## The Value of Playoff Games and "Championship Probability Added"

I was thinking about the one game wild card playoff that's coming to the MLB postseason structure for the first time in 2012, and about the value of that game: how much is a one game playoff worth, in terms of how likely a team is to win the World Series?

I made the assumption that all 10 teams in the postseason are of equal strength, and that the teams that made it through the wild card game would not be adversely affected by having to play an extra game. I created this chart, based off very simple binomial probability data:

It's relatively self-explanatory; each game in each round of the postseason can be given a value, in a very similar manner to WPA, that corresponds to how big a change it will result in in a team's chances of winning the World Series. The value is dependent on the state of the series heading into it; a game 4 with the series at 2-1 is three times more important than one with the series at 3-0.

The chance that a team wins the World Series if it wins the wild card game is 1/8 (given the assumption that all teams are equal), while, obviously, if it loses, it can't win the World Series. Similarly, the difference between winning and losing Game Seven of the World Series is one championship.

After the jump: some more thoughts about the value of postseason games, and a look at how, by combining this with WPA from playoff games, we can create a metric showing a player's contribution to a championship effort.

The games that are in bold and underlined hold the same value - 1/8 of a championship - as the one game wild card playoff will - answering my original thought: the new playoff will be equivalent to Games Three (if the series is tied) and Four of a Division Series, Game Three (unless the series is tied) of an LCS, and a Game Four (if the series is at 3-0) of the World Series, while being just a little bit less important than Games One and Two of the LCS.

The chart's results are generally quite intuitive, but have some interest in terms of being able to quantify the differencess in importance of games, especially between rounds; an LCS game 1 or 2 being more important than a Division Series Game 4, for example, as well as the opening games of the Division Series being ten times less important than Game Seven of the World Series.

I then realised that I could apply my new found values, by multiplying a game's Championship Value by a player's Win Probability Added in that game. I call this new metric Championship Probability Added.

Here is this concept applied to this year's World Series, for four of the most prominent hitters involved in the series - Albert Pujols and David Freese for the Cardinals, Josh Hamilton and Mike Napoli for the Texas Rangers.

The chart is obviously dominated (as the Series itself was) by Freese's heroics in Game Six; his 0.969 WPA in that game was an addition of 48% to the Cards' chances of winning the World Series (27% on the 9th inning 2-out triple and 19% on the walk-off homer). He then added another 20% in Game Seven. Pujols' homers in Game Three were treated harshly by WPA, as they did not come in clutch situations.

I picked some memorable post-season games and plays, to see how CPA viewed them:

Edgar Martinez's Double - 0.32 WPA * 1/4 CV = 0.08 CPA http://www.baseball-reference.com/boxes/SEA/SEA199510080.shtml
Roy Halladay's NLDS No Hitter - 0.3 WPA * 3/32 CV = 0.03 CPA http://www.baseball-reference.com/boxes/PHI/PHI201010060.shtml
Barry Bonds can't throw out Sid Bream (value for the whole play) - 0.74 WPA * 1/2 CV = 0.37 CPA http://www.baseball-reference.com/boxes/ATL/ATL199210140.shtml
Aaron Boone's HR - 0.36 WPA * 1/2 CV = 0.18 CPA http://www.baseball-reference.com/boxes/NYA/NYA200310160.shtml
Don Larsen's Perfect Game - 0.586 WPA * 1/2 CV = 0.293 CPA http://www.baseball-reference.com/boxes/NYA/NYA195610080.shtml
Bill Mazeroski's HR - 0.37 WPA * 1 CV = 0.37 CPA http://www.baseball-reference.com/boxes/PIT/PIT196010130.shtml (Herb Smith's three run homer in the bottom of the 8th was worth 0.64 CPA, almost certainly the highest ranking play of all time)
Bill Buckner's Error - 0.4 WPA * 1/2 CV = 0.2 CPA http://www.baseball-reference.com/boxes/NYN/NYN198610250.shtml (The wild pitch before was actually worth slightly more)
Kirk Gibson's HR - 0.87 WPA * 5/16 CV = 0.27 CPA http://www.baseball-reference.com/boxes/LAN/LAN198810150.shtml
Joe Carter's HR - 0.66 WPA * 1/2 CV = 0.33 CPA http://www.baseball-reference.com/boxes/TOR/TOR199310230.shtml

This metric has the same strengths and flaws as WPA, only magnified massively; a walk in Game Seven of the World Series is worth the same as a no-hitter early in the Division Series, but it takes the WPA narrative stat idea to its logical conclusion, and I think it's interesting to be able to say that, in terms of the chances that his team would win the World Series, Kirk Gibson's legendary Game One homer was worth the same as David Freese's 2-out triple, but less than Carter and Mazeroski's walk-off homers. The stat obviously has no predictive value, as it is so heavily skewed towards situations late in the game, late in the series, and deep into the post-season, but I think that CPA is an interesting idea, and a fun bit of trivia to consider, and that the concept of Championship Value is a useful one.

---

Long time reader, first time contributor. Firstly, I'm pretty sure that all the math in the CV chart is correct, but I'm not 100%, as it is late at night, and I have a tendency to get basic arithmetic wrong. Anyway, I'm aware that both the concepts and the math in this piece are really rather simple for sabermetrics, but I thought it was an interesting idea, and I couldn't find anyone else having done something similar, which really surprised me (although I was not overly thorough in my searchings).

But, yeah, if you find this idea interesting (or, more likely, spotted something I've done wrong!) then leave a comment, and give me some feedback.

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