Here is one of Slaughter's original emails explaining his implementation of the Glicko rating system we use:

"OK, I finally finished the Glicko rating system, it is now fully working for every game style (I left out epics since they are basically like ctons ÃƒÂ¢Ã¢â€šÂ¬Ã¢â‚¬Å“ if we decide to use Glicko I will put it in, saves a lot of coding). For every game being reported the system now calculates the new skill with both the Ante system AND the Glicko system, both values are stored in the database then and can be compared easily (I put in a new section where both values are compared for the actual standings). We can track how each system is performing during beta and select the better for the final version ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ since the Glicko uses more information than the Ante system it needs some more fine tuning so it works best, the values to determine are r = the initial skill after registration (r is set to 1500 atm); RD = the initial rating deviation (RD is set to 300 atm); c = the RD volatility multiplier and t = the inactivity period modifier (for now c = 60, t = 1). Last two are needed to calculate a new RD value after a player was inactive for a longer period, t should be a value which describes how many rating periods a player was inactive (at the moment a rating period is set to 1 day, so for each day being inactive t is increased by 1) and c is a constant that will be multiplied (simply spoken) by t to determine what is added to RD to simulate the deviation volatility. The value of the constant c can be derived by a formula from the starting RD and the rating period, so basically we only need to set the starting values and the rating period.

That are lots of values though, letÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s have a look at an example to make it more clear:

A Player has a skill of 1500 at start with a RD set to 300. A simple explanation would be that the system now assumes that this playerÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s skill lies somewhere between 1200 (= 1500-300) and 1800 (= 1500+300) skill since the player canÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢t be rated exactly because the system did not yet compare this player to any other players. After his first report the playerÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s skill and RD values will now change, no matter if he wins or loses, the RD value will ALWAYS decrease since the system ÃƒÂ¢Ã¢â€šÂ¬Ã‹Å“learnedÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ something about the playerÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s performance and has at least 1 more comparison to another player. The more games a player plays and the more frequent he does it, the smaller will be the RD value and the more exact will be the actual skill value. Basically the rule is, the greater the RD value the bigger the skill gain or loss. LetÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s assume that in our example the player plays against a player with 1900 skill, if he wins itÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s really hard to say if it was an equal matching or not, it might have been actually 1200 vs. 1900 skill or only 1800 vs. 1900 skill, so the player will gain a lot of skill for that win and the RD value will be decreased. LetÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s say he gained 200 skill and his new RD value is now 250, so for the system his real skill will now be somewhere between 1450 and 1950, still not really exact but better than before. With a decreasing RD value the skill gain/loss will decrease too until the actual skill value becomes stable and does a good job representing the playerÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s performance. So in the beginning players will have big jumps or drops in skill until the system learns more about those playersÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ performance and can rate them good enough ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ now it comes to the volatility of the RD value, where c and t enter the scene.

LetÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s say our player did play regularly for quite some time and now has a skill of 1800 and a RD value of 60 which means that his ÃƒÂ¢Ã¢â€šÂ¬Ã‹Å“realÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ skill lies between 1740 and 1860, so the skill value does represent the playerÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s performance somewhat exact now ÃƒÂ¢Ã¢â€šÂ¬Ã¢â‚¬Å“ but suddenly the player stops playing because of unknown reasons and becomes inactive for letÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s say 7 days (wives can be very annoying :p). After returning and playing his first match, the system now recalculates his RD value before it actually calculates the gain/loss of skill for this match because it assumes that a player will perform a bit worse after a break without ÃƒÂ¢Ã¢â€šÂ¬Ã‹Å“trainingÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢. Now with a rating period set to 1 day the t value for this player would be t = 7. Putting this t and c = 60 into the new RD calculation it will give 255 as the playerÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s new RD value, so the system assumes that the playerÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s skill now is more imprecise by 55 after the break and will go into the skill calculation with 1800 skill and RD = 255.

Back to determining the best values, the starting RD value will also be the highest value that can result from a recalculation after inactivity, that means that a player who was inactive for a really long time is only as bad to rate as a new player. Also the rank drop for being inactive needs to compensate the greater gain of skill after inactivity caused by a higher RD value, we donÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢t want players to exploit the system by determining a good value to stay inactive just to gain more skill for their next match.

IÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢m not sure about the best values yet, but my calculations showed that the system did perform well starting with 1500 skill, RD = 300 and with c = 60, t = 1 day ÃƒÂ¢Ã¢â€šÂ¬Ã¢â‚¬Å“ but I think we will get a better view once testing started. Since the RD volatility is calculated with a Pythagoras like formula we might need to change the skill drop from percentage (like itÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s now for the Ante system) to a slowly increasing exponential function if we use Glicko for rating. ItÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s also possible to change values after the system did run for some time and ratings become stable, it will not change much at all but lowering the initial RD value for new players will then prevent too heavy fluctuations, but thatÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s something to be seen later. It might also be an idea to have a minimal RD value which ensures that thereÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s always some movement in the league, some players with 3+ games a day may get really low RD values so their skill gain/loss will become somewhat stagnant unless they play players with a big gap in skill. For now all values are hard-coded, but if you like to have the possibility of changing values regarding the rating system I will make them changeable for the headadmin in the league settings later."

Hope this helps.

SPM