Median rating not 1500, why? • page 2/2 • General Chess Discussion • lichess.org

with symetric bell shape (allowing bumps, if they are symmetric too) avg=median. otherwise not.

the bumps are not symmetric they tend to augment or weigh more in the right most part of 1500, or did I dream?

although the bumps are also preceded by inverted bumps, which might cancel... forget the bump thing.

with symetric bell shape (allowing bumps, if they are symmetric too) avg=median. otherwise not. the bumps are not symmetric they tend to augment or weigh more in the right most part of 1500, or did I dream? although the bumps are also preceded by inverted bumps, which might cancel... forget the bump thing.

petri999

#12

@h2b2 said in #10:

I wonder what the percentage of provisional plays UB has? I suspect it's high. People play a few games, lose, don't play any more.
It high ratio but there do not affect too much the distribution as it from active player i.e number of them is low

@h2b2 said in #10: > I wonder what the percentage of provisional plays UB has? I suspect it's high. People play a few games, lose, don't play any more. It high ratio but there do not affect too much the distribution as it from active player i.e number of them is low

#13

CM Sarg0n

#14

It's the median of whole population.

So if only two players play in that particular week they should be normalized to 1500?

It's the median of whole population. So if only two players play in that particular week they should be normalized to 1500?

#15

petri999

#16

@Haymarket Glicko-2 makes no assumption about normality of the distribution. actually it makes no assumption about all and rating system itself does not set the median. Lichess rating tens to have median of 1500 and this artifact of

starting rating of 1500
rating system being roughly zero sum game - new players and player hitting minimum rating are the two thing that make non zero-sum

Fact that tat chess playing skill is sum of multiple stochastic variables makes likely that strength on player would be normally distributed as it seems to be. Bit of mystery to why logarithm of Bradley-Terry score is normally distributed not the score itself. Explaining is left as an exercise to more math abled readers like @dboing.

in a system more leavers than for instance system can settle to whatever median or mean.

@Haymarket Glicko-2 makes no assumption about normality of the distribution. actually it makes no assumption about all and rating system itself does not set the median. Lichess rating tens to have median of 1500 and this artifact of - starting rating of 1500 - rating system being roughly zero sum game - new players and player hitting minimum rating are the two thing that make non zero-sum Fact that tat chess playing skill is sum of multiple stochastic variables makes likely that strength on player would be normally distributed as it seems to be. Bit of mystery to why logarithm of Bradley-Terry score is normally distributed not the score itself. Explaining is left as an exercise to more math abled readers like @dboing. in a system more leavers than for instance system can settle to whatever median or mean.

normal is symmetric so median=avg. small many factors added gives normal in the limit. multiplicative small many factors gives log normal if I remember well. here the pairing might be the multiplicating source. i am guessing and remembering after long time. so... noise possible.

Glicko does not prescribe the population distribution only the players individual probability, it lets the whole population distribution converge to whatever it will converge to with big size population and times series of pairings data feeding it. hence we can see the bumps.. and other things.

but the median not being the average, systematically, would be more about it being not emerging symmetric. I would bet on the pairing being the multiplicative ingredient. multiplying the probabilities somehow. conjonction of events. maybe in glicko paper there is some characterization at limit of high numbers for the population on players undergoing random pairings (they are random are they here?).

normal is symmetric so median=avg. small many factors added gives normal in the limit. multiplicative small many factors gives log normal if I remember well. here the pairing might be the multiplicating source. i am guessing and remembering after long time. so... noise possible. Glicko does not prescribe the population distribution only the players individual probability, it lets the whole population distribution converge to whatever it will converge to with big size population and times series of pairings data feeding it. hence we can see the bumps.. and other things. but the median not being the average, systematically, would be more about it being not emerging symmetric. I would bet on the pairing being the multiplicative ingredient. multiplying the probabilities somehow. conjonction of events. maybe in glicko paper there is some characterization at limit of high numbers for the population on players undergoing random pairings (they are random are they here?).