As per my proposed ranking system, England should fall to 4th position, but I do not think that would fairly reflect last night's bout at all! England still, in my opinion, belong in 3rd, and above Australia. How should we adjust the ranking system? Any ideas?
Bout scores:
| Team | Pts | LJ | PJ | |
|---|---|---|---|---|
| 3 | England | 70 | 7 | 4 |
| 1 | USA | 296 | 32 | 5 |
Your fundamental problem is that basically all of your post-World Cup bouts are against Team USA. Other than Team England just now, no-one has managed a better than 1:10 scoring ratio against Team USA, and mostly in power jams. This means that these scores are very sensitive to randomness in the bout, compared to the majority of bouts where the teams are more balanced in skill. As a result, I'm really not sure how useful they are as ranking bouts.
ReplyDelete(It would be nonsensical to push Team England lower as a result of this bout - their performance, both in "score difference" and "score ratio", was better than that of the 2nd place team, Team Canada, in their last bout against Team USA. Any ranking system shouldn't result in a "good" loss against a superior team pushing you below teams who lost worse against the same team.)
Yeah, right now everything's within the margin of error, especially with Team USA. Perhaps a results-based rankings system is a long-term goal.
DeleteHonestly, England may have earned the #2 spot as a result of last night. I think you've just made the argument for such a ranking.
There's a lot of ways to use results based ranking. Since I believe you're mathematically inclined, you might find this paper: https://umdrive.memphis.edu/ccrousse/public/MATH%207375/PERRON.pdf
Deleteinteresting. The "score based" ranking scheme seems somewhat suited to the ladder you want to build (although it ignores errors, of course).
Similarly (to spam you with links!) http://ccrg.rit.edu/~whelan/talks/whelan20101008.pdf seems to hint at the way to apply a Bayesian estimator to the same ranking mechanism, to provide error estimates as well. This is especially important when the data is as sparse as ours is presently...
DeleteUmm, legend? I'll read all of these, and if you have more, bring 'em on!
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