New player rating problem

This is a hypothetical problem but the disagreement between my friends has surprised me.

Imagine a chess league of 20 players who play each other round robin style once as white and once as black over the course of a year.

So that total league games played is 380 each of the 20 players play 38 games each 19 as black and 19 as white against the 19 other league players.

The league uses it's own ELO ranking system to rate the players and has been running for many years and players rankings are considered accurate.

As a new year is about to start one of the players drops out and is replaced by another (new) player. As is the norm this player is given a ranking of 1200 and the year is played out and at the end of the year the new players ranking is 2000.

It now becomes apparent that the new player was better than his 1200 beginners ranking suggested. Because of this the other players rankings will not be accurate because the ELO ranking system would have been assuming the new player was worse than he actually was and over and under awarding ranking points to his opponents under this mistaken assumption.

Now that the year has ended and a more accurate guess of this players initial skill can be made would it be not be advisable to award the new player 2000 points at the start of the season and recalculate all the games on this assumption. This would award his opponents a more accurate set of points per game and give the leagues final standings a more accurate final table.

Taking this suggestion one step further would it not be more accurate to feed all the leagues final rankings into the start of the year and recalculate all the matches again. The same could be done again and again until there is no more movement in the end of year's rankings.

Would this work?

As I'm aware... with an "elo" system.  A provisionally rated player (in most systems) will not 'steal' as many points from you as a non provisional player of the same rating. 

Either way... I like the rating system as is.  

No, because ratings only ever claim to be accurate in a given pool of players.  Ratings are never absolute measurements like liters or kilometers.  At the end of the new year, the points the new player took out of the system while climbing to 2000 would bring the new pool to a more accurate rating.  It could be said that at the beginning of the year, before the 1200 rated player had played any games, the pool's ratings were at their most inaccurate, and at the end of the year was the highest accuracy.

If you did re-calculate the ratings, then the 2000 rated player would not have taken as many points out, and as a result, everyone, including the new player, would have a higher rating.  Arguing that these are now more accurate ratings, at that point you could similarly argue another re-calculation, and another and another etc.  So you can see this logic doesn't work.

As ih8sens said, systems adjust for new players by giving them a provisional rating which limits their effects on the established pool while giving the provisional rating the ability to fluctuate wildly in an attempt to quickly estimate the correct rating.  This can be seen on this site (or just about anywhere else) when a new player wins a game and gains hundreds of rating points while an established player may gain less than 10.

There is only one reason for a "provisional" rating. It is a means to fit a player into the draw in Swiss events, somewhere in or near the middle of the field.

In a RR, it really doesn't matter.

AFTER the tournament, based on the unrated's performance, his rating should be calculated. in the example, in a 38 round tourney, against known strength, this should be fairly accurate.

[edit] The ideal would be that if the new player is stronger than the player he replaced, the total rating points in the pool should increase, if he is weaker, the pints should decrease. That way, you can protect the integrity(?) of the ratings within the pool. A 2000 rated player would be as strong as a 2000 rated player was 10 years ago. Does that make sense?

Maybe I should have a few more pints?

The reason I think that the ratings need to be re-run at year's end is because of the effect of all the other players playing this new player with an inaccurate rating.

I am happy that after 38 games the new player is accuratly rated. What I am not happy about is the fact that in getting to this rating all the other players will have played a player with a rating that ranged from very inaccurate to accurate at the end.

It seems logical that rating all the season again would give a more accurate rating.

I have coded an experiment based upon the league in my original question.

At the end of the year I recalculate the whole league again using the final standings of all players as the start of the year ratings. I then do this 100 times.

At the end of the 100th recalculation run the players ratings are the same at the end of the year as they were at the start.

When these (100 run) ratings are compared to the (1 run) ratings they differ by 1-5%.

Should they be considered more accurate?

From what I have known of the Elo system, there is really no problem. If you play regularly, there will be wins, losses and upsets to underrated players etc...but over time, your rating will just fluctuate about 50 points around an average rating level.

I say worry about the chess and let the blasted ratings sort themselves out

How come so many big differences in rating points? One gets for a victory -let's say - 25 points and for a comparising game in rating points only 5 or 6?

Is there somebody with an answer for me, because I see the differences everyday and sometimes they are enormous.