MAKING YOUR GRANDMASTER NORM.

It's possible for a team in a sub-major conference to go undefeated in its regular season and be a bubble team. That's what Wisconsin-Green Bay's Kevin Borseth is dealing with.

"We had to go through the same thing they did — losing in the tournament a couple of times — and then we won a couple of games and go to the regionals and beat a couple of teams we shouldn't have," [Connecticut's Geno] Auriemma said after his team pulled away for a 94-70 victory over UWGB. "Then everybody's looking at us and saying, 'These guys are good. Let's give 'em a higher seed from now on.'"

It's called dues-paying, apparently, and Green Bay have gone from winning the Mid-Continent tournament and earning an automatic bid as a #14, having to deal with a Stanford in the first round, to earning an automatic bid as #8 or #9, and a crack at Connecticut in the second round.

[Borseth's] frustration over having to play a top-seeded team such as Connecticut in the second round was evident. He had perhaps the best team he's assembled in his 20 years as a head coach. It went into the UConn game ranked 21st in the Associated Press poll and with the nation's longest winning streak at 26 games. He went 3-0 against teams from the Big Ten, yet because the Horizon League is so bad, UWGB's RPI dropped all season, costing it valuable seeding positions.

The problem he faces is one in which there are 64 positions to fill in a tournament, although it appears paradoxical that a team can win games and yet lose positions. In chess, the worst thing that could happen is that his rating would stay unchanged. Consider the re-rating formula,

R_n = R_o + k(W-W^e),

where R_n = new rating,
R_o = old rating,
W = observed wins,
W^e = expected number of wins, and
k = coefficient of difficulty.

Let's work backwards from the coefficient of difficulty.

A lower coefficient gives more weight to previous events and changes the rating at a slower rate. A higher coefficient gives more weight to the most recent events and changes the rating faster.

A beginning chessplayer has his or her rating adjusted with k = 40, and this coefficient is adjusted downward until it reaches a value of 10 after the player has played sufficiently many games. I don't know whether the power ratings are adjusted for early in the season. The worst thing that could happen to Green Bay is that its power rating would not change after conference play began, and that would require W - W^e = 0. Perhaps Green Bay had a sufficiently strong team that it would be expected to run the table in the conference: there have been sufficiently many chess games played that there's an actuarial table for games between players of differing strengths.

The problem, however, is that to be invited to play in the higher levels of the tournament, one cannot simply win a lot of games against mediocre opponents. That's where the grandmaster norm comes in. (Here's the official explanation.) A player cannot earn the rank of Expert, Master, Grand Master (in the U.S.), or International Grand Master (internationally) without winning sufficiently many games against other Experts, Masters, Grand Masters, or International Grand Masters. Going 16-0 against a field of patzers with an anticipated 14 wins (Illinois-Chicago and Wisconsin-Milwaukee might have won) does not a grandmaster norm make.