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win-expectancy-and-leverage-braves-9-phillies-8 | September | 2007 Articles

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Win expectancy and leverage (Braves 9 - Phillies 8)

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Deja vu? Perhaps. My last post at Chop-n-Change was a quick look at the recent Braves-Phillies clash where Atlanta hauled back a six run deficit. During that post I talked about two concepts: Win Expectancy and Leverage Index.  I had a couple of emails asking to take a few seconds to develop these concepts a bit more fully, so here goes. Win Expectancy is the probability of a team winning given the current state of a game. What do we mean by state? Well, the most important parameters are the score, how many base runners there are and which bases they are on, and the number of outs. Based on this Win Expectancy gives you the probability of each team winning. An example may help. Take the start of a game between two evenly matched teams. At the top of the first with no-one on, no-one out and the game tied at 0-0 the probability of the home team winning is 50% (ignoring home team advantage). If the home team then retires the side it has an advantage as it has an extra half inning in which to hit. Win expectancy jumps to around 55%. If the home team loads the bases with no outs obviously the chances it wins the game increases exponentially. Okay, not exponentially but the home team is expected to win 70% of the time. If it hits a grand slam then win expectancy is 87% -- in other words from this point the visiting team only wins 13% of the time. So how do we know all this? There are a couple of ways that we can calculate these numbers. The first is to look at every game played and log every single play. From each play isolate all the possible states (base, out, score) and work out how often the home team wins. That gives you a win expectancy table. We can also calculate win expectancy mathematically but that is more complicated. Let me introduce you to Leverage Index (LI), which I think is more important and interesting. LI reflects the importance of the game situation. Imagine a man on second and third, two out, with the home team behind by one, in the bottom of the ninth. That feels like a clutch at bat. The LI is 8.4. To put that into context the average LI is 1. This particular at-bat is 8.4 times as crucial as an average at-bat. What do we mean "8.4 times more crucial"? Good question, if I do say so myself. LI measure the overall swing in win expectancy for a given game state. In the situation above an out will result in a win expectancy of 0 for the home team. A single means it will be 1. The swing in win expectancy is large and hence LI is high. By contrast take the first at-bat in a game. Irrespective of whether the batter squeezes one into the seats of goes down swinging the change in win expectancy is a heck of a lot lower. Hence LI is lower. For those interested the LI here is 0.9, marginally below average. LI is relatively complicated to calculate as you need to know a) the possible swing in win expectancy for every game state and b) the frequency of each game state. But tools LI tables are available on the internet. Here are some resources for the curious that explains all of the above in more detail: So, let's have a look at the recent Phillies Braves clash in terms of LI and win expectancy. It was 8-2 entering the bottom of the eighth. The Braves odds of winning were a mere 1.1%. LI was 0.04! In other words the Phillies had all but won. When the Braves loaded the bases with one out the score was 8-4. At this point Woodward was up and the Braves' win expectancy was still 7.7%, although LI was 1.8 -- that was a relatively important at bat as a home run would have tied it all up (although a HR in that event was unlikely) so the Phillies were still hot favorites -- a GIDP would have ended the rally. LI rose to 6.1 in the last at-bat of the inning when Chipper flied out with the bases loaded and the score 8-6. At that point the Braves' odds of winning were 24%! If you watched the game I bet your heart was beating just that little bit faster. That is a good way to think about LI -- it should reflect your heartbeat as the game progresses! The maximum theoretical LI is 10.9, which is heart attack country. Finally let's turn out attention to the ninth and Matt Diaz' walk off double. The bases were loaded with two outs and the Braves two behind. Was you heart pumping? You bet. The Braves had a win probability of 18% but LI was a massive 7.1 -- the highest at any point in the game. Why? A double would have won the game (scoring three, which it did), whereas an out would have been goodnight. As we all know Diaz came through and the Braves won. If you want to track LI live during game time I suggest turning to fangraphs. It also logs play-by-play LI after each game. Here is the log for the Braves game described here. Another cool chart is the graph of win expectancy at each point. Again fangraphs provides here. Check out the upswing at the end! I love LI and win expectancy. A look at a win expectancy chart along with a log of LI  tells you all you need to know about a game. A look at the chart of this particular games tells you that if you weren't there or watching on telly then you missed something quite special.
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