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diff --git a/data/help/glicko b/data/help/glicko new file mode 100644 index 0000000..d4614b2 --- /dev/null +++ b/data/help/glicko @@ -0,0 +1,219 @@ + + +-------------------------------------------------+ + | Vek-splanation of the Glicko Ratings System | + +-------------------------------------------------+ + +As you may have noticed, each FICS player now has a rating and an RD. + +RD stands for "ratings deviation". + +Why a new system +---------------- + +The new system with the RD improves upon the binary categorization that was +used before on fics and elsewhere, where players with fewer than 20 games were +labeled"provisional" and others were labeled "established". Instead of two +separate ratings formulas for the two categories, there is now a single +formula incorporating the two ratings and the two RD's to find the ratings +changes for you and your opponent after a game. + +What RD represents +------------------ + +The Ratings Deviation is used to measure how much a player's current rating +should be trusted. A high RD indicates that the player may not be competing +frequently or that the player has not played very many games yet at the +current rating level. A low RD indicates that the player's rating is fairly +well established. This is described in more detail below under "RD +Interpretation". + +How RD Affects Ratings Changes +------------------------------ + +In general, if your RD is high, then your rating will change a lot each time +you play. As it gets smaller, the ratings change per game will go down. +However, your opponent's RD will have the opposite effect, to a smaller +extent: if his RD is high, then your ratings change will be somewhat smaller +than it would be otherwise. + +A further use of RD's: +---------------------- + +Vek asked Mark Glickman the following: + +> Given player one with rating r1, error s1, +> and player two with r2 and s2, do you have a formula for the probability +> that player 1's "true" rating is greater than player 2's ? + +Mark said: + + Yes - it's: + + 1/(1 + 10^(-(r1-r2)f(sqrt(s1^2 + s2^2))/400) ) + + where f(s) is [the function applied to RD in Step 2 below]. + +How RD is Updated +----------------- + +In this system, the RD will decrease somewhat each time you play a game, +because when you play more games there is a stronger basis for concluding what +your rating should be. However, if you go for a long time without playing any +games, your RD will increase to reflect the increased uncertainty in your +rating due to the passage of time. Also, your RD will decrease more if your +opponent's rating is similar to yours, and decrease less your opponent's +rating is much different. + +Why Ratings Changes Aren't Balanced +----------------------------------- + +In the other system, except for provisional games, the ratings changes for the +two players in a game would balance each other out - if A wins 16 points, B +loses 16 points. That is not the case with this system. Here is the +explanation I received from Mark Glickman: + + The system does not conserve rating points - and with good + reason! Suppose two players both have ratings of 1700, + except one has not played in awhile and the other playing + constantly. In the former case, the player's rating is not + a reliable measure while in the latter case the rating is a fairly + reliable measure. Let's say the player with the uncertain rating + defeats the player with the precisely measured rating. + Then I would claim that the player with the imprecisely + measured rating should have his rating increase a fair + amount (because we have learned something informative from + defeating a player with a precisely measured ability) and + the player with the precise rating should have his rating + decrease by a very small amount (because losing to a player + with an imprecise rating contains little information). + That's the intuitive gist of my extension to the Elo system. + + On average, the system will stay roughly constant (by the + law of large numbers). In other words, the above scenario + in the long run should occur just as often with the + imprecisely rated player losing. + +Mathematical Interpretation of RD +--------------------------------- + +Direct from Mark Glickman: + +Each player can be characterized as having a true (but unknown) rating that +may be thought of as the player's average ability. We never get to know that +value, partly because we only observe a finite number of games, but also +because that true rating changes over time as a player's ability changes. But +we can *estimate* the unknown rating. Rather than restrict oneself to a +single estimate of the true rating, we can describe our estimate as an +*interval* of plausible values. The interval is wider if we are less sure +about the player's unknown true rating, and the interval is narrower if we are +more sure about the unknown rating. The RD quantifies the uncertainty in +terms of probability: + +The interval formed by Current rating +/- RD contains your true rating with +probability of about 0.67. + +The interval formed by Current rating +/- 2 * RD contains your true rating +with probability of about 0.95. + +The interval formed by Current rating +/- 3 * RD contains your true rating +with probability of about 0.997. + +For those of you who know something about statistics, these are not confidence +intervals, but are called "central posterior intervals" because the derivation +came from a "Bayesian" analysis of the problem. + +These numbers are found from the cumulative distribution function of the +normal distribution with mean = current rating, and standard deviation = RD. +For example, CDF[ N[1600,50], 1550 ] = .159 approximately (that's shorthand +Mathematica notation.) + +The Formulas +------------ + +Algorithm to calculate ratings change for a game against a given opponent: + +Step 1. Before a game, calculate initial rating and RD for each player. + + a) If no games yet, initial rating assumed to be 1720. + Otherwise, use existing rating. + (The 1720 is not printed out, however.) + + b) If no RD yet, initial RD assumed to be 350 if you have no games, + or 70 if your rating is carried over from ICC. + Otherwise, calculate new RD, based on the RD that was obtained + after the most recent game played, and on the amount of time (t) that + has passed since that game, as follows: + + RD' = Sqrt(RD^2 + c log(1+t)) + + where c is a numerical constant chosen so that predictions made + according to the ratings from this system will be approximately + optimal. + +Step 2. Calculate the "attenuating factor" due to your OPPONENT's RD, + for use in later steps. + + f = 1/Sqrt(1 + p RD^2) + + Here p is the mathematical constant 3 (ln 10)^2 + ------------- + Pi^2 400^2 . + + Note that this is between 0 and 1 - if RD is very big, + then f will be closer to 0. + +Step 3. r1 <- your rating, + r2 <- opponent's rating, + + 1 + E <- ---------------------- + -(r1-r2)*f/400 <- it has f(RD) in it! + 1 + 10 + + This quantity E seems to be treated kind of like a probability. + +Step 4. K = q*f + -------------------------------------- + 1/(RD)^2 + q^2 * f^2 * E * (1-E) + + where q is a mathematical constant: q = (ln 10)/400. + +Step 5. This is the K factor for the game, so + + Your new rating = (pregame rating) + K * (w - E) + + where w is 1 for a win, .5 for a draw, and 0 for a loss. + +Step 6. Your new RD is calculated as + + RD' = 1 + ------------------------------------------------- + Sqrt( 1/(RD)^2 + q^2 * f^2 * E * (1-E) ) . + +The same steps are done for your opponent. + +Further information +------------------- + +A PostScript file containing Mark Glickman's paper discussing this ratings +system may be obtained via ftp. The ftp site is hustat.harvard.edu, the +directory is /pub/glickman, and the file is called "glicko.ps". It is +available at http://hustat.harvard.edu/pub/glickman/glicko.ps. + +Credits +------- + +The Glicko Ratings System was invented by Mark Glickman, Ph.D. who is +currently at the Harvard Statistics Department, and who is bound for Boston +University. + +Vek and Hawk programmed and debugged the new ratings calculations (we may +still be debugging it). Helpful assistance was given by Surf, and Shane fixed +a heinous bug that Vek invented. + +Vek wrote this helpfile and Mark Glickman made some essential +corrections and additions. + + Last major update: April 19, 1995. + Minor revisions: August 28, 1995 by Friar. + |