I am totally fascinated by WPA/LI, even though I can’t really tell you what it is. The title says what it is: Win Probability Added divided by Leverage Index, but that doesn’t really help. We are probably better off calling it Situational Wins, which is a less geeky name for a very geeky concept. I tried my best to describe Situational Wins in this article (see the end), in which I called it “a number that indicates who ‘won’ the at-bat, and by how much.” Hence, the name. Situational Wins.
A vague explanation isn’t the only issue with Situational Wins. Here are some others.
- Some people just don’t like WPA, and using WPA/LI (which corrects some of the things people don’t like about WPA) feels like jumping further into the rabbit hole.
- Total WPA/LI for a team doesn’t equal the team’s won/loss record. WPA does (which is one of WPA’s main attractions).
- Because of rounding and the infrequency of some situations, you sometimes get results that are a bit off. I’ll show you a couple of examples below, but these small differences shouldn’t make much difference for players over the course of a season. Still, they exist.
- WPA/LI is calculated by comparing two tables that Tangotiger has derived: WPA and LI by situation. We all trust Tango, but are we certain his tables are completely correct?
- WPA/LI has a bias in favor of home runs, because not all baseball events are randomly distributed across situations (personally, I don’t think this is a bias; it’s just a fact. But I thought I’d mention it.)
Having said all that, my intuition is that WPA/LI works. To me the proof is in the postseason scenario (as described in my previous article) in which the added “championship value” of winning a game has a constant relationship to its leverage index. As a result, when you divide each game’s championship outcome by its leverage index, you get the same number. Each game is equal in importance. Really, read the article.
Situational Wins do the same thing to plate appearances. They ensure that each plate appearance is treated the same as every other plate appearance regardless of how important it is to the game. The result is a measure of how successfully the batter or pitcher approached the situation.
This is not just an exercise in baseball math, by the way. Situational Wins are useful; they do something few other stats do. To quote Tango:
The key point of Situational Wins is best described in this extreme situation: with the bases loaded, tie game, bottom of the 9th, Situational Wins (and WPA) are the ONLY metrics around that will give equal contributions to the walk as it does to the homerun.
So what’s stopping us from using this useful stat? To me, there is a bottom line issue with Situational Wins. When you neutralize the criticality of a situation (divide by Leverage Index), what’s left? When you take out the critical impact of the score, inning and base/out situation, what is left for WPA/LI to consider? What are the key elements of the “situation” in Situational Wins? And how are they calculated?
Today, I’d like to experiment with Situational Wins to see if we can get a better handle on this issue. I plan to calculate the WPA/LI of several different situations and outcomes just to see what we see. I will discuss the results and encourage you to add your own comments. By working together, perhaps we can come to a better understanding of what this elusive stat is.
I’m going to use the WPA Inquirer for my results, which you can find below (you can also find it at our WPA Inquirer page). You’re welcome to play with the WPA Inquirer, add your own scenarios to the conversation and leave them in the comments.
In all cases, I will assume a run environment of 4.5 runs per game. All values will be expressed from the batting team’s perspective but we will also try to incorporate the pitching team’s perspective.
First up: What happens when the score changes?
|Value of Leadoff Event in Bottom of Seventh|
|Home Team Score Diff||Out||Single||Double||Home Run|
|Down by Two||-0.025||0.044||0.065||0.094|
|Down by One||-0.026||0.040||0.069||0.119|
|Up by One||-0.025||0.038||0.071||0.131|
|Up by Two||-0.026||0.038||0.072||0.134|
An out has the same negative impact regardless of the score. How can this be? Doesn’t an out hurt the team more when you’re behind than when you’re ahead? Yes it does, but that is what WPA captures. Situational Wins count a bases-empty out as the same value, regardless of the score, inning or number of outs. Bases-empty outs are the constant in the Situational Win universe.
Try it yourself. Plug a bases-empty out into the Inquirer in lots of different situations to see what you get. Remember that one- and two-point differences are insignificant and that rare opportunities are affected by rounding in the tables. As an example, try a seven-run lead in the bottom of the eighth. The Leverage Index is so low in that situation (0.01) that you know it’s rounded. The WPA/LI value won’t line up as well.
Anyway, does this make sense? Should bases-empty outs have the same value regardless of the situation? Well, when a pitcher gets a bases-empty out from a batter, he has won the contest and moved the game clock forward by the same amount each time. Situational Wins should be consistent here, and the fact that WPA/LI works this way is a confirmation of the system. Things are different when there are runners on base; I’ll explore that in a minute.
There’s another wrinkle here: a single is valued more highly when a team is down, but a double and home run are valued more highly when a team is tied or ahead. Playing with the WPA Inquirer, we find that this effect is much less pronounced in earlier innings and more pronounced in later innings. So game time is a factor here, but the trend is the same across all innings. What’s up with that?
Remember that we’re talking about leadoff situations in this example. Hitting a single at the beginning of an inning when you’re down by two is better than when you’re ahead because you need to score runs. By hitting a single, you keep the inning going and set up the potential for more runs.
On the other hand (from the pitcher’s perspective), the output is saying that giving up a solo, leadoff home run is more harmful when you’re behind and trying to catch up than when you’re ahead and trying to maintain a lead. The same is true for a double, but to a much lesser extent.
I’ve thought about this a lot, but I haven’t been able to find the ideas or words that tease out what is going on here. Why does the single follow a different pattern than the extra-base hit?
Next, let’s first see how Situational Wins change when the number of outs change:
|Value of Event with Runner on Second in the Top of the Fourth of a Tie Game|
|# of Outs||Out Without Moving Runner||Bunt Runner to Third||Run-scoring Single||Home Run|
First of all, the negative impact of not moving the runner over to third is larger with none out than with one or two out. This makes sense, of course, because a runner on third can score on a sacrifice fly with one out but not with two out. Conversely, bunting the runner to third with none out (which is a negative play nonetheless) is a much better play than doing the same thing with one or two outs. Once you think about the sacrifice fly, this will make perfect sense to you.
On the other hand, the value of a positive batting event, such as singling in the runner or hitting a home run, increases as the number of outs increases. This makes sense, too, because teams have more time to score runners when the inning is still young. When the inning is running out, however, run-scoring events are more meaningful.
Think of it from the pitcher’s point of view. With a runner on second and no outs, you sort of expect that some runs are going to score. But with a runner on second and two outs, you’re hoping no runs will score. So giving up the run-scoring hit hurts more–is a worse result for the situation–than earlier in the inning.
Finally, how do things change as the game progresses?
|Value of Event with Runner on First, One Out in Tie Game in Top of…|
|Inning||Stolen Base||Caught Stealing||Double Play||Single Runner to Third|
Once again, outs have the same value regardless of the inning. The new insight is that these aren’t outs that occur with no one on base, but outs that finish with no one on base. So we can update our previous finding to say that all outs that finish with no runners on base have the same value. Of course, caught stealing has a bigger negative value than a bases-empty out because it eliminates a baserunner.
Now positive offensive events, such as stolen bases and singles, go up a bit in the ninth inning (and a bit less in the seventh). Similar events in Win Probability Added increase dramatically in the late innings of a game. It appears that the WPA/LI value of positive batting events also increase in the late innings of a game, but to a lesser extent.
This is another tough one for me to tease out. It’s obvious that batting events have more positive value as the game clock runs down. Is that all that is going on here? If so, how is this quantified in a way that differentiates it from WPA? If not, what else is being considered?
I’m afraid I’ve posted more questions that answers today. Hopefully, this will be one of those articles in which the best insights are left in the comments. Got any?
References and Resources
Kincaid’s article about WPA/LI is worth reading because it demonstrates that the average WPA/LI values of events line up well with their linear weight values.