IBL Rating System

Introduction

For the most part, this is a technical document *not* meant to entertain. Read this only if you are curious about the inner workings of the IBL. There will be no quiz.

The ratings scheme for the IBL is based on the Elo system (named after the musical group) which is just an approximate form of a least squares estimator. It is used for rating chess players in the USCF (United States Chess Federation) and ICS (International Chess Society). The system was specifically adapted for IBL by Sluggo, our staff rocket scientist, and Wild Duck, our representative from the Euro Bolo League (where they have used such a system for years), then optimized by yours truly.

Methods

To summarize, here's how we adapted the Elo system for IBL:

1. We ranked all players before the season started. Ranks are integers like #1, #2, etc. which determine division match-ups. Rankings were based on last season's final ranks, with some vets reshuffled as described before.

2. We assigned Initial ratings, which were floating point numbers ranging linearly between approximately 800 and 2400 (average = 1600). Better players had higher ratings points.

3. All games are played on 1 of 2 IBL official nights, no exceptions allowed. All players join #ibl and are assigned to divisions of 4 based on their current ratings. The 4 players in each division play 3 2x2 games.

4. Each player's rating will be adjusted by a floating-point "delta" factor, calculated using the Elo formula. We will explain the formula in terms of a 1x1 match-up. First we give the math formula, then we explain it all in plain English in the next section #5.

   Suppose your rating is r1, and the opponent's is r2. Let w be 1 if you win, .5 if you draw, and 0 if you lose. After a game, your new rating will be:

                                           1
                      r1 + K (w - (-----------------))
                                         (r2-r1)/400
                                   1 + 10

   You may find it easier to understand in smaller pieces:

   p = win expectancy = 1/(1+10^[(r2-r1)/400])
   w = did you win? (1 if you win, 0.5 if you draw, 0 if you lose)
   K = your K-factor (maximum points you can win/lose per game)
   d = delta factor or rating change = K * (w - p)
   if abs(d) < 1, then d = 2w - 1

   new rating is r1 + d

   K is the largest change your rating can experience as a result of the game. The value K=32 is used in the chess world, but we bumped it up by quite a bit (to about 100) to encourage more dynamic changes in ratings and thus IBL match-ups. To prevent top players from getting too many points, K is decreased to 0.75 K for players with ratings between 2100 and 2399, or 0.5 K for players above 2400 points.

   For 2x2 team play, simply substitute r2 with the sum of all ratings on the opponents' team, and substitute r1 with the sum of all ratings on your team. Note that since we continue to use 400 instead of a doubled 800, we are in effect tightening the dispersal of ratings.

5. The players are re-ranked according to their updated ratings.

Discussion

1. HOW DOES THE FORMULA WORK? In plain English, every game you play changes your ratings by a non-zero amount. The better your opponent is, the more points you will gain by beating them but the less points you will lose by losing to them. Another way to think of it: if you crush a newbie you get only 1 point, if you beat an equal then you get K/2 points, but if you upset a bolo god you get K points. Conversely, in those situations your opponent *loses* the same amount of points as you gained. This formula has the property that the sum of the rating changes is zero, which is unique among all the "systems" we considered.

   Below is a plot of the number of points you would gain or lose as function of the difference between you and your opponent's ratings. If you win, you gain points according to the solid curve, while if you lose, you lose points (negative change in ratings) according to the dotted curve. The x-axis is the number of points you are less than your opponent (so if you are better then it is negative to the left), and the y-axis is your change in points. This plot uses K=100. From left to right, the x-axis corresponds to you being an obvious favorite to you being an obvious underdog. Four situations are pointed out to illustrate the extremes in point gain or loss as a newbie faces off against a god. Note that if you beat somebody who is your equal (x=0), then you still gain 50 points. You are encouraged to play people slightly better than you, thus maximizing your benefit while minimizing your risk. This seems appropriate for the purposes of IBL.

   

2. HOW WAS THE SYSTEM OPTIMIZED FOR IBL? The constant K was set to approximately 100, which in our computer modelling provides a desirable level of "dynamicness" in IBL so that people don't play the same other 3 players over and over again. My goal is to get 1-2 reshuffles for every level. The secret value of K corresponded to the point difference across 3 ranks in the initial linear rating scheme (see #2 above). This has a special meaning to IBL. The theoretical maximum that somebody can get after each week's 3 games is as a result of going 3-0 and thus 3 K points or about 9 ranks. This would be like if I entered IBL at the bottom of the ratings, partnered with a raw newbie, and beat a team consisting of HB and Samhain. For somebody who happens to go 3-0 in a division of equally skilled players, s/he would move up 1.5 K points or 4.5 ranks, which happens to be equivalent to being promoted well into the next division under Wmute's old system.

3. LETS GO ON WITH THE NO-SHOWS. In the current incarnation of the IBL system, there is no penalty for being absent. If you are absent for 3 consecutive weeks, the ranking scripts automatically omit you in the short ratings list, but you are still kept in the system in case you return at a later date. All ratings, including inactive players, are shown in thefull ratings list. We used to enforce a rule that one could not miss more than 3 weeks per season, but that turned out to be more busywork for us the organizers without significantly encouraging people to play more, so we scrapped that rule.
   In the past, several "integral delta" systems (such as Guy and Max's systems) used rank demotion to punish no-shows. The disadvantage was that demoted no-shows then beat up significantly worse players the next week. Under the Elo system, the ratings depend *only* on games actually played. If one skips a week or two, or leaves IBL and returns the next season, his ratings remain inviolate to ensure the fairest teams, but his rank can go up or down slightly, depending on how his neighbors do.