good day, and nine innings of well-pitched baseball is nothing to sneeze at. But a complete game is more than that. It’s a sign of manliness. It’s like shouting, “I don’t need no stinkin’ bullpen!” It’s a cultural touchstone. It’s the guy yelling at his TV, “Finish what you started, you silly overpaid, coddled millionaire. I finish my day of work without calling in a reliever.” A pitcher who completes a game is just getting in touch with the common man.

There’s a certain fascination surrounding the pitcher who goes deep into games, even if he doesn’t complete them. It’s been argued that such a player provides value well beyond the confines of the game in which he pitches. Logically, the argument makes sense. Coin Wyers pointed out that the deeper into a game a pitcher goes, the better the bullpen performs. Mostly, that has to do with the fact that if a manager can get through the seventh with his starter, he can tell his third- and fourth-best relievers to take the night off. In some bullpens, the last thing you want is that fourth-best reliever throwing any pitches. Others have suggested that if a manager has a starter on whom he can count to go deep into a game, it affects his choices on how to work the bullpen the day before (he doesn’t have to “save” as many arms for the next day) and after (all of the relievers are rested). In that way, the complete game affects three different games!

And then someone says it. “How do you really figure out the full value of the complete game? I mean, there’s the game itself, but there’s all that value that he’s adding in the game on either side, and that’s not being captured in the stats. There’s just no way to fully value that.”

I do believe that was the sound of a gauntlet being thrown down.

Warning! Gory Mathematical Details Ahead!
To solve this problem I decided to create the perfect pitcher. He is so good that his manager knows that on his day, no one in the bullpen will need to lift a finger. They might as well not be at the ballpark. It’s 100 percent guaranteed. On the day before his scheduled start, the manager can use the bullpen to his heart’s content. On the day after, he’ll have a rested pen.

The funny thing is that this pitcher already exists, and no one gives him any credit. Ladies and gentlemen, I give you the perfect bullpen saver: Scheduled Offday.

Every season, a manager has a handful of situations in which he knows for sure that his bullpen will not be needed tomorrow. Worried about getting four outs from your closer because it might mean that he won’t be available tomorrow? Don’t worry. There is no tomorrow!

Thanks to Retrosheet, we have files that show the original schedule for a season. (Of course, rainouts and other unfortunate events change what actually happens, but that’s life.) Using these files, I looked for games where a team had an offday scheduled for the next day. To make sure that no makeup games were snuck onto the schedule, I made sure that no game was actually played the next day as well. I looked to see how managers behaved on the day before an off-day versus when they did not. All numbers are from 2009-2013.

So let’s see how well each of the standard arguments holds up:

The manager can have a quicker hook with his starter, because he can extend his bullpen a little bit.

It’s a tribute to the sample sizes that we’re dealing with (24,000 games!) that the difference between the numbers of batters faced is almost significant (p = .059), but that’s not even a one percent change over baseline.

The manager can use more relievers and mix and match more effectively. He can feel more free to use a pitcher for a batter or two.

Here we see that before a day off, managers do feel at liberty to make more calls to the bullpen, although again, the effect sizes are not huge.

The manager can use all of his good relievers, rather than holding one back in case he should be needed tomorrow. He can also extend his good relievers a bit.

We can see that there is a difference between the types of pitchers used by managers before a day off and those used when there’s a game the next day. At first blush, this might seem like a big deal, but let’s drill down a little further. The difference in results for a day off was 0.27 runs per nine innings. Since we know that managers aren’t going to their bullpens earlier, we can assume that relievers are picking up the same basic workload.

In 2013, the average major league bullpen pitched just shy of 500 innings (499.23, to be exact). We can figure that if managers always used their bullpens the way that they did before a day off, they would save 15 runs (actually a little less, because some of that is already baked into the results, but let’s ignore that for a minute). That’s not insignificant. The strategic ease that comes from the ability to say “tomorrow, I won’t have to worry about the bullpen” is like having a ghost 1.5 win player on the roster. The problem is that the manager has that luxury only a handful of times per year.

To make sure that there weren’t weird things going on, I limited the sample to games that were reasonably close, defined as games that were within three runs either way at the start of the seventh inning. I also took out any games after September 1, figuring that the expanded rosters might play havoc with the findings. The numbers, of course, wiggled a bit, but the overall message was the same.

Now, let’s come back to reality. This would necessitate a situation where a team played games only on alternating days so that the manager absolutely knew that tomorrow was always a total freebie, or that the manager always had totally delusional levels of confidence that tomorrow, his starter would throw a complete game. If we assume that managers are not actually delusional, then we would expect them to understand that while a pitcher might often give him seven or eight strong innings, and could very well throw a complete game tomorrow, he at least needs to consider what tomorrow will bring. There goes some of that ease factor.

On top of that, any one starter is going to be tomorrow’s starting pitcher only about one-fifth of the time. So, even if we assumed that Mike Matheny managed his bullpen differently when Adam Wainwright was scheduled for the next day, that ease is present in only 30-something games per year. The upper limit of an effect that one pitcher could have from a reputation as a complete gamer would be 0.3 wins or so, and that’s if the manager believed that he would always start and finish the next game. The effect is probably smaller, and while 0.1 or 0.2 wins of additional value per year isn’t irrelevant, the order of magnitude is well below what it’s made out to be by those who sing the praises of the complete game.

But wait, what about the next day’s games? If a pitcher throws a complete game, then the bullpen had a day off and the manager has some leeway to use pitchers a little more liberally, right? I identified games that were played after a day off and found the following.

When a manager has the luxury of giving his bullpen the previous day off, they do pitch a little better, and he’s a little more likely to use them. Whether that’s because he’s able to optimize matchups or because the arms are rested, there is an added effect. If a team was somehow able to have its bullpen pitch all game with its members having always had the previous day off, the effect would be about two runs over the course of a season. Of course, that luxury happens only when the previous day’s starter actually completes a game. Even if a starter completed all 34 of his starts, the benefit for the next day would be just a fraction of a run.

The Cult of Complete
I can appreciate the value of a complete game (or even a good eight-inning outing) unto itself. It’s usually also a well-pitched game, so huzzah for that. And yes, there are effects beyond the game itself. But those effects are relatively minor, and on the scale of maybe a small fraction of a win over the course of a year for any one pitcher. And that’s the upper limit. “How his complete game sets up the rest of the team” is nice to talk about, but once you run the numbers, you see that the actual effect is much less than those who sing its praises seem to believe. Maybe it does make the manager feel better about life, but you can’t put happy feelings on the scoreboard.

If you want to make the case that a pitcher who throws a lot of complete games lessens the workload on the players in the bullpen over the course of a season and keeps their arms fresher and perhaps less injury prone, that’s a reasonable hypothesis (for another day). But let’s not make the complete game or the pitcher who goes deep into a game more than he really is. The knock-on effects that it has are not some deep mystery that takes 50 years of study to fathom. They can be easily estimated. The effect of those heroics is not zero, but let’s keep some sense of perspective.