Now let us consider the normal progression of a baseball game. Before an at bat, the game is in a distinct state with an associated probability of victory (the probability of the home team and visiting team winning intuitively adds up to 1.0). After an at bat, the game transitions into an entirely different state, with a different associated probability. The way that WPA works is that the change in probability from one game state to the next is assigned to the players involved. In most cases, the hitter is assigned the associated change in probability for the team at bat, while the pitcher is likewise assigned the change in probability for the team in the field. (Sometimes the change is assigned to a fielder if an error occurs on the play). If this statistic is tracked throughout the entire season, we can see which players added the most to their teams’ chances of victory (and also which players subtracted the most). I would love to see this statistic incorporated into an analysis of the MVP winners throughout the years.

In any case, here’s a good description of WPA from hardballtimes.com. Consider this example taken from that article:

Here’s an example: Bottom of the ninth, score tied, runner on first, no one out. The home team has a 71% chance of winning according to the Win Expectancy Finder (in this situation, the home team won 1,878 of 2,631 games between 1979 and 1990). Let’s say the batter bunts the runner to second. Good idea, right? Well, after a successful bunt, with a runner on second and one out, the Win Probability actually decreases slightly to 70% (home team won 1300 of 1,848 games), according to the WE Finder. The bunter hasn’t really helped or hurt his team; his bunt was a neutral event.

A greater understanding and use of WPA by managers could revolutionize the art of managing baseball games. This leads to the core of what I am trying to get at: Pitchers used in “closer” roles have an inherently low contribution to their teams victories because of the game situations in which they are typically used.

To harden my point, I was inspired by this article from sabernomics.com. In it, John Wright presents a game that he tracked using a WPA analysis. I contacted John and he sent me his spreadsheet complete with WPA tables and macros to track a game. So I decided to track a game myself to shed some light on the closer role problem. The game that I chose to track was the Red Sox vs. White Sox game that took place on August 15. It bodes particularly well for this article because Curt Schilling blew a save in that game. Let’s first take a look at the WPA graph of the game itself:

As you can see from the graph, when Schilling entered the game in the bottom of the 8th, up by 2 runs, with 2 outs and a man on first, the probability of the Red Sox winning the game was 0.886. If you think about this, this means that essentially the most WPA that Schilling can contribute to the team’s victory is about 0.12 or so. In fact, most “save” situations have a very high probability that the team currently winning will win the game (this should be intuitively obvious). So what is my point? The point is that even by converting a lot of saves, closers do not contribute a significant amount to the probability of a team’s victory. Additionally, when a closer blows a save, the WPA that they contribute to the team is typically a very large negative value. In the case of Schilling’s blown save here, his overall WPA for the game was -0.869. Thus for every blown save that a closer gives up, it takes roughly 7 or 8 converted saves to nullify the blown one. Most closers (even very very good ones) blow 4 or 5 saves a year. Now consider a pitcher that saves 40 games in one year, pretty good season right? Well if you did a WPA analysis of his total contribution to the team, it would likely result in a very neutral value not much higher than 0 (assuming the pitcher has blown a few saves which is very likely).

Moneyball revolutionized mainstream thinking about offensive performance with the realization that statistics like OBP and SLG are significantly more relevant than those like AVG and RBI’s. I think we need something similar in the mainstream media to accentuate the serious flaws that the closer role has brought to the effective use of pitching talent during a baseball game.

Also as an aside note. I am happy to see that Curt Schilling will be rejoining the Red Sox rotation. See my previous post on this topic.

First, let us consider the official definition of a save taken from a sports encylopedia:

A save is credited to a pitcher who fulfills the following three conditions:

1. The pitcher is the last pitcher in a game won by his team;
2. The pitcher is not the winning pitcher (for instance, if a starting pitcher throws a complete game win);
3. The pitcher fulfills at least one of the following three conditions:
   1. He comes into the game with a lead of no more than three runs, and pitches the remainder of the game, gaining at least one out.
   2. He comes into the game with the potential tying run being either on base, at bat, or on deck. In other words, the potential tying run is either already on base or is one of the first two batters he faces.
   3. He pitches at least three “effective” innings (this is the only subjective criterion and is judged by the official scorer).

In the first part of this series, I’m going to stay away from some of the statistical arguments and outline the perhaps “common-sense” reasons why saves and the concept of a closer is a misguided tool in measuring pitching performance. The first thing that should be easy to notice from the above definition is that not all saves are created equal. The most obvious and most common save oppurtunities are those in which the pitcher enters the game in the 9th inning with a 1, 2, or 3 run lead. Clearly it is easier to hold a 3 run lead than it is to hold a 1 run lead. However, in both cases, the pitcher receives a save that for statistical purposes, is the same size and shape. Even more difficult saves than your standard 1 run lead, 9th inning save is a situation where a pitcher must enter in the 8th inning with a 1 run lead and runners on base. Still, if the save is converted it’s worth the same as that 3 run lead breeze through the 9th.

Perhaps the greatest atrocity to the save rule, though, is the final condition mentioned in the above definition. Consider the following two situations:

1. A pitcher enters a game at the start of the 7th inning. The game has gotten out of hand and his team has already compiled a 13-0 lead. The pitcher proceeds to give up 6 runs in the final three innings of the game and his team wins 13-6
2. A pitcher enters a game with one out in the 8th inning with the bases loaded. His team is leading 4-3. He induces a double play ball and then pitches a 1-2-3 9th inning to complete the 4-3 victory.

Guess what. Both pitchers earn a save even though the performance by the first pitcher is significantly short of stellar. This is the problem with the save rule. It is a superficial statistic that is completely dependent on game conditions and not all “save situations” are equal. The result is a statistical category that has very little meaning in terms of a pitcher’s overall value (it is true that there is some merit in saves but the correlation between saves and talent is not strong). However, it is still used as a primary category when evaluating relief pitchers and negotiating contracts.

The final point that I want to mention is that basically all teams have a designated “closer” who comes in whenever there is a save situation. Usually the closer is the most talented relief pitcher on the staff. However, the problem with using your greatest talent in this way is that most save situations are not the must crucial situations in the game, and usually there are higher stakes circumstances that occur during a game that a lesser talented “set-up” man is used for. Because of this, you can argue that the closer role is the least valuable role on the entire team. In the next part of this series, I’m going to bring statistical merit to this statement using probably one of the most interesting statistics I’ve seen: Win Probability Added or WPA. Stay tuned.