2010-08-16, 07:00 AM
I was going to post something like this in the middle of last week, but then my browser crashed and my entire post went with it. Anyway, here goes:
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Your (thus far) limited data kinda fits an ELO model -- commonly used to calculate player ratings in two-player games. So does your data fit such a model? (The rest of this post explains how it might fit.)
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Consulting this for reference: http://en.wikipedia.org/wiki/Elo_rating_...al_details
The rating change for a win or loss is RA' - RA = K (SA - EA). Furthermore, SA = 1 for a win, 0 for a loss; EA = probability (percent chance in decimal) of winning and the formula for this is given. So the big unknown would be that multiplicative factor K.
1) Your data from Table 1 seems to indicate: K of 20~21 (for both players) if the winner made the first move. Possible K of 40~42 (again for both players) if the winner was second to move. (This case happened only once in this data set.)
2) Data from Tables 2 and 3 seems to indicate:[INDENT]Player 1: Moving first - K of 20~21 is still a decent guess/estimate. Moving second - K of 40~42 is a decent guess/estimate.
Player 2: K values seem to be roughly double of what applies to Player 1 (IIRC, roughly 40~42 and 82~84 -- remember: I originally wanted to post something last week). As mentioned in the Wikipedia article, it's common to apply a different K to players of different ratings or when total number of games played (i.e., number of samples) is low.
[/INDENT]So going forward, you want to obtain data that:[INDENT]a) proves or refutes K of 20~21 for Player 1. And/or find the precise value of K.
b) shows if a 2x multiplier is applied when the winner was second to move.
c) shows what the different rating brackets are.[INDENT]Before the possible 2x multiplier:
It looks K = 20~21 for 2463~2508. --> rating bracket is 2400+? Or is the floor for this bracket something else? Is there a ceiling to this rating bracket?
K = 40~42 for 2000 and below? Or what is the floor/ceiling for this bracket?
[/INDENT]d) Are there different rating brackets for different total number of games played?
[/INDENT]NOTE: IIRC, assuming the game rounds rating change down, up, or to the closest integer didn't exactly match when I specifically tried K = 20, 20.5, or 21 to your Table 1 data. (Thus, I specified a possible range for K.) I'd have to double-check this though; or you/someone else can. Additionally, more data and targeted data could help pinpoint the precise K value(s).
- - - - -
Your (thus far) limited data kinda fits an ELO model -- commonly used to calculate player ratings in two-player games. So does your data fit such a model? (The rest of this post explains how it might fit.)
- - - - -
Consulting this for reference: http://en.wikipedia.org/wiki/Elo_rating_...al_details
The rating change for a win or loss is RA' - RA = K (SA - EA). Furthermore, SA = 1 for a win, 0 for a loss; EA = probability (percent chance in decimal) of winning and the formula for this is given. So the big unknown would be that multiplicative factor K.
1) Your data from Table 1 seems to indicate: K of 20~21 (for both players) if the winner made the first move. Possible K of 40~42 (again for both players) if the winner was second to move. (This case happened only once in this data set.)
2) Data from Tables 2 and 3 seems to indicate:[INDENT]Player 1: Moving first - K of 20~21 is still a decent guess/estimate. Moving second - K of 40~42 is a decent guess/estimate.
Player 2: K values seem to be roughly double of what applies to Player 1 (IIRC, roughly 40~42 and 82~84 -- remember: I originally wanted to post something last week). As mentioned in the Wikipedia article, it's common to apply a different K to players of different ratings or when total number of games played (i.e., number of samples) is low.
[/INDENT]So going forward, you want to obtain data that:[INDENT]a) proves or refutes K of 20~21 for Player 1. And/or find the precise value of K.
b) shows if a 2x multiplier is applied when the winner was second to move.
c) shows what the different rating brackets are.[INDENT]Before the possible 2x multiplier:
It looks K = 20~21 for 2463~2508. --> rating bracket is 2400+? Or is the floor for this bracket something else? Is there a ceiling to this rating bracket?
K = 40~42 for 2000 and below? Or what is the floor/ceiling for this bracket?
[/INDENT]d) Are there different rating brackets for different total number of games played?
[/INDENT]NOTE: IIRC, assuming the game rounds rating change down, up, or to the closest integer didn't exactly match when I specifically tried K = 20, 20.5, or 21 to your Table 1 data. (Thus, I specified a possible range for K.) I'd have to double-check this though; or you/someone else can. Additionally, more data and targeted data could help pinpoint the precise K value(s).