## The Manning Index Revisited

Last year in this space, I observed that Peyton Manning’s teams had won exactly as many playoff games as they had been the higher seed in. This fact, to my mind, ran contrary to the popular wisdom that Manning is a choker. So I came up with something I called the Manning Index, which essentially measures how many playoff games a quarterback has won compared to how many he “should have” won. Click the link above for more discussion; I won’t re-hash much of it here, but I will give a quick summary of the specifics.

Based on a logit regression of all playoff games during the past 30 years, I arrived at this formula for determining the probability of a given team winning a given playoff game:

Probability of winning = (1 + exp(-.43(windiff)-.24(homefield)))^(-1)

where windiff is the team’s wins minus the opponent’s wins and homefield is 1 if it’s a home game, -1 if it’s a road game, and 0 if it’s at a neutral site (i.e. a Super Bowl). For an example, let’s look at the Steelers’ and Seahawks’ 2005 playoff runs:

```                                           prob of
Game                  windiff   homefield  winning
--------------------------------------------------
Steelers vs. Bengals      0        -1        44.1%
Steelers vs. Colts       -3        -1        18.1%
Steelers vs. Broncos     -2        -1        25.3%
Seahawks vs. Redskins    +3        +1        81.9%
Seahawks vs. Panthers    +2        +1        74.7%
```

Roethlisberger’s team won three games this postseason, when it should have been expected to win only about .88 games, so I’ll give Big Ben credit for 3 – .88 = 2.12 wins worth of clutchness. As I said last year, I think that awarding wins to quarterbacks is a suspect practice, but people are going to do it anyway. My only goal here is to put a quarterback’s postseason win-loss record into the proper perspective.

The main point of this post is to refresh the rankings with another year’s worth of data now in the books. So here they are. Some discussion follows.

```                      Expected  Actual  Marginal
Quarterback            record   record    wins
------------------------------------------------
Tom Brady               6- 5    10- 1     +4.4
Trent Dilfer            3- 3     5- 1     +2.2
Jake Delhomme           3- 4     5- 2     +2.3
Ben Roethlisberger      2- 3     4- 1     +1.6
Jeff Hostetler          2- 2     4- 1     +1.5
Mark Rypien             3- 5     5- 3     +1.6
Wade Wilson             2- 4     3- 3     +1.3
Joe Montana            14- 9    16- 7     +2.3
Troy Aikman             9- 7    11- 5     +1.8
John Elway             12-10    14- 8     +1.8
Jay Schroeder           2- 3     3- 2     +0.6
Drew Bledsoe            3- 4     4- 3     +0.7
Doug Williams           3- 4     4- 3     +0.6
Phil Simms              5- 5     6- 4     +0.6
Jim Everett             2- 3     2- 3     +0.4
Brad Johnson            3- 4     4- 3     +0.5
Brett Favre            10-10    11- 9     +0.8
Mark Brunell            4- 6     4- 6     +0.5
Jim Harbaugh            2- 3     2- 3     +0.3
Steve McNair            5- 4     5- 4     +0.4
Kurt Warner             5- 2     5- 2     +0.1
Rich Gannon             4- 4     4- 4     +0.1
Stan Humphries          3- 3     3- 3     +0.0
Donovan McNabb          7- 5     7- 5     +0.0
Jim Kelly               9- 7     9- 7     -0.3
Dave Krieg              3- 6     3- 6     -0.4
Kerry Collins           3- 3     3- 3     -0.3
Vinny Testaverde        2- 3     2- 3     -0.4
Bernie Kosar            3- 4     3- 4     -0.5
Jake Plummer            2- 4     2- 4     -0.5
Mike Tomczak            4- 2     3- 3     -0.6
Steve Young             9- 5     8- 6     -1.1
Dan Marino              9- 9     8-10     -1.4
Randall Cunningham      4- 6     3- 7     -1.2
Kordell Stewart         3- 2     2- 3     -1.0
Peyton Manning          5- 4     3- 6     -1.6
Jim McMahon             4- 2     3- 3     -1.2
Warren Moon             5- 5     3- 7     -1.9
```

First note that the records are all rounded to the nearest integer — records just don’t look right if they’re not integers — but the Marginal Wins column is not rounded (well, less rounded). Also, note that the list is sorted not by the Marginal Wins column, but by an approximation of the probability that an average quarterback would achieve the given record or a better one by sheer chance. For example, Joe Montana is +2.3 wins and Jeff Hostetler is +1.5, but Hoss rates higher than Joe because it’s less likely that random chance would produce a 4-1 record in the games Hostetler played in than that it would produce a 16-7 record in the games Montana played in. Incidentally, only one of the 38 guys on the list appears to be significantly better than chance, and none are significantly worse than chance. Make of that what you will.

Bonus fun fact I uncovered while running these numbers: according to the formula given at the top of this post, this season’s Steeler team is the most improbable Super Bowl team in history. Their estimated win probabilities were .441, .181, and .253, which means that their probability of winning all three (making all the usual incorrect assumptions about independence) was about .02, which is the lowest figure of any team to ever make a Super Bowl. Now that’s not too surprising, since they played three games and most Super Bowl teams only play two. But if you throw out the Cincinnati game, their probability would be .045, which would still be the lowest in history.

Most Improbable Super Bowl Teams

```Team    Probability
-------------------
pit 2005    2.0
nwe 1985    5.1
dal 1975    5.3
car 2003    7.6
ram 1979    8.6
bal 2000    9.9
oak 1980   10.9
ten 1999   11.2
sfo 1988   11.5
den 1997   12.3
buf 1992   12.8
```

### One Response “The Manning Index Revisited”

1. Vince says:

I didn’t see Michael Vick on that list, so I calculated it myself. If I’ve done it right, he should have been expected to win about 1 1/2 playoff games, and he’s actually won two. So his rating comes out to +0.5, which looks unremarkable until you realize he’s right there with Brad Johnson, Phil Simms and Doug Williams, Super Bowl winners all.