Bad Statistics and Worse Economics in Baseball

A lesson on conditional probability

Photo by Bill Stephan on Unsplash

The no-hitter. It’s on every baseball fan’s list to see in person. To witness a pitcher retire 27 batters and not allow a single hit is something a fan can talk about for the rest of their life. No-hitters are rare, with only a couple occurring each year across the 2,400+ games in an MLB season. But they do happen most years - the last season without a no-hitter was 2005. For true baseball fans, a no-hitter is always lurking in the background, an unspeakable desire that must not be said aloud, not least of all because most pitchers finish the first inning with a no-hitter intact. Buzz grows in the stands if a pitcher goes into the fifth or sixth inning with zero hits. By the eighth inning, ESPN is doing live look-ins and social media is blowing up. When a pitcher completes a no-hitter, the celebration begins. The catcher and pitcher bear hug on the mound. Fans will remember the pitcher’s name forever.

One of the most alluring aspects of the no-hitter is that it isn’t only an achievement by the pitcher. It’s also an embarrassment for the team that is no-hit. Even in ninth-inning situations where the outcome of the game is not in doubt, batters will aggressively try to avoid being on the losing end of a no-hitter. Players will be aggressive at the plate, managers will leave starters in, and some even bunt to avoid being no-hit. Just when pitchers are reaching exhaustion, batters will bring their A-game. This makes a no-hitter especially impressive.

Yet, the days of the no-hitter may be numbered. For decades, an unwritten law of baseball was pitchers were kept in the game as long as they were pitching a no-hitter. With several exceptions, such as a clear loss of command or a recent return from injury, pitchers were kept on the mound. Relief pitchers were left on the bench. Over the last few years, this unwritten rule has been abandoned. Today, managers are pulling their pitchers in the midst of no-hitters. Last year alone, this happened six times. Compare that to the 1990s, when only two pitchers were pulled during a no-hitter over the entire decade. What’s the deal?

The problem, of course, is that nerds have taken over everything. Despite always being the most statistically oriented sport, baseball has often not properly utilized numbers. For years, batting average was considered the most important statistic for a batter. On base percentage and number of walks were not. Now, hitting a single is better than earning a walk, because a baserunner on third will almost always score on a single and a baserunner on second often will. That said, a walk is still good. It gets a runner on base who can later score. This was one of the main insights of Billy Beane during the Moneyball era, which spawned a book and one of the best sports movies of all time.

Since then, analysts have taken over baseball. Complicated statistics like WAR and wRC+ are now used to compare players across positions and account for differences in ballparks. One trend desk jockeys have noticed is batters tend to do much better against pitchers during their third at-bat. This makes sense. Pitchers have the edge at the beginning of a game. Batters haven’t seen that pitcher, possibly for years, and the pitcher has a fresh arm. As the game goes on, batters can discuss what the pitcher is doing, what pitches are working and which aren’t, and how to best get hits. Pitchers, meanwhile, are tiring. Beginning with the third time through the order, the odds shift and begin to favor the batter. Because of this, pitchers are now routinely being pulled from games in the sixth or even fifth inning, even if the pitcher has been throwing well. Even if the pitcher has a no-hitter.

This is an incorrect use of statistics. It may well be that it is statistically optimal to pull a pitcher once he has been through the batting order twice. This, however, refers to any pitcher. If a pitcher has a no-hitter going, the correct stat is not whether a generic pitcher does worse the third time through the batting order, it’s whether a pitcher on a no-hitter does worse the third time through the batting order. In statistics terms, baseball analysts are using the marginal probability of a pitcher giving up hits, when they should be using the conditional probability.

It would be interesting to know if the “third time through the batting order” rule still holds for pitchers doing well. For example, for pitchers who allow three or fewer hits and pitch a complete game, when do those hits typically come? Are they weighted toward the last three innings? What about pitchers who only allow one hit? This might be difficult to ascertain, as there was never a stigma of pulling a pitcher who had only allowed one hit after seven innings, especially if the game was close. Regardless, if the baseball geeks are usually marginal probability, they are not using the best statistic.

Worse, this ignores the economics of the decision. People love to see no-hitters. It provides free advertising for the sport. Preventing pitchers from achieving one seems like an economic loser. Professional sports is successful because it entertains. Diminishing the entertainment value because the analytics claim a small increase in the chance of a win by benching a player is not sound in the long run. More than a grand slam or even a playoff win, a no-hitter is something baseball should seek to keep intact, not relegate to a former era. It’s hard to justify spending significant money on a game when the star players are being benched only halfway through. The MLB will be better off economically if they stop pulling pitchers who are performing well.

The one caveat to both the statistics and economic concerns is injury. If pitchers are being pulled because of injury risk, then it might be the best thing to do from both a statistical and economic point of view. After all, a star pitcher is paid tens of millions of dollars a year. It isn’t worth risking his season so one game can end with a final score of 4-0 instead of 4-1. Managers will often talk about injury risk for this very reason. I’m skeptical, however. Is there any evidence pitching a few extra innings significantly increases the chance of injury? Moreover, that brings up a host of issues that aren’t talked about much. Would it behoove pitchers to avoid throwing fastballs, or at least, avoid throwing as hard as they can? Maybe pitchers would be better off throwing at 90% strength the whole game, especially if their curveball is working. What is the cause of most pitching injuries? I doubt it can be traced back to that one game where the pitcher through 130 pitches instead of 105.

Baseball has made some good changes recently. The pitch clock is a godsend. Designated hitter is still an abomination that should be banned by constitutional amendment, but I recognize this is a losing battle. Let’s not let bad analytics ruin the no-hitter.