What would top players Usatt rating be?

[TensorBackhand]

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. For instance, if the standard deviation is 50, and the player's rating is 1050, then there is a 68% change that their ranking is between 1000 and 1100, and a 95% chance of being between 950 and 1150. In practice, those with a smaller standard deviation have a more accurate rating than those with a higher standard deviation.

Also, players that win/lose, if they have a higher standard deviation, their ratings points will go up or down further than those that play league multiple times a week.

Ratings Central have an explicit probability of an upset, based on the rating (playing strength). For instance, a player ranked 200 points lower has roughly a 5% chance of winning. Obviously the volatility mentioned above will make this much less perfect than this function portrays:

Some may argue that this is what happens when you let mathematicians run the show lol, but at least it attempts to factor in the volatility.

More info for those that are curious:

How the Rating System Works

How the rating system works.

www.ratingscentral.com

Theoretically, the win % would be similar... however, as Dr Evil mentioned, there's no factoring in for volatility... besides the examples he gave, there's also the case where lower ranked players have more obvious weaknesses that mean some matchups don't suit them (e.g. not handling pimples or slow spinny loops). Whereas higher ranked players are more robust to different styles, so you'll see less upsets.

Also, the USATT ratings system is about as simple as you can get, getting an explicit win % is futile without considering volatility. You could infer the win % based on the USATT formula, but it's extremely crude. For instance, if the difference in ratings is between 188 and 212, if the expected winner wins, then the players exchange 1 point, and if they lose, then 40 points is exchanged. You could do 1/40 = 2.5% as the winning percentage, but really, this is definitely not reliable because of the volatility.

So to answer your question, 2.5% for both scenarios, with between 0-100% accuracy 🤣

More info on the USATT ratings system:

https://usatt.simplycompete.com/info/ratings

Good thing is you're trying to provide mathematics to provide an answer. So according to their model, a 200pt deficit would approximate a 5% chance of upset. A 100 pt deficit would approximate 20% chance of upset. Sounds reasonable, although slightly lower than I would have guessed.

 

[PoppaChubby]

I didn't quite follow every post
your whole fancy calculation has it at 24%
then it became 15%
is it now at 2%?

When I said in France a 1300 could win a 1500, it's actually right here: the 1 over 4 chances. So it happens a lot more. An FFTT 1300 = USATT 1800 and an FFTT 1500=USATT 2000. You're in the middle class here in France, as the average level is way higher than in the US. The normal/average club here always have at least 4 or 5 guys rated FFTT 1700/1800 + one or two 1900. You start being in the best 1000 players at 2000/2100.

Now the only FFTT 1900s I've seen beating FFTT 2100/2200 were kids in Pôle Espoir (young talent FFTT academies all over the clountry) beating 2100 in their 40's, means somewhere 2300 young talents USATT beating old 2500/2600 USATT. You can see that in Pre-Nationale, Nationale 2 tier 4-5 leagues, and now it's being serious. But then it happens maybe once or twice a month, not once or twice each week like in the PR, R3, R2.

 

[McSmasher]

Good thing is you're trying to provide mathematics to provide an answer. So according to their model, a 200pt deficit would approximate a 5% chance of upset. A 100 pt deficit would approximate 20% chance of upset. Sounds reasonable, although slightly lower than I would have guessed.

yeah it's really tough to gauge how likely an upset would be based purely on the rating. For instance, both Anders Lind and Dima Ovtcharov have recently played in the German league, so their ratings are on Ratings Central:

• Anders Lind is rated 2663. However, since his standard deviation is 61, his rating has a 68% chance of being between 2602 and 2724 (https://www.ratingscentral.com/Player.php?PlayerID=45119)
• Dima is rated 2753. However, since his standard deviation is 59, his rating has a 68% chance of being between 2694 and 2812 (https://www.ratingscentral.com/Player.php?PlayerID=9864)

Even though there's a 90 point difference between Anders and Dima, Anders' rating upper limit (2724) is higher than Dima's lower limit (2694)... so unless they're both playing 10+ singles matches a week, the rating will only really be vaguely accurate.

USATT doesn't cover any of these nuances, so I'd take these ratings with a grain of salt.

 

[PoppaChubby]

Theoretically, the win % would be similar... however, as Dr Evil mentioned, there's no factoring in for volatility... besides the examples he gave, there's also the case where lower ranked players have more obvious weaknesses that mean some matchups don't suit them (e.g. not handling pimples or slow spinny loops). Whereas higher ranked players are more robust to different styles, so you'll see less upsets.

Also, the USATT ratings system is about as simple as you can get, getting an explicit win % is futile without considering volatility. You could infer the win % based on the USATT formula, but it's extremely crude. For instance, if the difference in ratings is between 188 and 212, if the expected winner wins, then the players exchange 1 point, and if they lose, then 40 points is exchanged. You could do 1/40 = 2.5% as the winning percentage, but really, this is definitely not reliable because of the volatility.

So to answer your question, 2.5% for both scenarios, with between 0-100% accuracy 🤣

More info on the USATT ratings system:

https://usatt.simplycompete.com/info/ratings

This is the problem with ELO rating modified in the USATT: volatility. Now with more years and more experience of what the FFTT and the WTT have shown us, the inflationist rating seems better: it shows to non-expert people WHY actually Félix is so much better now than Simon, or why WCQ and LSD dominates so much. You have to be an expert in ratings to understand why Carlsen almost never loose with so few difference in ratings, I mean... with an FFTT or WTT rating, the guy would be the actual SYS of chess.

 

[PoppaChubby]

yeah it's really tough to gauge how likely an upset would be based purely on the rating. For instance, both Anders Lind and Dima Ovtcharov have recently played in the German league, so their ratings are on Ratings Central:

• Anders Lind is rated 2663. However, since his standard deviation is 61, his rating has a 68% chance of being between 2602 and 2724 (https://www.ratingscentral.com/Player.php?PlayerID=45119)
• Dima is rated 2753. However, since his standard deviation is 59, his rating has a 68% chance of being between 2694 and 2812 (https://www.ratingscentral.com/Player.php?PlayerID=9864)

Even though there's a 90 point difference between Anders and Dima, Anders' rating upper limit (2724) is higher than Dima's lower limit (2694)... so unless they're both playing 10+ singles matches a week, the rating will only really be vaguely accurate.

USATT doesn't cover any of these nuances, so I'd take these ratings with a grain of salt.

Pitch, the best player in the US now, is rated 4036 in France, and Alexis is 4386. The last match shows the difference.
Xiang Peng is 4354, Félix 4434, Peng has already beaten Félix, then félix has beaten Peng in WTT Montpellier. Quadri is 4366, both have beaten félix with less than 100 pts rating difference, when at the same time Alexis has literally torn Pitch in pieces with nearly a 400 pts difference. It makes everything way more easier to understand for everyone.

 

[NextLevel]

Pitch, the best player in the US now, is rated 4036 in France, and Alexis is 4386. The last match shows the difference.
Xiang Peng is 4354, Félix 4434, Peng has already beaten Félix, then félix has beaten Peng in WTT Montpellier. Quadri is 4366, both have beaten félix with less than 100 pts rating difference, when at the same time Alexis has literally torn Pitch in pieces with nearly a 400 pts difference. It makes everything way more easier to understand for everyone.

You don't live in the US, when you say that Pitch is the best player in the US right now, you need to be specific - best player where and by what measure?

 

[TensorBackhand]

This is the problem with ELO rating modified in the USATT: volatility. Now with more years and more experience of what the FFTT and the WTT have shown us, the inflationist rating seems better: it shows to non-expert people WHY actually Félix is so much better now than Simon, or why WCQ and LSD dominates so much. You have to be an expert in ratings to understand why Carlsen almost never loose with so few difference in ratings, I mean... with an FFTT or WTT rating, the guy would be the actual SYS of chess.

Yeah I always wondered why Carlsen's rating is only a bit higher than the next player

 

[Dr Evil]

Sorry, what I meant to say is:

What is the win % for a 1600 with a 200 deficit (1800 opponent)?

What is the win % for a 2200 with a 200 deficit (2400 opponent)?

Short answer: A standard Elo formula predicts about a 25% chance for the lower rated player to win in both cases. Adjusting for rating level in a principled way (see long answer) might improve the expected win rate for the 1600 player to about 30%, and knock down the 2200 player's chance to about 15%.

Long answer: The standard Elo formula for calculating the expected win probability of player A against player B is: E(a) = 1 / (1 + 10^((Rb - Ra) / 400)), where Ra is player A's rating and Rb is player B's rating.

The only variable in the formula is the ratings difference (Rb - Ra), so the absolute ratings of the players are ignored. A 2800 vs 3000 match gives the same expected win rate as an 800 vs 1000 match. For a 200 point rating difference E(a) is 1 / (1 + 10^(1/2)) = 0.24, so the weaker player is expected to win just under 1 out of 4 times. This is unrealistic for both 800 vs 1000 (a close to even money bet) and 2800 vs 3000 (overwhelming odds on favorite).

It’s interesting to estimate where this naive calculation is most accurate. Where on the US ratings ladder would you expect a -200 player to win 1 out of 4 times? This would be the point where performance variance has the smallest effect on the expected win rate calculation. I’d put it somewhere between 1600 and 2000. Probably 1800 (so estimating 1700 beats 1900 about 1 out 4 times). Not very confident in this estimate, just my best guess.

To correct for typical level correlated performance variance, we have to incorporate that variance into the expected win probability formula. So together with ratings, Ra and Rb, we also include measures of variance/standard deviations, Sigma-a and Sigma-b, each calculated from the ratings Ra and Rb of the players. This involves a little more math and a number of assumptions.

We need to map a sigma value to each rating level, and then make a statistical model that generates an expected win probability formula based on the R and sigma values for each player. Typical assumptions: (1) Ratings based player performance in a given match is drawn from a normal distribution, so you can use the appropriate cumulative distribution function, (2) sigma can be meaningfully calculated in a rating-dependent way for example by setting a fairly arbitrary variance minimum for elite players, a maximum for low-rated players, and a midpoint rating such as 1800 which will be the inflection point of (3) an again somewhat arbitrary function that ensures a smooth curve between minimum and maximum, such as sigma(R) = sigma(min) + an exponential function of the sigma range and the difference between R and the midpoint rating. While the choice of minimum, maximum, midpoint, etc., is somewhat arbitrary, it can be refined using empirical match data, especially from rating systems with large player pools.

 

[TensorBackhand]

Short answer: A standard Elo formula predicts about a 25% chance for the lower rated player to win in both cases. Adjusting for rating level in a principled way (see long answer) might improve the expected win rate for the 1600 player to about 30%, and knock down the 2200 player's chance to about 15%.

Long answer: The standard Elo formula for calculating the expected win probability of player A against player B is: E(a) = 1 / (1 + 10^((Rb - Ra) / 400)), where Ra is player A's rating and Rb is player B's rating.

The only variable in the formula is the ratings difference (Rb - Ra), so the absolute ratings of the players are ignored. A 2800 vs 3000 match gives the same expected win rate as an 800 vs 1000 match. For a 200 point rating difference E(a) is 1 / (1 + 10^(1/2)) = 0.24, so the weaker player is expected to win just under 1 out of 4 times. This is unrealistic for both 800 vs 1000 (a close to even money bet) and 2800 vs 3000 (overwhelming odds on favorite).

It’s interesting to estimate where this naive calculation is most accurate. Where on the US ratings ladder would you expect a -200 player to win 1 out of 4 times? This would be the point where performance variance has the smallest effect on the expected win rate calculation. I’d put it somewhere between 1600 and 2000. Probably 1800 (so estimating 1700 beats 1900 about 1 out 4 times). Not very confident in this estimate, just my best guess.

To correct for typical level correlated performance variance, we have to incorporate that variance into the expected win probability formula. So together with ratings, Ra and Rb, we also include measures of variance/standard deviations, Sigma-a and Sigma-b, each calculated from the ratings Ra and Rb of the players. This involves a little more math and a number of assumptions.

We need to map a sigma value to each rating level, and then make a statistical model that generates an expected win probability formula based on the R and sigma values for each player. Typical assumptions: (1) Ratings based player performance in a given match is drawn from a normal distribution, so you can use the appropriate cumulative distribution function, (2) sigma can be meaningfully calculated in a rating-dependent way for example by setting a fairly arbitrary variance minimum for elite players, a maximum for low-rated players, and a midpoint rating such as 1800 which will be the inflection point of (3) an again somewhat arbitrary function that ensures a smooth curve between minimum and maximum, such as sigma(R) = sigma(min) + an exponential function of the sigma range and the difference between R and the midpoint rating. While the choice of minimum, maximum, midpoint, etc., is somewhat arbitrary, it can be refined using empirical match data, especially from rating systems with large player pools.

But did you see the ratingscentral article and upset graph? It was suggesting a 5% upset chance

 

[Dr Evil]

But did you see the ratingscentral article and upset graph? It was suggesting a 5% upset chance

Saw the graph, but read the article a long time ago. If I recall correctly, he doesn't use the standard formula. *And I think his approach is quite a bit better.

 

[lightspin]

OMG I cannot believe people are still claiming a 2200 player has a 20% or 25% chance to win against a 2400 player. Have you ever seen a 2400 player play a 2200 player? It is usually a massacre.

Forget that though. 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. So each time the 2200 player wins he gets 40 points, each time the 2400 player wins he gets 1 point. If they played 41 times for their ratings to remain the same, the 2200 player would win exactly once. What happens after 41 matches? If things happen according to what is expected, the 2200 player is still 2200 and the 2400 is still 2400.

Now lets suppose the 2200 player actually has a 1/4 chance of winning. Every 4 matches he would score 37 points, and the 2400 player loses 37 points. Is that stable? Not at all. After 8 matches one would expect the 2200 player to magically be close to 2300 from below and the 2400 player is magically close to 2300 from above. But the whole point of the rating system is to keep the points stable if the players level remains stable. With a 25% chance, the ratings are anything but stable even after 8 matches.

TLDR: the ratings system is designed such that a 200 point gap means an around 2% chance of winning so the entire ratings system remains stable. If you want an exact mathematical analysis, someone message HEAVYSPIN. The only thing that hits harder than his forehand loop is his explaining rigorous mathematical truths.

 

[TensorBackhand]

OMG I cannot believe people are still claiming a 2200 player has a 20% or 25% chance to win against a 2400 player. Have you ever seen a 2400 player play a 2200 player? It is usually a massacre.

Forget that though. 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. So each time the 2200 player wins he gets 40 points, each time the 2400 player wins he gets 1 point. If they played 41 times for their ratings to remain the same, the 2200 player would win exactly once. What happens after 41 matches? If things happen according to what is expected, the 2200 player is still 2200 and the 2400 is still 2400.

Now lets suppose the 2200 player actually has a 1/4 chance of winning. Every 4 matches he would score 37 points, and the 2400 player loses 37 points. Is that stable? Not at all. After 8 matches one would expect the 2200 player to magically be close to 2300 from below and the 2400 player is magically close to 2300 from above. But the whole point of the rating system is to keep the points stable if the players level remains stable. With a 25% chance, the ratings are anything but stable even after 8 matches.

TLDR: the ratings system is designed such that a 200 point gap means an around 2% chance of winning so the entire ratings system remains stable. If you want an exact mathematical analysis, someone message HEAVYSPIN. The only thing that hits harder than his forehand loop is his explaining rigorous mathematical truths.

Do you have a source that shows the 2% figure you claim?

The other guy posted a graph and documentation, suggesting 5%. It's a lot easier to believe him than you because he is providing an actual documented source.

5% is still very low. But losing 1 in 20 matches is a world apart from losing 1 in 50 matches.

 

[McSmasher]

Do you have a source that shows the 2% figure you claim?

The other guy posted a graph and documentation, suggesting 5%. It's a lot easier to believe him than you because he is providing an actual documented source.

5% is still very low. But losing 1 in 20 matches is a world apart from losing 1 in 50 matches.

To be clear, the 5% per 200 ratings points is for Ratings Central, not USATT, so hard to compare.

At the end of the day, table tennis is a competitive sport. If I'm playing someone 200 ratings points higher than me, for the 15-30 minutes that I'm playing I'd be expecting my win % to be 100%... after I (most likely) lose, I'll shake hands and say "just wait till next time" haha

 

[Sland]

While I appreciate this post and TB's contributions to our comsumption and entertainment, I really think that an objective analysis around where the conversation steered into trying to bring elo math into human sporting is just extremely difficult and can't be qualified.

Math in sporting is definitely a real thing- look at the booming sports betting industry- all math. But also completely different.

The elo system and chess I feel are great when the environment is controlled and extremely similar across all games played. With table tennis, I feel like there are just way too many external factors (humidity, lightning, air density, flooring, ball type, cameras flashing in the crowd, playing with injuries, etc) that contribute to play and outcomes for them to be debatable around this idea that they mean more than just a quick understanding around where the level of player is.

This explains all the the upsets (like wcq losing to BF) and other examples that tb's is saying don't quite add up when viewed in real time.

Anyways, carry on but I'm not expecting much else

 

[TensorBackhand]

While I appreciate this post and TB's contributions to our comsumption and entertainment, I really think that an objective analysis around where the conversation steered into trying to bring elo math into human sporting is just extremely difficult and can't be qualified.

Math in sporting is definitely a real thing- look at the booming sports betting industry- all math. But also completely different.

The elo system and chess I feel are great when the environment is controlled and extremely similar across all games played. With table tennis, I feel like there are just way too many external factors (humidity, lightning, air density, flooring, ball type, cameras flashing in the crowd, playing with injuries, etc) that contribute to play and outcomes for them to be debatable around this idea that they mean more than just a quick understanding around where the level of player is.

This explains all the the upsets (like wcq losing to BF) and other examples that tb's is saying don't quite add up when viewed in real time.

Anyways, carry on but I'm not expecting much else

My assumption was that elo predictions are well documented and mathematically provable questions. I thought someone with knowledge would be able to answer definitively quite easily.

But i still havent found a definitive authoratative answer.

Just a lot of "trust me bro, i can win 50 matches easy"

 

[lightspin]

I tried to explain to you where the 2% number came from. If you want to be nit-picky, it is 2.5%. Let me try again.

Suppose someone has a rating of 2200. He plays someone whose rating is 2400. Their rating difference is 200 points.

The USATT has decided that if the lower rated player wins, they get 40 points and the higher rated player loses 40 points.
The USATT has decided that if the lower rated player loses, the higher rated player gets 1 point and the lower rated player loses 1 point.
The USATT wants their rating system to be stable. They do not want rating deflation or inflation to happen over time. That means, if the 2400 player plays the 2200 player trillions of times, the 2400 player will remain 2400 and the 2200 will remain 2200. 2400 is bigger than 2200. The 2400 player is expected to win more than the 2200 player.
Now the question is, how much more if the 2200 and 2400 players level does not change over time?
Let x = the number of times they play where the 2200 player wins and y be the number of times he loses.
The 2200 players rating after playing (x + y) games is 2200 + 40x - 1y.
Now let x and y tend to infinity. The only way for the number 2200 to stay 2200 is if 40x-1y = 0. ERGO
x/y = ratio of wins/loses = 1/40 which is a 2.5% chance of winning.
The same analysis can be done with the 2400 player with his equation being 2400 -40x + 1y. The exact same math says his loss percentage will be 2.5%.
Now if you want to be super anal, you can argue that the ratings change slightly after each match which might change the math slightly but if you go crazy, you will still end up with something close to 2,5%.

That is the math explained simply as possible. The bottom line is if you show me a 2200 player with a 25% chance of beating a 2400 player, that 2200 player is actually 2300 or so. It is an easy exercise for the reader to determine why they are actually 2300 and not 2200. HINT (rating points won by higher player per match)x(number of wins by higher player) - (rating points lost of higher player in an upset per match)x(number of losses of higher player) = 0 as the number of games played tends to infinity. BRO.

There are math papers out there about designing ratings systems for games that are stable. In case anyone is really really interested or bored.

 

[zeio]

The 2% figure is worked out from the USATT rating chart that is likely made up. Other than TTD members, MyTT members have also worked out the probability of win/loss.

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.

The 5% figure for Ratings Central comes "from a fit to data from the current system" as Marcus stated in his paper "New table-tennis rating system", specifically chapters 5. Model and 6. Model development.

 

[Tony's Table Tennis]

why all those theory...
tb, should just enter into a rating tournament 200 points higher than him, and experience it first hand.

 

[Grumms]

Yeah I always wondered why Carlsen's rating is only a bit higher than the next player

Because he's getting old. At some point, Carlsen was almost 100 point higher than the 2nd best player, which is insane. Don't forget that there is draw in chess, and draws are the most common result at high level, which change a loooooot of things for the rating.

 

[David J. Marcus]

The USATT rating system is not Elo. Elo is not the gold standard. Also, the USATT rating system is more than the rating chart: Initial ratings and adjustments make a big difference to the ratings. Chess organizations that use Elo often do more than just use the basic Elo formulas.

In Ratings Central, the probability that the lower-playing-strength player will win is given by the graph on https://www.ratingscentral.com/HowItWorks.php . This should also apply to the USATT rating scale, since I produced the graph by fitting to USATT tournament data. I believe the scale is uniform, i.e., the probabilities apply to players at all levels. The Ratings Central system tries to make this true when it produces the numbers.

Unfortunately, Ratings Central hasn't had access to ITTF data since 2022. Maybe this will change in the future.

The world champion is around 3200 on the Ratings Central scale. Kanak Jha plays in the German league and that data is in Ratings Central. We have him as around 2700:

Jha, Kanak, Rating History

Events played by Jha, Kanak.

www.ratingscentral.com

On the USATT scale, Kanak Jha would be around 3000. That's just my guess from discussing it with Sean. There is no question that the USATT scale is several hundred points higher than the Ratings Central scale.

The Ratings Central scale is the same as the USATT California (and western states) scale was in the late 1990s. This was 100 points higher than the USATT scale for the rest of the country in the late 1990s.