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.