Monday, September 03, 2007

A Matter of Semantics and Mathematics

I noted with great interest the US Chess League "Power Rankings" posted by OrangeKing and Arun Sharma. In both cases, the authors note that their rankings are somewhat (or largely) subjective and reflect their personal opinions alone. As OrangeKing (OK) notes:
These rankings are based on nothing other than my own (mostly worthless) opinions, which are in turn based on about 5 minutes of thinking about the order these teams should be in. The idea is to mix current form with overall expectations, then rank the teams - this is why the rankings are not solely based on records or recent results.
As for Sharma (AS), he is quite clear about the fact that his "feelings" are a primary driver of his rankings:
This year I shall be doing "Power Rankings" for all the teams each week to see how strong I feel each team is week in and week out. The primary criteria for this will of course be a team's record, and the other criteria will be a team's upcoming chances in potential matches, any internal problems they might be having, and several small intangibles of the type that I talked about in my preseason article.
The two different rankings share some similarities, but they depart noticeably from each other for three teams:
  • New York (OK-3, AS-5)
  • Seattle (OK-5, AS-9)
  • Dallas (OK-6, AS-3)
A Matter of Semantics

While I find these rankings to be interesting and useful, and while I have no problem whatsoever with the subjective methodologies on which they are based, I nevertheless believe it is a bit of a misnomer to refer to them as "Power Rankings." In general usage in other sports, "Power Rankings" originally referred to rankings developed largely through quantitative, not qualitative, methodologies. Instead, OrangeKing's and Sharma's rankings seem to me to have more in common with Sportswriters' or Coaches' polls in, say, College Football -- albeit, in these cases, polls of one.

Now before everyone starts commenting about how this sportswriter or that one produces qualitative power rankings in this sport or that, I'm happy to concede that the definition of "Power Rankings" has probably become muddled over time. So enough about semantics; if they want to call them "Power Rankings, then "Power Rankings" they'll be.

A Matter of Mathematics

I am still left with the notion that the USCL could benefit from a set of "Power Rankings" which are quantitatively based -- no more "feelings" about how a team was better or worse than their actual performance, instead something more consistent with Bill Parcell's "we are what we are" concept. Therefore, I would now like to introduce the US Chess League Quantitative Power Rankings.

These rankings are based on a proprietary methodology for which the Boylston Chess Foundation has recently made application to the US Patent Office. Nevertheless, here is an outline of the key elements of the approach:
  • The rankings are based on five variables -- Match Record, Games Score, Games Score w/ Black, Team Performance Rating (based on USCL ratings), Current Match Records of all Opponents played to date.

  • Each variable is scaled such that the team with the highest value receives 1.000, the team with the lowest value receives 0.000, and the teams in between are scaled proportionally to these top and bottom values.

  • The scaled variables are then weighted with higher weighting going to Match Record and Games Score, and lower weighting to Opponents' Match Records.
Here are the results after Week 1:
  1. San Francisco (1.0, .875) - The Mechanics come out ahead of the other 3-1 winners because they went 2-0 with the black pieces.

  2. Baltimore (1.0, .825) - The Kingfishers had the highest performance rating of any team.

  3. Dallas (1.0, .795)

  4. Boston (1.0, .728) - The Blitz edged out the Inventors due to a slightly better performance rating.

  5. Philadelphia (1.0, .711)

  6. Queens (0.5, .476) - The Pioneers come out ahead of the Knockouts since they entered last week's head-to-head matchup with a lower rated team.

  7. New Jersey (0.5, .465)

  8. Miami (0.0, .250)

  9. Seattle (0.0, .242)

  10. Carolina (0.0, .189) - Although the Cobras have a slightly lower performance rating than the Tempo, 2182 vs. 2194, the fact that their win came with the black pieces gives them the edge.

  11. Tennessee (0.0, .118)

  12. New York (0.0, .100) - I realize this is a shocking result; but if a team has the lowest Match Record, lowest games won, no points with Black, and the lowest performance rating in the league, where else can they end up?
Obviously New York's ranking is quite different from those in the subjective rankings, and I'd be very surprised if they don't move up substantially as the season progresses. Excluding the Knights, you'll notice a certain level of congruity between these quantitative rankings and those of Arun Sharma (less so with OrangeKing). For example, the top 4 teams are the same in each, though ranked in a different order. Of course, a quantitative ranking based on just one week of data can't be taken too seriously. So let's wait and see how the US Chess League Quantitative Power Rankings develop as the season moves ahead.
The lineups are out for this week's match between Boston and the Queens Pioneers. SM Jorge Sammour-Hasbun will be making his USCL debut for the Blitz on Board 2 and Ilya Krasik will be anchoring the team for the first time this season. Fans can also look forward to another GM vs. GM clash up top.

Here are the matchups (Boston has White on Boards 1 & 3):

Disclaimer: BCC Weblog provides independent coverage of the United States Chess League. It is not affiliated with the USCL or the Boston Blitz.

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