P and Volatility – A Quick Explanation

In case you don’t want to get too in-depth researching WPA, P, and Volatility in order to understand my posts and spreadsheets, here’s my somewhat quick explanation:

WPA is short for “win probability added.” Win probability is based on historical baseball data on a team’s likelihood to win a particular game, given the game’s current score, inning, number of outs, and runners on base. Win probability added, therefore, tracks the change in win probability based on a player’s hitting, pitching, or fielding. Keith Woolner and Tom Tango (tangotiger) came up with the probability tables, and Dave Studeman is The Hardball Times’ resident expert on the subject. Dave also developed the spreadsheet I use to track each Braves game. Again, you can find out much more by reading the win probability article he wrote to introduce it on The Hardball Times.

Example: The home team in an average National League game bats in the bottom of the first with no one out and no one on base. The game is scoreless. Their win probability at this point is .548, since they got through the top half of the inning without allowing a run. The first batter for the home team hits a home run to right-center, just clearing the fence. The win probability for the home team now increases to .646 (1-0 lead, bottom of the first, still no one out and no one on). The difference here is .098 (.646 – .548 = .098), so the batter who hit the home run receives +.098 for his WPA, while the visiting pitcher gets -.098.

P refers to the amount of win probability that a pitcher can add if he finishes the current inning without allowing a run. This serves to illustrate the importance of the situation from the pitcher’s perspective. Baseball Prospectus, TangoTiger, and others use various forms of P, calling it “leverage,” or something similar. Tango’s crucial situations articles (found at tangotiger.net) and Dave Studeman’s THT article illustrate this in more depth. Using the same example as before, the pitcher for the visiting team entered the bottom of the first, and the P was .048. Had he not allowed the home run and instead finished the inning scoreless, the visiting team’s win probability (which was .452, or one minus the home team’s .548) would have increased back to .500.

P is especially important in late game situations, and as Tango found, managers don’t do the best job giving important innings to their best relievers. In many games, the most crucial situations occur in the 7th or 8th inning, which most managers give to the “setup man.” Joe Torre has lost the Yankees numerous games in recent postseasons by refusing to use Mariano Rivera until a “save situation” arises. In the process, he ignores that a 3-run game in the bottom of the ninth is won by the leading team about 97% of the time (even before the dawn of the modern closer). The P in such a situation is .041, less than at the start of a game! Meanwhile, the P in a tie game in the seventh is over twice that, at .089. I blame this misuse on Tony LaRussa, whose seemingly smart reliever specialization dating back to the 1980s has been imitated without further critical thinking today.

Volatility, on the other hand, looks at the importance of a situation from the hitter’s perspective. The worst that a hitter can do in any situation is usually a strikeout, unless there are runners on base to create a double play scenario. Any type of out that does not advance a runner would fit into this group of poor outcomes. Conversely, the best thing a hitter can do is (always) hit a home run. Volatility is the difference in win probability from the best to the worst.

Example 1: A hitter comes up with his team down 2-1. There are two outs in the bottom of the ninth, and a runner stands at second. The volatility of this situation is 1.000, since any type of out ends the game with a loss, while a home run wins it.

Example 2: The same hitter comes up in the same situation, except the score is 7-1 in the favor of his opponents. Since the game was already a virtually certain win for the other team (my tables tell me the win probability is 0.000, though it’s likely .0000001 or something), a home run does little to help that. The homer would increase it to .001, so the volatility is a miniscule .001. These situations happen quite often, so it’s important to get a handle on how important they are.

Now, here’s how I use these crazy stats: Of course, I track WPA first and foremost, since it’s the particular stat that has the most impact on how the games turn out. Similarly, I track equivalent wins (EQW), which turns WPA into a number that represents how many wins (or losses) a player has been worth overall. A win is worth +.500 in WPA, so I just take the player’s WPA and divide by .5 to get EQW.

I use P in a couple of ways. First, it’s important to look at the average P of a reliever’s appearances. The reliever who sees the highest average P should, in theory, be the closer, or the best reliever. It makes sense for your best reliever to pitch in the most crucial situations. Then, I use it as a leveler to place all the relievers on the same footing for comparison. A reliever who sees higher-P situations is going to have a better chance for a high WPA. So, I track win probability over total P, or WPTP.

For relievers, I also use a stat (unrelated to P) called effective outing percentage (EO%), which tells me how often a pitcher adds win probability in an appearance. I use volatility similarly to P, although hitters have very little control over whether they appear in crucial situations. They do, however, also deserve to be compared equally. Like the relievers, I divide their offensive WPAs by the total volatility they have faced, and then I throw in a multiplier so it’s not a miniscule number. I call this number WV, short for win probability added over volatility. I’ll be working out the bugs in my system this week as I track the Braves’ 6-game schedule and work on a number of writing assignments for my classes. Check back this weekend for another weekly review post.


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