What would top players Usatt rating be?

[David J. Marcus]

The rating system is designed to be stable in the sense that if an 2200 player played a 2400 for eternity and they remained at the same level, their ratings would remain the same.

It wasn't designed that way. However, at one point in the distant past, someone tried to adjust the ratings chart using that criterion. It never made sense to me: For one thing, it only tells you the ratio of the two numbers. For another, a rating system must adjust ratings as players get better or worse. So, how it behaves if players don't change isn't the key issue. You can immediately see the lack of foundation of the rating chart by asking yourself, Why do you get 8 points if you beat a player of the same rating? Where did this 8 come from? The answer is someone just decided they liked that number.

 

[David J. Marcus]

The 24% figure for Elo rating is derived "using the calculus of statistical probability theory" as Elo stated in his book "The Rating of Chessplayers, Past and Present", specifically chapters 1.4 The Normal Probability Function and 2.1. The Percentage Expectancy Table.

When I read Elo's book, I was not impressed. While he does have a model in there, he doesn't derive the update formula from the model. He spends a lot of his book comparing players through time. His system is not stable enough for those comparisons to be valid.

 

[David J. Marcus]

The USATT wants their rating system to be stable. They do not want rating deflation or inflation to happen over time.

I'm not sure what USATT wants. I suspect no one in authority in USATT has looked at the rating system for some time. While some in USATT may want the ratings to be stable, the ratings are not. The USATT rating system has significant inflation. There is no easy fix for this. It is a result of the lack of memory in the system (and how the adjustments are done).

In the short term, inflation can encourage players to play since the more they play, the higher their rating becomes. However, if there is too much inflation, players figure out that the ratings just mean you played a lot, not that you got better, and stop caring. This has happened to the Canadian rating system in the past.

 

[David J. Marcus]

This is what I like about the Ratings Central ratings. It has some consideration to this volatility (measured as a standard deviation for those maths gurus) such as:

• Juniors / quick improvers that are consistently beating players with a higher ranking
• Players who don't often play leagues / tournaments vs those that play leagues multiple times a week

If a player is consistently beating others with a higher ranking, or don't play leagues often, then their standard deviation will be higher.

Almost everything you wrote is correct. But, "consistently beating others with a higher ranking" doesn't get you a greater standard deviation. The standard deviation just measures how certain we are that we know the player's playing strength. We don't attempt to model individual players.

The 2019 addition of the Poisson jumps to the model lets the system react quickly to rapidly-improving players.

 

[McSmasher]

Almost everything you wrote is correct. But, "consistently beating others with a higher ranking" doesn't get you a greater standard deviation. The standard deviation just measures how certain we are that we know the player's playing strength. We don't attempt to model individual players.

The 2019 addition of the Poisson jumps to the model lets the system react quickly to rapidly-improving players.

yep, my intuition was incorrect... from a non-maths level, I noticed that when people go on a decent undefeated streak, the standard deviation goes higher, which affects how much the rating goes up (and how much it goes down in losses).

Either way, you've developed an excellent points system, great job!

 

[David J. Marcus]

I noticed that when people go on a decent undefeated streak, the standard deviation goes higher

That can happen. But, usually the standard deviation goes down when you play. It depends. If the main part of the player's law was a narrow bump and the results smush that away, then a wider bump may be all that's left. But, usually the results just remove part of the main bump.

 

[David J. Marcus]

Note that even if the ratios in the rating chart matched the probabilities, and you just use the rating chart (i.e., don't do the "adjustments"), this won't ensure that the ratings don't inflate/deflate.

In such a system, the rating chart does not change the total points (summed over all players). So, the total points only change when there are new players (or you remove an existing player). But, most players improve (compared to their initial rating). So, such a system would deflate.

It is hard to justify the numbers in the rating chart. The adjustments are more logical, but because the USATT system has no memory, they often overshoot. The lack of memory is also why the USATT ratings are more volatile than they should be.

Of course, the original Ratings Central algorithm was developed when I was on the USATT Ratings Committee. But, when we were ready to have USATT adopt it, the board had been taken over by foolish people, and they voted to keep the existing, flawed system.

 

[David J. Marcus]

I agree but not even that far, as it's based on the elo system.

Even assuming the USATT system was based on the Elo system (better to say it was inspired by it, i.e., chess has ratings, so table tennis should too and let's use similar numbers), there is no reason why the rating scales should be the same. It is like feet and meters: Not only do you need to pick the units, you also need to pick the origin. That's why we put some videos on https://www.ratingscentral.com/Videos.php so people can see what scale Ratings Central is using.

When we started, I tried to make the scale match the USATT scale, since that was the scale we were familiar with. I posted the ratings from USATT and from my algorithm on my website. Several people in California complained that their ratings from my algorithm were too low. So, we added 100 points to everyone. They stopped complaining.

Since then, the USATT scale has moved three hundred points or so.

 

[David J. Marcus]

This should also apply to the USATT rating scale, since I produced the graph by fitting to USATT tournament data.

To elaborate a bit, I calculated it from the post-tournament ratings in the USATT data set described in my "New table-tennis rating system" paper. I first tried to use the pre-tournament ratings. This gave a rather different graph (greater probability of upset), which didn't work in the algorithm. I soon realized that the post-tournament ratings were closer to the player's actual playing strengths (in the tournaments).

Ratings Central gives the accuracy of each rating, so you could take that into account when trying to predict who will win an upcoming match. But, if you are interested in how often a player with a true level of X will beat a player with a true level of X + Y, then the graph on the website is the best I have. I think it should apply for all X. But, I will agree that low-rated players are probably not as consistent (not sure how to define "low-rated" here).

My guess is the graph still applies to the current USATT rating scale, even though that rating scale has inflated since I last had access to USATT data.