Editor’s Note: This is the third and final installment in a series of articles from Tom regarding his invention, Leverage Index, and what it says about crucial situations. In his first article, Tom revealed the secret recipe to Leverage Index. In the second article, he analyzed other definitions of leverage. In this final article, he reviews several important Leverage Index nuances.
The biggest misconception about Leverage Index is about its function. People want it to do one thing, but it does another, and then people dismiss Leverage Index because it didn’t do the first thing. Heck, people do this with virtually everything. Trying to fit a round ball into a square hole is tough, but don’t take it out on the ball … take it out on the guy trying to do the fitting. Don’t shoot the messenger. Any other sayings?
Leverage Index is simply a measure of the fire the player faces. It doesn’t matter if the fire was arson, self-inflicted by the poor reliever who just keeps making the situation worse until the Leverage goes down to zero (either by getting out of the inning unscathed or by burning down the building). Leverage Index (LI) gives us the power to measure what we want. There are four different points of interest: gmLI, inLI, paLI, exLI.
- gmLI is the Leverage Index when the reliever enters the game. Its use is mostly to show a manager perspective, as it indicates the level of fire that the manager wanted his reliever to face.
- inLI is the LI when the reliever enters the inning. This is useful for those two-inning stints, where his team has had a chance to bat and give the manager a new fire level for him to contemplate. The gmLI could have been a 3.0 for Mariano Rivera in the middle of the eighth, but then the Yanks could have scored a bunch of runs. If Joe Torre decides to bring Mo back in the ninth for an LI of 0.4, then the inLI was an average of 1.7 for this game.
- paLI is the LI on a plate appearance by plate appearance basis. It doesn’t matter who caused the fire, or if the reliever is getting himself into jams. The LI is whatever the batter and pitcher happen to see during a particular at-bat. You could technically say that the manager is bringing back the reliever to face the next batter. While not readily apparent, even the inLI is affected somewhat by the performance of the reliever. Mo had gotten out of the eighth inning unscathed, and so he affected the LI for the rest of the game, including when he comes back in the ninth inning. The paLI makes this much more clear.
- exLI is the LI when the reliever exits the game. Does the manager pull the reliever out when the fire is burning, or does he wait for the fire to be out?
Each has its own use, and will appeal to a different reader, or to a reader who wants to look at things in different ways.
Now, let’s get on to …
The Last Secret Recipe
Through games of June 19, Jonathan Papelbon (paLI of 1.60) trailed Mike Timlin (1.63) in the level of fire he had had faced. While Timlin had been pitching well, Papelbon had been tremendous. Why would the manager want them both to face around the same level of fire?
On June 2, the Red Sox were on the road against the Tigers. Entering the bottom of the ninth, the Red Sox were ahead 3-2, and Papelbon came on to pitch. The LI to start the bottom of the ninth was 3.6. That would be the gmLI and inLI for Papelbon. Papelbon struck out the first batter, thereby reducing the fire a little bit, with the LI now standing at 2.8. The second batter grounded out, and the LI to face the third batter dropped to 1.9. Papelbon struck him out, and the game was over. The exLI was 0.0.
The three batters he faced had levels of fire of 3.6, 2.8, 1.9, for an average of 2.8. As you can see the gmLI (3.6) was higher than the paLI (2.8). Papelbon pitched so well that he reduced the level of fire expected. In fact, if we had known that Papelbon would have gotten three straight outs, the gmLI and paLI would have been zero. That is, if you have a burning building, but you know that Superman is there, that building will stop burning in one second. The LI is based on the normal change in win probability, and that means a normal set of performances is expected at that point in the game.
While Papelbon is not Superman (and we should not expect him to be perfect), we could instead expect that Papelbon will pitch very well. While the gmLI was expected to be 3.6 with an average reliever, perhaps we should have expected the gmLI to be lower if we had a great reliever, like Papelbon or Mariano Rivera. That is, the quality of the pitcher changes the leverage of the situation.
Let’s go to Tables 8 and 9 in The Book—Playing The Percentages In Baseball, which show us the number of runs expected to score against the average pitcher and the great pitcher. Let’s start with the average pitcher (Table 8). He will have a scoreless ninth inning (and win the game) 70.2% of the time. He will allow exactly one run, and send the game into extra innings, 15.7% of the time, giving him a win 7.85% and a loss 7.85%. He will allow 2 or more runs the rest of the time. Add it up, and the average pitcher will win 78.1% of the time and lose 21.9% of the time.
How about the great pitcher (Table 9)? Going through the same process, a team with a great pitcher on the mound is expected to win 85.0% of the time, and lose 15.0% of the time. The potential win gain, in this particular situation, with a great pitcher is .850 – .781 = +.069 wins.
And what is the potential win gain in a random situation? Since we defined our great pitcher as a .680 pitcher, this means that he is +.180 wins per nine innings better than the average pitcher, or +.020 wins per inning. Our leverage for the bottom of the ninth, up by 1, bases empty, no outs, is therefore .069 / .020 = 3.45. The standard LI for this situation is 3.60.
What happens here is that the great pitcher is expected to change the fire level enough so that just his presence (and the expectation of pitching great) would reduce the fire a bit. It’s not Superman-like in its effect (by reducing it to zero, just by being there), but it’s enough that it is noticeable.
Now, let’s go back to …
Papelbon and Timlin
What happens when you take a decent idea like Leverage Index and couple that with someone who spends alot of time on baseball? Fangraphs is tracking the LI (and Win Expectancy) for every single PA of every single game, and presenting the results to the fans in data and graph form, the day after every game. The result is spectacular.
According to jewtang (post #17), through games of May 7, Papelbon had a paLI of 1.59, but an inLI of 1.76. Timlin, on the other hand, had a paLI of 1.86, but an inLI of 1.46. That is, when the manager calls on the reliever to enter an inning, Papelbon faced a higher level of fire than Timlin. However, since Papelbon has been so effective, after almost every batter he faces, the leverage goes down, so that his paLI ends below his inLI.
Leverage Index doesn’t give you a different way to look at the game. In fact, it forces you to keep looking at things the same way you always have. The only difference is that Leverage Index simply quantifies your qualitative feelings, so all you have left is a cold-hearted number, which you can use to tell the story in a more consistent fashion.