Win Expectancy

Win Expectancy (WE) is the percent chance a particular team will win based on the score, inning, outs, runners on base, and the run environment. These percentages are calculated using historical data, meaning if a team is losing and has a 24% win expectancy, only 24% of teams in similar situations in the past have ever come back to win.

To get an in-depth feel for how win expectancy works, check out Tom  Tango’s Win Expectancy Charts or download and explore this extremely detailed and adjustable spreadsheet.

Calculation:

Calculating win expectancy from scratch is one of those things that’s extremely easy conceptually and very challenging in practice. All you would have to do to find the win expectancy of a situation would be to identify all similar situations in the last ten years or so (the sample you choose depends on the run environment) and then find the winning percentage of teams who found themselves in those situations.

This isn’t exactly the kind of thing you’d want to mindlessly do between pitches, which is why FanGraphs hosts live Win Expectancy Graphs for every regular and postseason game. Click on an individual game under the “Scores” tab at the top of the page to find the WE graph from the game of your choosing. It updates every time the inning, score, and base-out state changes and tells you the probability of the home team winning the game. A win expectancy of 57%, for example, means that the home team is expected to win 57% of the time and the road team is expected to win 43% of the time.

Our WE numbers start at 50% for each club, but you could factor in a home-field advantage and the quality of both pitchers and lineups to derive a more accurate starting point for that particular game. Our Game Odds feature does that! Remember though, that standard win probability only knows the inning, score, and base-out state. It doesn’t know anything about who is playing, who is due up, etc.

Why Win Expectancy:

Win Expectancy is the ultimate story statistic. It tells you which moments in the game had the biggest effect on each team’s chances of winning and also gives you a sense of how likely it might be for the trailing team to rally back and win. You have to remember that WE is merely reporting the long-run averages, so a 24% WE doesn’t necessarily mean the true odds in this exact moment are 24%.

WE is also going to provide the basis for Win Probability Added (WPA), which is a statistic that tracks each players impact on the team’s odds of winning the game by measuring the change in WE from the beginning of their PA to the end of it.

How to Use Win Expectancy:

Using Win Expectancy is extremely easy. It is simply the percent chance that teams in similar situations in the past have won their game. You don’t need to know anything else to make use of this statistic. WE is the long-run average, however, so you need to remember that a 40% chance of winning is based on average players. If Miguel Cabrera is at the plate against Aaron Crow, the true odds favor the Tigers more than the WE graph indicates.

Context:

As a game goes on, the win expectancies for both teams are constantly changing on a play-by-play basis.  This is what a win expectancy chart for a game looks like:



This is the win expectancy chart for Game Six of the 2011 World Series. Notice how as the game goes on, the green line moves closer and closer to the Rangers’ side of the chart, indicating that the Rangers are becoming more and more likely to win. That peaks in the ninth inning, when the Rangers came one strike away from winning the game before the Cardinals rallied to tie the game and then win it.

Those final innings were a whirlwind, and the bouncing win expectancy line mimics indicates that. Win expectancy is a great story-telling stat.

Also, notice that certain key events change the win expectancy more than others (see: Win Probability Added).

Links for Further Reading:

Get to Know: Win Expectancy – FanGraphs

The Game State, Run Expectancy, and Win Expectancy – Lookout Landing

Misunderstanding Win Expectancy – The Book Blog