Championship Leverage Update

Back in June, I wrote about Championship Leverage in the NFL. My particular interest was determining the value of a postseason game relative to that of a regular season game (and vice versa). In the original formula, I used a figure for wildcard games that was not intuitive to me. After careful consideration,1 I have tweaked the formula to change the 8.33% odds in the wildcard round to 6.25% odds. This means seasons since 1978 now have a higher weight for postseason games. Nothing else has changed yet.

Championship Leverage

Read the table below thus: In the 2017 NFL, there were 11 playoff games, 16 scheduled regular season games per team, and 32 teams. That means a generic regular season game changes a team’s odds of a title by 0.244%, and a first round playoff game is worth 25.60 times more than a regular season game (in this case, that’s the wildcard game. Relative to a regular season game, the divisional round is worth 51.20, the championship round is worth 102.40, and the championship is worth 204.80.

LYPGsLGsTeamsRSG WgtR1WgtWCDRCCCHP
AAFC194611481.339%37.3337.33
AAFC194711481.339%37.3337.33
AAFC194821481.116%22.4022.4044.80
AAFC194931271.020%24.5024.5049.00
AFL196011481.339%37.3337.33
AFL196111481.339%37.3337.33
AFL196211481.339%37.3337.33
AFL196321481.116%22.4022.4044.80
AFL196411481.339%37.3337.33
AFL196511481.339%37.3337.33
AFL196611490.838%29.8429.8459.68
AFL196711490.838%29.8429.8459.68
AFL1968214100.643%19.4419.4438.8977.78
AFL1969414100.500%25.0025.0050.00100.00
NFL193611291.440%34.7134.71
NFL1937111101.455%34.3834.38
NFL1938111101.455%34.3834.38
NFL1939111101.455%34.3834.38
NFL1940111101.455%34.3834.38
NFL1941211101.273%19.6419.6439.29
NFL1942111101.455%34.3834.38
NFL194321081.563%16.0016.0032.00
NFL1944110101.600%31.2531.25
NFL1945110101.600%31.2531.25
NFL1946111101.455%34.3834.38
NFL1947212101.167%21.4321.4342.86
NFL1948112101.333%37.5037.50
NFL1949112101.333%37.5037.50
NFL1950312130.888%28.1728.1756.33
NFL1951112121.157%43.2043.20
NFL1952212121.042%24.0024.0048.00
NFL1953112121.157%43.2043.20
NFL1954112121.157%43.2043.20
NFL1955112121.157%43.2043.20
NFL1956112121.157%43.2043.20
NFL1957212121.042%24.0024.0048.00
NFL1958212121.042%24.0024.0048.00
NFL1959112121.157%43.2043.20
NFL1960112131.085%46.0946.09
NFL1961114140.875%57.1757.17
NFL1962114140.875%57.1757.17
NFL1963114140.875%57.1757.17
NFL1964114140.875%57.1757.17
NFL1965214140.802%31.1831.1862.36
NFL1966214150.587%42.5742.5785.14
NFL1967414160.446%28.0028.0056.00112.00
NFL1968414160.446%28.0028.0056.00112.00
NFL1969414160.446%28.0028.0056.00112.00
NFL1970714260.380%32.8632.8665.72131.44
NFL1971714260.380%32.8632.8665.72131.44
NFL1972714260.380%32.8632.8665.72131.44
NFL1973714260.380%32.8632.8665.72131.44
NFL1974714260.380%32.8632.8665.72131.44
NFL1975714260.380%32.8632.8665.72131.44
NFL1976714280.364%34.3034.3068.60137.20
NFL1977714280.364%34.3034.3068.60137.20
NFL1978916280.260%24.0024.0048.0096.00192.00
NFL1979916280.260%24.0024.0048.0096.00192.00
NFL1980916280.260%24.0024.0048.0096.00192.00
NFL1981916280.260%24.0024.0048.0096.00192.00
NFL1982159280.340%18.3818.3836.7573.50147.00
NFL1983916280.260%24.0024.0048.0096.00192.00
NFL1984916280.260%24.0024.0048.0096.00192.00
NFL1985916280.260%24.0024.0048.0096.00192.00
NFL1986916280.260%24.0024.0048.0096.00192.00
NFL1987915280.278%22.5022.5045.0090.00180.00
NFL1988916280.260%24.0024.0048.0096.00192.00
NFL1989916280.260%24.0024.0048.0096.00192.00
NFL19901116280.255%24.5024.5049.0098.00196.00
NFL19911116280.255%24.5024.5049.0098.00196.00
NFL19921116280.255%24.5024.5049.0098.00196.00
NFL19931116280.255%24.5024.5049.0098.00196.00
NFL19941116280.255%24.5024.5049.0098.00196.00
NFL19951116300.250%25.0025.0050.00100.00200.00
NFL19961116300.250%25.0025.0050.00100.00200.00
NFL19971116300.250%25.0025.0050.00100.00200.00
NFL19981116300.250%25.0025.0050.00100.00200.00
NFL19991116310.247%25.2925.2950.58101.16202.32
NFL20001116310.247%25.2925.2950.58101.16202.32
NFL20011116310.247%25.2925.2950.58101.16202.32
NFL20021116320.244%25.6025.6051.20102.40204.80
NFL20031116320.244%25.6025.6051.20102.40204.80
NFL20041116320.244%25.6025.6051.20102.40204.80
NFL20051116320.244%25.6025.6051.20102.40204.80
NFL20061116320.244%25.6025.6051.20102.40204.80
NFL20071116320.244%25.6025.6051.20102.40204.80
NFL20081116320.244%25.6025.6051.20102.40204.80
NFL20091116320.244%25.6025.6051.20102.40204.80
NFL20101116320.244%25.6025.6051.20102.40204.80
NFL20111116320.244%25.6025.6051.20102.40204.80
NFL20121116320.244%25.6025.6051.20102.40204.80
NFL20131116320.244%25.6025.6051.20102.40204.80
NFL20141116320.244%25.6025.6051.20102.40204.80
NFL20151116320.244%25.6025.6051.20102.40204.80
NFL20161116320.244%25.6025.6051.20102.40204.80
NFL20171116320.244%25.6025.6051.20102.40204.80

Notice that I have not made any changes to either the NFL or the AFL from 1966 through 1969, despite the fact that I bemoaned that I believe those years to be an issue. I have two solutions for the problem, but I did not update the table with the findings. This is because the problem has more to do with the intended future use of this information than it does with the math used to determine the Championship Leverage figures. Here is the problem in a nutshell: There are two separate leagues, but those leagues play the same championship game. The weight of a an AFL playoff game in 1966 is lower – relative to a regular season game – than the weight of an NFL playoff game. That’s fine, mathematically, but it presents a problem if we want to use these numbers the way Neil Paine did in his terrific Quarterback Pantheon article. It means that Len Dawson would receive a 59.68 multiplier for Super Bowl I, while rival Bart Starr would receive an 85.14 multiplier for the same game.

An easy solution is to find a happy medium between the scores of the two leagues. For instance, you could multiply each league’s figure by the numbers of games they play in a season and then divide the sum of the products by the sum of games both leagues combined to play. Continuing the 1966 example, we’d multiply 59.68 by 126 (7520.21), and we’d multiply 85.14 by 210 (17878.38). Then we’d add those (25398.59) and divide the sum by 336 (126 games plus 210 games) to arrive at a combined-league value of 75.59. That’s 15.91 points higher than the original AFL value and 9.54 points lower then the original NFL value. Do this for each of the four trouble seasons, and we get values of 75.59, 93.17, 98.84, and 107.38. We would then work backwards to determine the values of earlier playoff rounds.

A slightly more complicated alternative was presented to me on Twitter from Moo12152. I’ll let you read his idea rather than rewriting the whole thing. Using Moo’s methodology, we get the following combined-league values for the 1966-69 Super Bowls: 106.10, 124.73, 130.36, and 136.77. This means Super Bowl IV is worth more, relative to a regular season game in either league, than any other Super Bowl until the 1976 season. Mathematically, there is no issue here. Philosophically, I think most would agree that we wouldn’t want to award players more for Super Bowl IV than for Super Bowl V or other Super Bowls till XI. And this is where the real issue lies: the notion to use these numbers for something they weren’t intended to be used for, and the intuition that tells you the numbers aren’t right because they don’t fit your perceptions (because you may be using them inappropriately).

Remember, please, that Championship Leverage is simply a measure of the relative values of playoff and regular season games, as they pertain to winning a championship. The figures are not intended to be a metric for league strength or ease of domination,2 and it may be a mistake to use them in a manner other than their specific purpose. Using these values as bonus for production, as Neil did in his article, is likely not the proper way to use this information when measuring the statistical profile of a player’s career (even if it is entertaining). That said, I’m absolutely going to do just that, and probably soon. Stay tuned.

 

  1. And after discussing it with many intelligent humans.
  2. When I apply my league strength modifiers to Championship Leverage values, the pre-merger Super Bowls decrease in value relative to post-merger Super Bowls, but that’s a story for another day.