Updated FargoRates are out

mikepage said:

The uncertainty in the ratings is a complicated problem. It's not like the uncertainty in the outcome after a certain number of coin flips or bernoulli trials--though we do expect some relation to that. A single game against a similarly rated opponent carries more information than does a single game against a much stronger or much weaker opponent. A game against an opponent who has 600 games in the system carries more information than a game against an opponent who has 300 games or 30 games. A game against an unrated opponent tells nothing about you.

(Brief gobblygook in this paragraph and then it gets understandable again next paragraph). What we maximize is the log-likelihood function, and that gives us the MLE (Maximum Likelihood Estimates) for the ratings. The Hessian matrix--the second derivative of log-likelihood--evaluated at the optimum ratings is what is called the observed Fisher Information Matrix. There is a theorem (Cramer Rao Bound) that relates the diagonal elements of the inverse of the Hessian to the variances/covariances--that's where we are going, analyzing that. But we're not there yet.

In the meantime we can get some brute force estimates of the standard errors under actual conditions. Here is an example. We took a player who has played a very large number of games (5500) in the last two years and has a rating of 622. Then we can take a random sampling of, say, 200 of those games and compute a rating just based on the 200 games. Then we do this many times. What we find is the standard error (standard deviation) of the 200-game rating is about 20 points.

That suggests when a rating is based on 200 games, just at the threshold of what we refer to as "established," it has about a two-thirds chance of being within 20 points of the "true" rating and about a 95% chance of being within 40 points.

These intervals decrease as you log more games with the square root of the number of games. So if you want to cut the uncertainty in half (68% chance you are within 10 points and 95% chance you are within 20 points) you have to go to 800 games.

The average number of games for players on the top 100 list is 3000. So in general when you look at those numbers it is fair to think of them as probably (68%) right within 5 points. And someone fairly new--like Aranas--is probably right within 10 points.

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poolscholar said:

Sorry my stats aren't super strong. So in the top 100 there are probably 5 players off by 3 or more standard deviations?

which at 3000 games would be at least 20 points off the real

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JohnnyOzone said:

I agree with everything you are saying, but I would submit to you therefore that the pros should be playing a different game where the break shot is not such a huge part of the result of the match, if the true aim is to determine who is the better player ( since 9 ball, and to a lesser extent 10 ball, mostly only proves who is the better breaker)

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Poolplaya9 said:

Have you ever used good reading and comprehension before? You didn’t this time. I didn’t say every single rack would be absolutely perfect (not that they necessarily are with the magic rack either, and not that it couldn't be possible with the triangle and good balls, good table, and good racker). What I said is that both players would be getting the same racks as each other with a neutral racker. Even if both players were making their best effort, the racks from two different people are never going to be as similar as the racks from just one person. That’s not nonsense, that’s a fact. And if one of the people had a different racking goal than the other (which always has a reasonably high likelihood of happening in a big gambling match), like say one was attempting to manipulate the rack while other was not, then they would be even less similar yet. Any way you cut it racks from only one person are going to be more similar to each other than racks from two different people and this holds true with any rack although some will show more difference than others.

On a side note I could have also suggested the neutral racker use the magic rack, which would have also given both sides the same racks as each other, and I don’t have a huge problem with that, but I suggested the triangle rack because I think it gives a much better chance for pool skills to determine the winner here, particularly in 9 ball and particularly when one of them is known for their prowess in reading/breaking the magic rack. It’s just too easy for somebody to figure out a great break for the magic rack, make the same ball in the same pocket over and over, often leaving very similar and easy patterns over and over, and that just wouldn’t tell you much of anything about who the better player is, and that was the whole point, to make a statement about who the better player is.

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donuteric said:

Thank you for the excellent explanation. Out of curiosity, if you find an estimator that does not attain the min variance of CRLB, what do you do?

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PoppaSaun said:

The chances of that are about 0.2%. That would basically be akin to a person who normally runs 3 balls winning the Open without losing a match.

Being off by 3σ would be a statistical anomaly.

The standard deviation refers to each person's statistics. Thus, the standard deviation is different for every person, depending on the quality and amount of results.

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poolscholar said:

[...]

So 5% of the top 100 might be off by 15 points plus or minus on average.

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mikepage said:

The 5% refers to the fraction expected to be off by TWO standard deviations (10 points)

15 points is THREE standard deviations, and only a few in a thousand (and none out of 100) are expected to be off by this much.

[once again referring to players with about 3,000 games]

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RonRosas said:

Bar Box Money Game King Alex Pagulayan Sky Woodward

Alex will be playing Sky Woodward using a Bulletproof Break Tip and my money was on Alex, but now Sky is using BulletProof Break Tips too! These things are insane!!!!!!!!!!
Better than Toam, Icebreaker, or any of these Phenolic Tips and more control than a hard leather Samsara!
Bulletproofbreaktips.com
https://youtu.be/9ymPT7K8efU
https://www.ebay.com/itm/264428053281

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RonRosas said:

Bar Box Money Game King Alex Pagulayan Sky Woodward

Alex will be playing Sky Woodward using a Bulletproof Break Tip and my money was on Alex, but now Sky is using BulletProof Break Tips too! These things are insane!!!!!!!!!!
Better than Toam, Icebreaker, or any of these Phenolic Tips and more control than a hard leather Samsara!
Bulletproofbreaktips.com
https://youtu.be/9ymPT7K8efU
https://www.ebay.com/itm/264428053281

Click to expand...

RonRosas said:

Bar Box Money Game King Alex Pagulayan Sky Woodward

Alex will be playing Sky Woodward using a Bulletproof Break Tip and my money was on Alex, but now Sky is using BulletProof Break Tips too! These things are insane!!!!!!!!!!
Better than Toam, Icebreaker, or any of these Phenolic Tips and more control than a hard leather Samsara!
Bulletproofbreaktips.com
https://youtu.be/9ymPT7K8efU
https://www.ebay.com/itm/264428053281

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u12armresl said:

Ron, how many threads are you going to put the exact same post in about these tips. Fargo, money match, cmon man really?

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MalibuMike said:

Bar Box Money Game King Alex Pagulayan Sky Woodward

Alex will be playing Sky Woodward using a Bulletproof Break Tip and my money was on Alex, but now Sky is using BulletProof Break Tips too! These things are insane!!!!!!!!!!
Better than Toam, Icebreaker, or any of these Phenolic Tips and more control than a hard leather Samsara!
Bulletproofbreaktips.com
https://youtu.be/9ymPT7K8efU
https://www.ebay.com/itm/264428053281

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RiverCity said:

And its the EXACT same post made by Malibu Mike.


https://forums.azbilliards.com/showpost.php?p=6544245&postcount=23

Its almost like its not Ron Rosas posting isnt it? :thumbup:

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RiverCity said:

And its the EXACT same post made by Malibu Mike.


https://forums.azbilliards.com/showpost.php?p=6544245&postcount=23

Its almost like its not Ron Rosas posting isnt it? :thumbup:

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jasonlaus said:

Ya'll talked shit when I brought up his bullsgit before

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