Wednesday, September 27, 2006

More Similarity Scores: Rutgers and Washington

Yesterday's attempt at team similarity scores got me wondering about what the future holds for other surprise teams. I chose two of the more interesting surprise teams IMO, Rutgers and Washington. With a quick glance at Rutgers preseason schedule, most prognosticators probably had them at worst, 3-1. Still, an undefeated Scarlet Knight's squad in late September is something to take note of. Certainly few expected the Washington Huskies to have already matched their win total for the past two seasons in one month. The mathematical details for calculating the similarity scores are at the end of this post so as not to discourage you from reading further. Also, as explained yesterday, I'm only using a one-season look back. Hopefully next week I'll expand the look backs to two or three seasons to get a more representative sample. Still, I think this method has its merits.

The most similar teams to Rutgers (2006) from last season--similarity score in parentheses and final record following

1. Minnesota (856) 7-5
2. UCLA (823) 10-2
3. Florida (775.25) 9-3
4. Penn State (666.75) 11-1
5. Wisconsin (666.5) 10-3

I think these comparables are pretty good for the Knights, except for Penn State. Like Rutgers, each team, with the exception of Penn State, went to a bowl game the season before. Also like Rutgers, all of these teams, with the exception of Penn State, were good, but hardly elite BCS conference teams. With Rutgers remaining schedule, a 9 or 10 win season is certainly a possibility.

The most similar teams to Washington (2006) from last season-- similarity score in parentheses and final record following

1. South Florida (649.5) 6-6
2. Kansas (456.5) 7-5
3. Texas A&M (198.25) 5-6

The Huskies don't have nearly as strong comps primarily because their record (2-9) was so bad last season. Both South Florida and Kansas seem like good comparables. They both finished 4-7 the year prior, before breaking out and participating in a low to mid level bowl game. I'd expect the same from Washington.

Here's the methodology.

1. Start with 1000 points

2. Through 'x' number of games take the difference in winning percentage multiply by 1000 and subtract from 1000
example: Team A is 4-0 and Team B 3-1, then the difference in winning percentage would be 1-.75=.25, multiplying this by 1000=250, subtract this number from 1000

3. For every game difference in home/road inequality subtract 50 points
example: Team A has played 2 road games and 2 home games, Team B has played 3 road games and 1 home game, subtract 50 points (neutral sites count as half games)

4. Subtract the difference in point differential through 'x' number of games

5. Subtract the difference in average opponents' Sagarin Rating (I think its a pretty good measure of schedule strength)

6. Subtract the difference multiplied by 1000 in previous year's record (we need to know how good the team's were in the previous season)

7. Subtract the difference multiplied by 1000 in previous year's Pythagorean Winning Percentage (a better indicator of team strength than actual record)

8. The remaining points are the teams' similarity score (the higher the better)


Anonymous said...

I've been thinking about the formula for the similarity score and I have a couple suggestions. First off let me say that I'm not trying to slam your formula, I wouldn't be making these comments if I didn't think it was pretty cool to begin with.

1. I would drop the point differential (Item 4) from the formula. Since you're including the Pythagorean win pct, including point differential is sort of a statistical double dip, as the PWP is basically an unbiased view of the point differential. Another reason to drop it is that it's value is dominated by the other parts of the formula. Having a 100pt difference in point differentials (a significant difference) is worth the same as two extra home games (not nearly as significant).

2. The schedule strength component (Item 5) needs to be enhanced. As it stands, this item really doesn't have any appreciable impact on the formula. If you look at the Sagarin Ratings archive of conference averages, there's usually about a 10-15pt difference between the average ratings for the BCS conferences, and a difference of about 30-40 pts between the best and worst 1-A conferences. To have this make more of an impact I'd multiply it by 10-20 depending on how important you think it is.

A way to test out the prediction power of different versions of this formula would be to run the numbers for a team after 4 games, 6 games, 8 games, etc and at the end of the season, and see how the lists differ. That would also let you see how many games it takes for the lists to converge to something resembling the final lists, which would also tell you how much of the season it takes to accurately characterize a team.

matt said...

Sam, thanks for contributing. Taking your points in reverse order:

1. First let me address schedule strength. I agree I definitely need to change that aspect of the formula. Using the current Sagarin ratings, Notre Dame has played the toughest schedule thus far with an average opponent rating of 26.75. Of Division I-A teams, New Mexico State has played the weakest schedule with an average Sagarin rating of 157.67. The difference is roughly 131 points. I doubt as the season progresses and conference play starts, we'll see any more extreme differences. So, instead of multiplying the difference by 10-20, I think multiplying it by 3 or 4 would be more prudent.

2. I think point differential needs to stay. The pythagorean win pct that is included is from the previous season. Hence, I believe there needs to be a measure to take into account 'dominance' (or lack thereof) in the early part of the current season. Normally, I would like to use the pythagorean win pct again, but with a sample size of only 4 or 5 games, the pythagorean win pct is not extremely accurate. This portion of the formula will definitely come into play when I look at Arkansas in the near future (3-1, but a point differential of -13).

Its still a work in progress, and if you have any other suggestions feel free to share them.

Anonymous said...

I was mixed up on which number you were using from the Sagarin Ratings. I thought you were used the actual "Rating" score, not the team's rank. There's far more variation in the rank, so I think you're right that it doesn't need to be inflated as much. I apparently also missed that you were using the previous year's PWP and not the current year's. Still I would prefer this year's PWP over simple point differential. The way I view the PWP is as an unbiased point differential, because it takes into account the total points (mine plus my opponent's)in all the team's games. If you took the exponents off of the equation you'd end up with the ratio of the points scored to the total points. So while it doesn't directly include the point differential it's based off of the same information and is much more telling about a team's performance than point differential alone. It might not be a good predictor of future results but it is important to the similarity score because it can differentiate between a team that wins five games with an average score 10-3 and one that wins with an average score of 45-38.