It seems like every time Trevor blows a save, or even makes one interesting, there are murmurings about making Heath Bell the closer-if not this year, then next year. My response is always the same: the worry should be less about who the closer is, but rather who gets to pitch in the highest leverage situations.
Protecting a ninth inning lead is certainly important, but how important it is depends on the magnitude of the lead, as well as the skill of the batters scheduled to bat in the inning. As Tom Tango writes: “The record books don't make distinctions between the one-run save and the three-run save, but it's rather clear that it's much easier to save a three-run game than a one-run game.”
With this in mind, Tango set out to quantify the relative importance of various situations within a game. To do so, he established a table of win expectancies. The table shows the probability of winning the game at any point in the game. For example, a home team winning by one run with two outs in the top of the eighth inning with no runners on base will win 84.7% of the time. Using the win expectancy data, leverage index, which measures the importance of any situation relative to the start of the game, was born. Baseball Prospectus explains that: “a leverage of 1.00 is the same importance as the start of a game. Leverage values below one represent situations less important than the start of a game (such as mopup innings in a blowout). Leverage values above one represent situations with more importance (such as a closer protecting a one-run lead with bases loaded in the 9th inning).”
To demonstrate the importance of a team getting its best reliever into the game in high leverage situations, I ran a quick regression analysis, which hopefully illustrates the intuition behind the leverage theory. The theory is that if teams are better off pitching their best reliever in high leverage situations regardless of whether it is classified as a “save situation,” there should exist a positive relationship between the proportion of a team’s high leverage innings pitched by the team’s best reliever and wins (once other factors such as a team’s total runs scored and runs allowed have been controlled for).
To test this theory, I first needed to define a way to measure the proportion of a team’s high leverage innings pitched by a team’s best reliever. Leverage does not account for innings pitched. Rather, it signifies the average importance of a team/player’s relief appearances. A minor league pitcher can get called up and throw one inning of high leverage ball. His leverage score will be high, but his impact on wins over the course of a 162 game season is negligible. For this reason, I have created what may be a new statistic called effective leveraged innings (note: there is a good chance someone has done something like this before; I am just unaware of it). Effective leveraged innings is the product of innings pitched and leverage index. Effective leveraged innings accounts for both the quantity and importance of innings pitched. A pitcher with 100 innings pitched and a leverage index of 1.20 would have pitched 120 effective leveraged innings. A team whose relievers pitched 500 combined innings with a leverage index of 1.1 would have pitched 550 effective leveraged innings.
Measuring the proportion of effective leveraged innings thrown by a team’s best reliever requires identifying each team’s best reliever. A team’s closer is not necessarily the best reliever. The closer may have the role based on the reputation of his past performance rather than his current skills. Also, managers may already recognize save situations are not always the most important, and purposely name a pitcher who is not the team’s best reliever “the closer.”
Traditional statistics such as earned run average (ERA) do an equally poor job of identifying a team’s best reliever. ERA often overstates the skills of bad pitchers who may have had some lucky success over a small sample of innings. Another shortcoming of ERA is it is dependent on factors outside of the pitcher’s control. Differences in the skill of the surrounding defense and ballpark configurations make ERA a poor choice for evaluating the skill of pitchers. Other frequently cited statistics such as WHIP (base runners allowed per inning) offer many of the same shortcomings as ERA.
The best measure of a reliever’s skill is WXL, the “expected wins added over an average pitcher, adjusted for level of opposing hitters faced.” WXRL could be used if you prefer to use replacement level as a comparison rather than average level. WXL factors in the MLV [marginal lineup value] of the actual batters faced by the pitchers. Then, WXL uses win expectancy calculations to assess how relievers have changed the outcome of games” (baseballprospectus.com). In this study, the player on each team with the highest WXL is considered the team’s best reliever.
My data comes from the 2006 and 2007 seasons. A larger sample size would be more telling, but data collection takes time, and I did not feel like spending hours collecting data to better prove such a widely accepted concept. I have removed data from the 2006 Atlanta Braves and 2006 Cleveland Indians because the Cleveland Indians traded their best reliever, Bob Wickman to the Braves in the middle of the season. Wickman’s proportion of effective leveraged innings pitched was not representative of his use while with either team.
Regression Results:
I first ran a regression using only runs scored and runs allowed to explain wins. These two variables explained approximately 83% of the variance in wins. Next, I ran the regression with a third independent variable-the proportion of effective leveraged innings thrown by a team’s best reliever. Not only was this variable significant at the 0.01 level, but the new equation did an even better job than the first at explaining wins. It had a higher adjusted R^2, lower Akaike, and lower Schwartz. I played around with different functional forms of the variables, and even added a variable that measured the proportion of effective leveraged innings thrown by a team’s second best reliever (as measured by WXL), but these equations had trouble passing the Ramsey RESET test for misspecification, or contained combinations of variables that turned out to be insignificant. Below, I am posting two images of the results. The first captures the pertinent information of my final equation. The second image compares the final equation to the control. Click on the images to enlarge and view more clearly.
Conclusions:The data shows that for each additional percentage of effective leveraged innings pitched by a team’s best reliever, a team can expect to add 0.33 wins to its record. The implication is a team could increase its win total by pitching its best reliever in an additional 3% of its effective leveraged innings. There are two ways to do this. A team could increase the innings pitched of its best reliever or increase its proportion of effective leveraged innings thrown by its best reliever. Increasing a pitcher’s innings thrown is unlikely to be successful because it could cause extra wear on the pitcher’s arm and lead to injury. The more practical method is to increase the leverage score of its best pitcher, while maintaining the same amount of innings thrown. Increasing the leverage score would entail that teams not reserve its best reliever for save situations, but instead employ their ace reliever in the highest high leverage situations possible.
I understand the argument that closing games in the 9th inning may take a special mind-set. This may or may not be true, but I am willing to cede the point for now. Luckily, that theory is not inconsistent with using a team’s best reliever in the highest leverage situations. Many save situations are in fact high leverage. What I encourage the Padres to do with Heath Bell (once Hoffy retires), or whoever their best reliever may be in the future, is to have him close out tight games in the 9th inning, but not necessarily games with a 3 run lead. Rather than wasting innings picking up easy saves with a huge lead, the Padres should allow their best reliever to pitch in other high leverage situations.
Of course, it is easy to pinpoint the highest leverage situation in a particular game after the fact, but not so easy to do mid-game. My solution to this is for the Padres to employ its statisticians to make up a chart outlining the probability of any given situation being the highest leverage moment in that game. Armed with this information, the manager will be able to make an informed decision about when best to bring in his best reliever. Using the “save situation” as a rule-of-thumb will no longer be necessary.
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