True Player Value: Finding Team Values

[EDITORS NOTE: This is a classic post]

We have mentioned that during the off-season, we will try to calculate true player value based upon individual performances against different teams. So I will (attempt to) define it now.

Basically, True Player Value attempts to answer the question "how do you compare player performances when players are going against different defenses?"

For example, in 2008, the Miami Dolphins defense gave up 42% more rushing yards than the average defense. That means that running for 100 yards against the Dolphins was equivalent to running for about 70 yards against a league-average run defense, such as the Colts. So we need to adjust the performance of a player that faced the Dolphins twice last season downwards for those two games, while a player that had to face the Vikings (38% better than league average) run defense twice should be adjusted upwards. This will give a us better idea of how good the players' seasons really were, beyond just looking at the final numbers.

There are 4 basic categories that we want to rate each defense in for fantasy football evaluation purposes: 1) Rushing Yards Against, 2) Rushing TDs Against, 3) Passing Yards Against, 4) Passing TDs Against.

Now, we start to get into a chicken-and-the-egg thing. When a defense gives up a lot of passing TDs to a team like the Patriots, shouldn't those TDs not count against the defense as much as if the TDs had been against the Vikings' passing attack? Of course. So before we can rate the defenses, we have to rate the offenses. But before we rate the offenses, we have to rate the defenses that THEY play. This seems to never end.

But there is a solution. For example, think about the New England Patriots passing TDs. Assume that in each game, they scored TD1, TD2, TD3, TD4, ... TD16 passing touchdowns. To get the number of touchdowns that they would have scored against a league average defense, divide the number of TDs scored each week by that week's opponents defensive rating for allowing TDs. This will be denoted NYJrate for the Jets in the equation below. This rating will be 1.00 for a defense that allows the league-average number of passing TDs, 0.50 for a team that allows half the league-average number of passing TDs, and 2.00 for a team that allows twice the league-average number of passing TDs.

So the equation for the Patriots looks like this:

Patriots True Passing TDs = TD1/NYJrate + TD2/SDrate + TD3/BUFrate + TD4/CINrate + TD5/CLErate + TD6/DALrate + TD7/MIArate + TD8/WASrate + TD9/INDrate + TD10/BUFrate + TD11/PHIrate + TD12/BALrate + TD13/PITrate + TD14/NYJrate + TD15/MIArate + TD16/NYGrate.

So now we have 1 equation with 13 unknowns, which is really no good. But to find the Jets defense rate, we just look at their performance against each offense. So for the Jets defense, we set up an almost identical equation to the one above, but instead of looking at opposing defensive ratings, we are looking at opposing offensive ratings. So in games 1 and 13 of the Jets defense ratings, we have a factor for the Patriots offense rating, which is what is calculated in the equation above.

This gives us another equation, with 12 more unknowns (only the Patriots offense is not a new unknown). But, if we create the equation for each team's offense and defense, we find that we get 64 equations (1 for each teams offense and defense) with 64 unknowns. This can be solved with a complex matrix.

So the next several weeks, I will be trying to plug all the numbers from this season into a big program that will calculate these four defensive ratings for each team in the league. I will publish the results as soon as they are available.

[EDITORS NOTE: The database and program are complete]