ed987
asked on
calculate ELO
function k_elo($e)
{
$eh=2400;$el=2000;
$kh=16;$kl=32;
if($e<$el)return $kl;
if($e>$eh)return $kh;
return ($eh-$e)*($kl-$kh)/($eh-$e
}
function calcELO(&$n1,&$n2,$won1,$c
{
$e1=$n1;
$e2=$n2;
$ea=1/(1+(float)pow(10,($e
$eb=1-$ea;
$k1=k_elo($e1);
$k2=k_elo($e2);
if($won1==2)$sa=1; //won
if($won1==1)$sa=0.5; //even
if($won1==0)$sa=0; //lost
$sb=1-$sa;
$n1=round($e1+$k1*($sa-$ea
$n2=round($e2+$k2*($sb-$eb
}
script above supposed to calculate ELO.
but it doesn't take information on previous games played !
how does one do that ?
{
$eh=2400;$el=2000;
$kh=16;$kl=32;
if($e<$el)return $kl;
if($e>$eh)return $kh;
return ($eh-$e)*($kl-$kh)/($eh-$e
}
function calcELO(&$n1,&$n2,$won1,$c
{
$e1=$n1;
$e2=$n2;
$ea=1/(1+(float)pow(10,($e
$eb=1-$ea;
$k1=k_elo($e1);
$k2=k_elo($e2);
if($won1==2)$sa=1; //won
if($won1==1)$sa=0.5; //even
if($won1==0)$sa=0; //lost
$sb=1-$sa;
$n1=round($e1+$k1*($sa-$ea
$n2=round($e2+$k2*($sb-$eb
}
script above supposed to calculate ELO.
but it doesn't take information on previous games played !
how does one do that ?
ASKER CERTIFIED SOLUTION
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SOLUTION
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counting Elo ratings one single game at a time can be better than taking avgOpponentsElo for multiple games
A 1500 player might be expected win more games on average playing one 2800 player and one 1000 player than playing against two 1900 players
A 1500 player might be expected win more games on average playing one 2800 player and one 1000 player than playing against two 1900 players
your extreme example is not real life, so i won't comment too much on it. find me a tournament keeping elo ratings that has that situation, and let's discuss this again. the elo rating has limitations, but it works better to adjust once per 10-swiss-round tournament of "like minds" (not master vs novice) than 10 individual times. why don't you check with professional organisations before you comment
SOLUTION
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It's also true that a 2015 player might be expected win more games on average playing one 2028 player and one 2010 player than playing two 2019 players, although the effect is more subtle.
An extreme example makes the effect more intuitively obvious and takes fewer games to be noticeable above the expected variation in expected wins.
The question was about how the given program worked, but how actual tournaments are conducted or how that may have been influenced by how simplifications in practical computations differ from Elo's theoretical model or how simplifications in his theoretical model differ from a more accurate model may also be interesting topics if the author wishes to ask about them as well.
An extreme example makes the effect more intuitively obvious and takes fewer games to be noticeable above the expected variation in expected wins.
The question was about how the given program worked, but how actual tournaments are conducted or how that may have been influenced by how simplifications in practical computations differ from Elo's theoretical model or how simplifications in his theoretical model differ from a more accurate model may also be interesting topics if the author wishes to ask about them as well.
ozo - I believe that's exactly the point you're missing. given the maths behind the ELO model, a 2015 player is expected to win EXACTLY AS MANY games against 2028 + 2010 as he is playing two 2019 players. You have to realise that 13 ELO points do not a better player make. a quick check for the latest real life games will reveal that to be true. they are considered statistically equivalent in the sense of sitting down and actually playing a game. the cutoff is 400 because at that range (and practically anywhere close), the difference is clear cut, assuming the current ELO rating of both players are _established_ by many prior (recent) games.
It's not a cutoff, it's an inflection point, which is why the more extreme example illiustrates the point better
it would take about 22000 games for the difference between 2150 vs 2280+2100 and 2150 vs 2190+2190 to be as significant as the effect of difference between 1500 vs 2800+1000 and 1500 vs 1900+1900 is in two games.
That's given the Elo model, which is itself a simplification of a more accurate model where each player has their own individual inflection point reflecting how well established by prior games their own individual rating is.
it would take about 22000 games for the difference between 2150 vs 2280+2100 and 2150 vs 2190+2190 to be as significant as the effect of difference between 1500 vs 2800+1000 and 1500 vs 1900+1900 is in two games.
That's given the Elo model, which is itself a simplification of a more accurate model where each player has their own individual inflection point reflecting how well established by prior games their own individual rating is.
ASKER
i believe script i gave in my question does not work properly.
any possibility someone could post a correct implementation ?
c++ or php or asp or pascal or ... pseudocode.
thnx
any possibility someone could post a correct implementation ?
c++ or php or asp or pascal or ... pseudocode.
thnx
startingElo, avgOpponentsElo, totalGamesPlayed, actualResult, i.e. 4.5 for (3 wins + 3 draws)
google has more info