The Interface

If you're looking at this page, you probably would be more interested in the-

Web Interface to the Rating System

But here's the lowdown on how that works.

Recent Notes

October 27, 2006

I've updated htis to include 2005 VA events and 2006 VA and NAC events, so far.

Since I last worked on this thing, the classification chart has changed, and there's a lot of confusion between what used to be an A8 and is now an A4, the new A4 which didn't used to exist, etc. I expect you will get the best results by not messing around with the classification part of this thing.

I have noticed that there are some flaws in my theory. E.g., the strength of the event reflects how hard it is to finish last in the event. So just entering a "strong" event and finishing last automatically makes you a strong fencer? No way. So I have to go back to the drawing board to solve the erronious strengths given to some fencers. It will take quite a bit of math, and then quite a bit more programming on my part, so don't hold your breath!

Rating Fencers and Tournaments

The USFA has a system for classifying fencers and tournaments:

For fencers it is a letter from A-E, followed by a number representing the year in which that rating was "earned". E.g., A2000 means an A earned in 2000. This is most often shortened to 1 or two digits, i.e., A0 or A00. After 4 years a rating goes down one letter and the number is reset.

For tournaments, it's the letter representing the highest rating a fencer can "earn" followed by the number of places to which that rating goes. E.g., A4 means the top 4 finishers earn an A.

The document specifying classifications for various tournaments is here.

Jeff's Idea

I've got this idea to classify fencers by the number of elimination bouts they tend to win, and assign values to tournaments indicating how hard they effectively are.

The Basic Math

If a fencer wins a tournament that has 16 people, he has won 4 DE bouts. If a fencer wins a tournament that has n people, he has effectively won log2(n) DE bouts. If a fencer finishes pth place, he has effectively won log2(n/p) DE bouts. If the tournament has a difficulty rating of r, then the fencer has effectively won log2(n/p)+r DE bouts.

How It's Done

wab is used to represent log2(n/p) for fencer a in tournament b.   fa is the strength of the fencer.   rb is the difficulty rating of the tournament.

The fencer's rating is the average of wab+rb for all the tournaments that fencer entered. A tournament's difficulty rating is the average of fa-wab for all fencers in it. In a perfect world, wab=fa-rb would be true for all fencers in all tournaments. But this isn't the case, so we have to compute an average based on lots of results.

To compute all the averages at once, we put all the wab for all fencers and tournaments in a big array just the right way, and do Gaussian elimination on it to come up with the answer. I'll expand on this some other day. Suffice it to say that all the averages work out for each fencer and for each tournament.

The Results

Look at the web interface to the rating system for some data.

To estimate how many DEs a fencer would win at a given tournament, take his strength and subtract the strength of the tournament from it. Use the standard deviation values to denote a range of DEs he might have won.

Conclusion

You want me to tell you what to think? Just look at the data and see if you feel they correspond to reality or not. Are the fencers and tournaments listed approximately strongest to weakest? Bear in mind I'm doing this for my own entertainment, not to educate every member of the web browsing public bored enough to make it to the bottom of this page.


snider.com/jeff