2nd Pass

Running Chess Tournaments
1

Rather than the old “feedback points” system, US Chess has what is known a the “Second Pass” system. Both are meant to avoid penalizing a player for having a vastly underrated opponent. So, a rating loss (or gain) against a player gaining 200 points in an event [i.e. a 1200 becoming a 1400] would change after the “Second Pass”. I was wondering if this system applies to provisional players?

If you loss to a player provisionally rated 1600 before the event, and provisionally rated 1800 after the event, then is there a reduction to the number of rating points you would lose? I am sure this would be of interest to players potentially having to play such opponents in any chess tournament.

Larry Cohen

2

All players ratings are updated during the “first pass” and the updated ratings are used to determine the net ratings changes for all players. This applies to players with established and provisional ratings, and unrated players.

3

Whether the opponent’s rating is provisional or established makes absolutely no difference. In the second pass, the rating change is based on the player’s pre-event rating, the opponent’s post-event rating from the first pass, the difference in those ratings, and the player’s “K factor”. The result of the second pass become’s the player’s post-event rating.

4

Thank you all. That is what I thought, but I did not want to be informing the players incorrectly.

Larry Cohen

5

Although the following is fairly lengthy, it is still a somewhat simplified explanation, as it doesn’t get into the mathematics at all and probably skips over a few special cases.

The ratings system divides players into several types:

Those who have no pre-event rating, for whom some pre-event approximation is made based on other information, such as a rating under another ratings system (not necessarily a US Chess ratings system) or the player’s age. This includes deciding how many games to based this approximation on, which can be as few as zero. Then this information is used to produce a more refined approximation using the special formula. (This is called the stage 3 rating, and is only computed for those players who were unrated prior to this event, for all other players their stage 3 rating is their pre-event rating.)

Once this is done for all unrated players, each player will fall into one of the following categories, which determines what formula is used to compute a new rating.

Those who have a pre-event rating based on 8 games or less, for whom the ‘special formula’ is used.

This category also includes players who have won all their games or lost all their games in their previous events. All we really know about these players is that the ones who have won all their games are PROBABLY stronger than anyone they’ve played so far and the ones who have lost all their games are PROBABLY weaker than anyone they’ve played so far. So the special formula is still used, regardless of how many games this player has from previous events.

Those who have a pre-event rating based on 9 or more games, for whom the ‘standard formula’ is used. These are the only players who receive bonus points.

Note that neither of these formulas match the usual definition of having an ‘established’ rating. That’s because the ratings formula doesn’t utilize that information. It keeps track of whether or not a rating is established (currently defined as a player who has played 26 or more rated games that were not all wins or all losses), but that doesn’t enter into how ratings are computed.

When computing a player’s new rating, it is done in two passes, as Larry noted. In the first stage, each player’s ‘stage 4’ rating is computed, using the appropriate formula (standard or special) Then that set of ratings is used as your opponents’ ratings for another round of computations.

This has an effect upon your final or stage 5 rating, because it changes the expected result based on the difference in ratings between you and each opponent. For example, if you played someone with a 1600 rating and their preliminary (stage 4) post-event rating is 1800, then if you lost the game the number of ratings points you would lose goes down a little, because your expected score goes down, and if you won the game it goes up a little, again, because your expected score goes down a little. (A draw is a bit more complicated.) But if you played someone with an 1800 rating and their preliminary post-event rating is 1600, then the opposite occurs.

Mark Glickman once told me that during the development of the current formulas, around 2000, they tried making more than 2 passes, and the system would sometimes start to oscillate. (Your rating might go up 10 points in pass 2, but go up only a total of 8 points in pass 3 and then 11 points in pass 4, up 9 points in pass 5, etc.) They settled on making just two passes.

6

I’m curious, would this oscillation still have occurred if floating point ratings had been implemented “around 2000” (i.e. whenever the current formulas were developed), rather than several years later?

Bill Smythe

7

I took a class in dynamic feedback systems in which we had labs where we looked at the parameters that would produce dampening/converging, stable (eg, a sine wave) and destabilizing patterns.

These were produced using both analog and digital systems, my guess is that the integer truncation could act as a dampener or as a destabilizer, depending on other factors.

Our professor had written several papers on the infamous 1940 Tacoma Narrows Bridge collapse, having helped produce a digital model of it in the 60’s.

8

I would think that integer truncation could cause a player’s calculated rating to oscillate between, say, 1806 and 1807 indefinitely, but that floating point would likely damp the oscillation and eventually stabilize, at least to within 2 or 3 decimal places.

Bill Smythe

9

The bonus factor would probably be the most significant factor in converging vs unstable systems, multiple passes in an integer-based system might lead to what Conway called stoplight patterns.

10

I would say that bonus points, ratings, etc should all be done in floating point, then converted to integer at the final stage only.

Bill Smythe

11

Hey, Bill, it’s 2020, ratings have been kept in floating point since, um, September of 2014. They’re converted to integers for posting on MSA and in the ratings supplements.

12

I guess what I’m saying is, it seems possible that all of the oscillation that Mark Glickman speaks of as having occurred in tests around the year 2000 might have been due to integer truncation, and that if the same multi-pass tests were tried again in today’s floating point system, there might not be an oscillation problem at all because it might all damp out.

Bill Smythe

13

Actually, the issue is with players with b/0 rating initializations. If everyone has positive prior games, the system is stable. If everyone has b/0 priors, there is no single solution. The added initial pass with b/1 for everyone with b/0 priors tacks the levels down a bit, but they still move a lot during passes 1 and 2 (as a result of the 400 point cutoffs) and are often still moving, generally to rather extreme values if you do more than 2 passes.