Monday, January 03, 2011

Crude NFL Ratings

I feel bad about starting 2011 with a post about the third-best professional sport, but the material is time-sensitive. I came up with a crude rating system for baseball teams last year, and it is equally applicable to teams from other sports. So I've been tracking NFL ratings throughout the season, and since the playoffs are about to start I figured that I would share them here.

(*) "came up" is a big stretch, actually, since while I'm not aware of anyone doing it in exactly the manner I did, that's mostly because the way I did it is not the best way to do it and because a lot of similarly-designed systems have worked with point differentials rather than estimated win ratios. "Implemented" would be a more appropriate and honest description.

I do not have a full write-up ready for the system yet; it's actually fairly simple (part of the reason why I'm only confident describing the results as "crude"), but I am going to do a full explanation that tries to express every thing in incomprehensible math formulas rather than words. It's backwards to post results before methodology, but results of an NFL ranking system aren't very interesting after the season unless you are a huge NFL fan, and I am not.

The gist of the system is that you start by calculating each team's estimated win ratio, based on points/points allowed ratio (I used this formula from Zach Fein for the NFL). Then, you figure the average win ratio of their opponents and the average win ratio for all 32 teams in the NFL. To adjust for strength of schedule, you take (team's win ratio)*(opponents' win ratio)/(average win ratio). Now you have a new set of ratings for each team, and so you repeat the process, and you keep repeating until the values stabilize.

At that point, I take each team's adjusted win ratio/average win ratio and multiply by 100. This is the Crude Team Rating. Similarly, I figure the strength of schedule for each team. The nice thing about these ratings is that they are Log5-ready. If a team with a rating of 140 plays a team with a rating of 80 on a neutral field, they can be expected to win 140/(140 + 80) = 63.6% of the time.

Since the system is crude, there are a number of things it doesn't account for: the field on which the game is actually played, the effect that a team has on its opponents' estimated win ratio (losing 31-7 reduces your expected win ratio, but it also makes your opponent look like a stronger team), any changes in team composition due to injuries and the like, regression, and this is by no means a comprehensive list.

The ratings are based solely on aggregate points and points allowed. Even if you restrict the inputs to aggregate season data, there are a number of possible other inputs that you could use--actual win/loss record, predicted win loss record based on total yards, turnovers, and other inputs (akin to using Runs Created rather than actual runs scored for a baseball rating), or some combination thereof. I have not done that here (I'm not sufficiently motivated when it comes to NFL ratings, and I will offer a set of ratings based only on W/L with a slight adjustment), but have done some of that for MLB ratings.

To account for home field in making game predictions, I've assumed that the home field advantage is a flat multiplier to win ratio. Since the average NFL home-field record is a round .570 (a 1.326 win ratio), the expected win ratio of the matchup is multiplied by 1.326 (or divided if it is the road team). For example, in the 140 v. 80 matchup, the expected win ratio is 140/80 = 1.75. If the 140 team is at home, this becomes 140/80*1.326 = 2.321, and if they are on the road it becomes 140/80/1.326 = 1.320. So the expected winning percentage for the 140 team is 1.75/2.75 = 63.6% on a neutral field, 2.321/3.321 = 69.9% on their home field, and 1.320/2.320 = 56.9% on the opponents' field.

In this table with the 2010 rankings, aW% is the estimated "true" winning percentage for the team against a league-average schedule; "SOS" is strength of schedule; and "s rk" is the team's SOS rank.

The next chart gives ratings for each division, which is simply the average CTR of the four teams that comprise the division:

The NFC West was truly a dreadful division, with an average CTR of just 29. If you treat the division ratings as team ratings, that implies that the W% for a NFC West team against an average NFL team should have been 22.5%. The NFC West teams combined for an actual record of 25-39, which is 13-27 (32.5%) when you remove intra-divisional games. Of course, thanks to the unbalanced schedule, their average opponent is not an average NFL team.

With the playoff picture now being locked in, one can use the ratings to estimate the probability of the various playoff outcomes. I offer these as very crude probabilities based on crude ratings, and as nothing more serious. For these playoff probabilities, I assumed that each team's effective winning percentage should be 3/4 of its actual rating plus 1/4 of .500, and converted this to a win ratio. I have no idea if this is a proper amount of regression or not; I would guess it's probably not aggressive enough in drawing teams towards the center, but I really don't know. The key word is "crude", remember. That results in the following rankings for the playoff teams (this won't change the order in which they rank from the original CTR, but it will reduce the magnitude of the differences):

This chart illustrates why I don't like the NFL playoff seeding system, although this year is worse than most. In both conferences, the wildcard teams are estimated to be better than the lesser two division winners. In the case of Seattle this is completely uncontroversial, but Indianapolis was not a particularly impressive team and Kansas City played the estimated weakest schedule in the NFL. When your divisions are as small as four teams, a crazy year like this is bound to happen eventually. At the very least, I would suggest that the NFL allow wildcard teams to host playoff games if they have a better record than the division winner they are slated to play. When an 11-5 team like the Saints to have to go on the road to play the 7-9 Seahawks, I suggest that your playoff structure is too deferential to your micro-divisions.

With those ratings, we can walk through each weekend of the playoffs. P(H) is the probability that the home team wins; P(A) is the probability that the away team wins. For later rounds, P is the probability that the matchup occurs (except for the divisional round, in which case P is the probability that the designated set of two matchups occurs):

According to the ratings, the road teams should be favored in each game this weekend. They suggest there's about a 16% chance that they all win, but only a 2% chance that all of the home team wins.

It's necessary to look at the possible division matchups together by conference thanks to reseeding. The most likely scenarios result in teams from just four of the eight divisions making it to the round of eight, with the AFC featuring divisional rematches (allowing the "Divisional" round to truly live up to its name) but a inter-divisional matchup in the NFC.

Once you get to the championship game level there are so many possibilities that there isn't much to say, so I'll move right on to the Super Bowl:

There are two potential Super Bowl matchups that come out at .1%; the least likely is considered to be Kansas City/Seattle (.013%, or about 7700-1).

Combining those tables, one can look at the advancement odds for each team:

Again, I need to issue the standard disclaimer--these are very crude odds based on a crude rating system.

Finally, here are ratings based on the actual W-L record rather than points/points allowed. I did cheat and add a half a win and half a loss to each team; as the Patriots and Lions have shown us in recent years, 16-0 and 0-16 are not impossible in the NFL, and either would break a ratio-based ranking system: