The way I did it before was okay, but there are a lot better ways of doing it. This is one of them.
The real way this should be done is based on performance rating, not just absolute rating. However, if you just base it on performance rating, then only one win over a 2400, and you've got a 2800 performance rating, which should win. So, therefore, you might as well have some minimum number of games played -- but that seems so artificial.
Therefore, I've developed a points system for determining top board honors that rewards (1) performance rating, (2) games played, and (3) score. It also differentiates performance ratings based on color, and whether your team won, drew, or lost the match.
Performance Ratings
Performance Ratings take into account the result of the games, whether the player's team won, drew, or lost and the color that the player had. (Performance Ratings are based on my USCL rating system.)
In regard to match and individual results, (as with the USCL rating system) if a player's game was drawn and the player's team won, the player is given 2/3 of a point. If a player's game was drawn and the player's team lost, the player is given 1/3 of a point. If a player drew and the match was drawn, the player is given 1/2 point. Wins and losses are counted as one and zero, regardless of the match outcome.
Performance ratings take into account color played as well. A win with white will give a player a performance rating of the opponents rating plus 328, while a win with black will give a player a performance rating of the opponents rating plus 472. Other outcomes are scaled similarly. This takes into account the empirical fact that having the White pieces is worth approximately 72 rating points.
Performance Rating for each game is calculated by adding the opponent's rating and the number specified.
If player had White:
Win +328
Draw (Team Won) +64
Draw (Match Drawn) -72
Draw (Team Lost) -208
Loss -472
If player had Black:
Win +472
Draw (Team Won) +208
Draw (Match Drawn) +72
Draw (Team Lost) -64
Loss -328
The Formula
Here is the actual formula to calculate the Top Board Honors Points.
TBH: Top Board Honors points
p(i): Performance Rating against opponent i
n: Number of opponents played
s(i): Score against opponent i
TBH = 0.0001 * ( SUM[i: 1..n; p(i)] * ( ( SUM[i: 1..n; s(i)] + 1) / (n + 1) ) ^2 )
Note that I added 1 to the numerator and denominator of the second term so that when you square the number it will not decrease.
Example...
Player plays in three matches.
- Match 1 - Team match is drawn. Player has White and draws opponent rated 2300 (worth 1/2 point). Performance rating is 2300-72 or 2228.
- Match 2 - Players team wins. Player has Black and draws opponent rated 2400 (worth 2/3 point, since team won). Performance rating is 2400+208 or 2608.
- Match 3 - Players team loses. Player has White and wins against opponent rating 2250 (worth 1 point). Performance rating is 2250+328 or 2578.
TBH = 0.0001 * ( (7414) * ( 3.17 / 4 ) ^2 )
TBH = 0.0001 * ( 7414 * 0.6281)
TBH = 0.0001 * 4656
TBH = 4.66
Basically, if you get a high performance rating, and play in a lot of games that you score well in, you'll have a lot of Top Board Honors points. Seems reasonable enough. It is multiplied by 1/1000 because it makes the points small enough to type.
Which Board?
Players get consideration for the board they have played the most games on. If they have played the most number of games on two or more boards, the board on which they played most recently (of those boards) will be the one for which they are eligible.
The Top Board Honors after Week 6
So, with all that, here are the Top Board Honors after week 6, with the number of TBH points they have in parentheses.
Board 1
Gold: Hikaru Nakamura (8.74), Seattle
Silver: Sergey Erenburg (8.58), Baltimore
Bronze: Jaan Ehlvest (7.09), Tennessee
Board 2
Gold: Alex Lenderman (13.96), Queens
Silver: Dean Ippolito (9.66), New Jersey
Bronze: Josh Friedel (8.47), San Francisco
Board 3
Gold: Angelo Young (9.13), Chicago
Silver: Sam Shankland (8.99), San Francisco
Bronze: Mackenzie Molner (7.18), New Jersey
Board 4
Gold: Eric Rodriguez (8.80), Miami
Silver: Marc Esserman (6.77), Boston
Bronze: Daniel Naroditsky (6.38), San Francisco
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1 comment:
Definitely a very viable system. You seem to be taking into account the most important of the factors that we do in determining the All Stars (score, performance rating, number of games).
Of course, there are certain things that your model doesn't (at least yet) consider, things like maybe making playoff games or games in the final week as counted to be more important (clutch factor) or just the fact that the circumstances your wins occurred under (i.e. due to playing well or opponents make horrible blunders, though not sure how you could reasonably model that statistic).
But given your model does include the most important factors, the main issue seems to be the weight you give to each of the factors; how much should each actually be? To be honest, I have no idea, it's not like we have a fixed way of doing All Stars ourselves either, but based on the totals you've come up with for the shown players, it definitely looks reasonable to me at this point (like your model seems to indicate that Nakamura and Erenburg are very close, but both reasonably higher than third place, something which I felt was true also, and same thing with Shankland and Young).
One thing that kind of exemplifies how our systems might differ is that I was very close to putting Friedel above Ippolito on my teams, given in large part to the circumstances around their respective games. As I decided not to despite that fact, it's not surprising that you had them in a reasonably big gap based purely on the statistics, but as I said, they were very close in my opinion (you have Esserman much closer to Naroditsky than Friedel is to Ippolito while I would definitely have that reversed).
It will be interesting to see how this compares to our end of season teams when we take into account the greater importance of the playoff performances, which as mentioned above includes a few factors that your model doesn't currently have so whether that will make a big difference or not remains to be seen.
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