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OPERA
**Q:**What is this tiebreaker and why does it have a silly name?
A: Opposition PEformance Rating Average was the best name I could come up with. Sorry about that. It is the average performance rating of your opponent. Performance Rating being their new recalculated Rating after processing the tournament results.
Performance Rating is most commonly seen as the exit rating after processing your tournament results. However we take the second derivative of that. That is we calculate everyone's exit rating, replace the entry ratings with the exit ratings, and recalculate again.
Q: What good is it?
A: This is essentially trying to do what SOS does, but with opponent rating instead of MMS. Four wins out of five against a 2000 opposition can be considered as better than as against a 1999 opposition. Not much better of course, but enough to break a tie. Note we don't do decimal points. That is were we draw the line of accuracy.
Q: Does it have any weaknesses?
A: Yes. Of course it does. Rating is the result of past performance, and we can thus bias the final standings according to that past performance. To reduce that effect we use the second derivative.
The European Go Rating system was developed back in 1996, over the years it has seen a few minor tweaks, but never any major changes. Mostly people have messed about with the Tournament Rating Classes and altered the anti-inflation parameter (inf) It is based on the Elo system, but it takes into account handicap stones.
The key formula, which are documented at http://europeangodatabase.eu/EGD/EGF_rating_system.php
The winning expectancy(X) of the lower rated player(A) is X(A) = 1 / [e^(D/A) + 1] - inf/2
The winning expectancy of the higher rated player(B) is X(A) + X(B) = 1 - inf
difference of opponents ratings D=Rating(B)-Rating(A)
Rating Change = CON * [ Result - X(?)]
A and CON are rating dependent variables which are documented in tables on the linked EGD page.
It should not be a matter for dispute if we decide to drop the anti-inflation parameter from the formula we use. We are computing an immediate performance, not looking at long term system behaviour. This also saves us a few lines of code. The other 2 changes which we make are clearly disputable.
My examination of the winning percentages from the EGD suggested to me that they were completely out of kilter with the expected values. In short, the 20% value around 2700 seemed to hold up, but by the time we reached 2000 we had hit 40% and around 100 we dropped back down to 20%. Since the ratings around 100 suffer from the 30-kyu reflection problem, I didn't worry too much about the latter. However, the 2000 value did concern me. Therefore I took the decision to re-align A. I decided to create a plateau of 40% around 1900, and descend linearly down to 20% at 2700.
Having changed A I decided there was nothing wrong with changing CON as well. I therefore effectively reduced it by about 50% at higher ratings, though it converges to the original value around 2700. This is effectively reducing the volatility of the rating.The reason for this is because we compute a second derivative. My research showed that correlation of MMS and Entry Rating is lower than correlation of MMS and Exit Rating. Therefore I couldn't conceive that the accuracy of the tiebreaker could be significantly harmed if we reduced the volatility, because we were using a second derivative, and that should still bring us with a reasonable correlation.
Between the limits of 200 and 70, A is equal to 200 + ((1900 - Rating(X)) * 0.1625);
After playing around with a few plots, I set CON as 10 + SQRT( INV*INV + INV ) where INV is 2700 - Rating / 100
The rest is as discussed above.