World Series Win Probabilities: Primer
Over the next few days, I will be running out a series based on win probabilities from the World Series not only using single game win probabilities like the ones in our game graphs, but also using overall series win probabilities, which will be introduced today.
The idea behind the series win probabilities is based around the same idea as the single game win probabilities we use here: both teams have a 50% chance of winning each game. As such, this flow chart describes every possible path for a team through the World Series (or any other seven game series; the part from 1-1 up would describe a five-game series):
Click to embiggen, and then follow the jump for more on what’s inside.
The chart reads from the top down, with the top row representing the end of the season, the second row representing Game Seven, the third row representing all possibilities for Game Six, and on down to the beginning of the series at Game One.
I decided to design the chart as reading from the bottom-up instead of top-down due to the way the probabilities are figured. Each percentage is calculated using recursion, a mathematical technique in which a set of rules is designed from a simple base case (and also the best Google search suggestion ever).
In this case, the probabilities are found recursively using the case of the 3-3 series as the base. In the base case, a win takes the team in question to a series victory (100%), and a loss takes the team to a series loss (0%). Given our assumption of a 50% win probability at the start of each game, that puts the 3-3 series as a 50% win probability for each team.
For example, with the case of the 3-2 lead, a game victory results in a series victory (100%) and a game loss results in a 3-3 series (50%) for an overall win probability of 75%. With the 3-2 (and therefore 2-3) series determined, we can now go down to the next level of games, 3-1, 2-2, and 1-3, and so on and so forth, continuing recursively.
With these probabilities in hand, we can determine the series win probability at any point for each team. For example, when Marc Rzepczynski induced a ground out from Esteban German with a 1-0 lead to end the top of the eighth in Game Two, the Cardinals had a 77.3% chance at winning the series. When Neftali Feliz entered for the bottom of the ninth in Game Six, the Cardinals had a mere 2.1% chance at winning the series.
The possibilities with this analysis are very wide in my opinion, and I very much look forward to presenting the most interesting aspects over the next week or so.
Jack Moore's work can be seen at VICE Sports and anywhere else you're willing to pay him to write. Buy his e-book.
This should be neat. On a related note, I would love to see the odds of the Cardinals winning the World Series every day from about August 1 onward. That would be an amazing graph.
Agreed, I was thinking exactly the same thing.
Love to see the same – from August or so – for the Red Sox. I’d get that printed on a shirt.
This seems rather simplistic. Doesn’t home field advantage produce some net effect?
Having the better team should also produce some net effect.
All Fangraphs analysis is based on the simplifying assumptions that location and team do not matter, only the state of the game. This is why for individual games, both teams start out at 50%. This post is completely in keeping with that policy.
I should think that the respective influence of the starting pitchers would be much larger.
Vegas (or bookies) could have real-time odds. Then again, they could have that now with any game.
The realtime odds, converted to probabilities, would be an interesting comparison with the Series WP in this analysis
This is a great idea. On a related note, if you take take a series that is 3-1 after four games, the odds say it is 50 percent likely to go five games, 25 percent to go six and 25 percent to go seven. My hypothesis is that it’s more likely to go six than seven, because more aggressive pitcher management by the trailing team in the fifth will give the leading team the edge in the sixth.
Your embiggening is still not very big. Seems cool, but it’s all too small to read.
Fixing…
Try it now. It’ll open a new tab, but it should be the correct size.
I did this too. One useful thing – you can use it to find championship probability added across a series – multiply the WPA from that game by the difference in win or loss for that game.
You can do that for the whole postseason multiplying the totals in the divisional (adjusting to a five-game series, which is basically starting 1-1) by .25, LCS by .5, WS by 1.
If you want to make a home-field adjustment, it’s not that hard, because you know where the games will be – so you could make the chart from the Cardinals perspective, and use (let’s say) 55%/45% for games 1 and 2, 45%/55% for the middle three, and 55%/45% again for games 6 and 7. And then the Rangers are just flipped.
You can do a “better team” adjustment the same way.
“Recursion…the best Google search suggestion ever.”
+10000
Those google fellows are pretty clever
I don’t see anything about “momentum” or “team(s) of destiny”…?
Obviously, the Cardinals had momentum and were the team of destiny because of their late-season surge.
So were they Rays.
There’s always the binomial distribution, p = 0.50….same results I think. Of course, if p is changing game to game (as it likely does), the overall probabilities will change some.
For example, I ran a computer simulation in which one team was up 1-0, and had alternating win expectancies (.3 to .7 to .3 to .7….) for each of the next 6 games. Despite two of its next three games having the disadvantage, the team that was ahead actually won about 67.53% of the series using 100,000 simulations. For the assumption above with .5 win probability every game, I got 65.645%, much closer to the theoretical expectation.
This probably comes from the fact that differing probability of success reduce the variance in the binomial distribution, giving the team with the one-game lead a slight theoretical advantage (with changing success probs).
This is pleasingly consistent with my comment on this topic about a month ago: http://www.fangraphs.com/blogs/index.php/ranking-ben-franciscos-3-run-home-run-by-wpa/#comment-1215248
This approach is also consistent with the research here, http://www.hardballtimes.com/main/blog_article/the-tht-annual-and-the-postseason/ , which adds to this discussion by framing it in the context of your average regular season game: “Said differently, a player’s contribution in the seventh game of the World Series is 167 times more important than his contribution in an average regular season game.”
That chart reminded me of Markov chains. Ugh.
Yes! This is what I was talking about (http://www.fangraphs.com/blogs/index.php/reliving-the-final-day-in-the-al-visually/) Could you do a recursion that not only includes the playoffs, but also the regular season?