Friday, October 03, 2008

Power Rankings - Sharma and Lime and Ham(ming)

Arun Sharma and I both do Power Rankings every week. I decided to do a comparison on how close they match up. I believe his are done entirely by hand, but mine are done only using mathematical formulas.

I used a variation of a Hamming Distance to calculate the similarity. Instead of binary comparisons between teams, I used the absolute value of the difference each of us gave for a ranking. For example, if he ranked Carolina 7th and I ranked it 5th, then I would use |5-7| or 2 as a component of the Hamming distance. The sum of these comparisons equals a value. The lower the value, the more similar our rankings are.

For example, let's look at week 6.

Week 6 AS BL Diff
QUE 1 1 0
SFM 2 2 0
NJK 3 3 0
DAL 4 4 0
CAR 7 5 2
MIA 6 6 0
CHI 9 7 2
SEA 5 8 3
BOS 8 9 1
ARI 10 10 0
PHI 11 11 0
BAL 13 12 1
TEN 12 13 1
NYK 14 14 0

Sum: 10

The Hamming Distance for Week 6 was 10, which means that, on average, our ranks were 10/14 or 0.71 ranks different from each other.

Here are the Hamming distances of each of the six weeks. As you might expect, the early weeks (with less data) are more different than the later weeks.

Week 1: 36 (avg diff: 2.57)
Week 2: 18 (avg diff: 1.29)
Week 3: 16 (avg diff: 1.14)
Week 4: 6 (avg diff: 0.43)
Week 5: 12 (avg diff: 0.86)
Week 6: 10 (avg diff: 0.71)

For the last five weeks (I'm discarding the first week's power rankings due to lack of data), the teams on which we have had the most different rankings have been Carolina and Seattle. Arun has consistently ranked Carolina lower than I have, by an average of 2.00 ranks. For Seattle, I have ranked Seattle lower on three weeks, and higher on two weeks, but again, we have ranked them an average of 2.00 ranks apart.

On the other hand, Arun and I have ranked New Jersey and Miami very similarly for the past five weeks. For both, there was only one week where we were different, and we were only different by one rank in that week.

If you have specific questions, please ask them in the comments.

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