Discussion:
Assessment of the skill component in backgammon
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Paul Epstein
2020-06-17 12:30:09 UTC
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What is the minimum match length required so that the probability of
a PR 3.0 player beating a PR 7.0 player is >= 95%?

Why am I asking?
I'm interested in assessing the luck and skill components.
If we consider a 7 as an average player, and assume that the world's
best play at around a 3, and if we consider 95% + as "almost certain",
then it seems a useful measure -- "How long do we need to make the
matches such that the world's best are almost certain to beat the
mediocrities?"

Thanks for your help.

Paul
Wally
2020-06-17 12:39:57 UTC
Permalink
Post by Paul Epstein
What is the minimum match length required so that the probability of
a PR 3.0 player beating a PR 7.0 player is >= 95%?
Why am I asking?
I'm interested in assessing the luck and skill components.
If we consider a 7 as an average player, and assume that the world's
best play at around a 3, and if we consider 95% + as "almost certain",
then it seems a useful measure -- "How long do we need to make the
matches such that the world's best are almost certain to beat the
mediocrities?"
Thanks for your help.
Paul
A don't think a PR 7 player exactly qualifies as a mediocrity. That was the error rate of many world-class players before the bots came along.

Having said that, and just guessing here, I'd peg it at about a 1000-point match. (And if forced to bet I'd take the over.)
Paul Epstein
2020-06-17 13:22:03 UTC
Permalink
Post by Wally
Post by Paul Epstein
What is the minimum match length required so that the probability of
a PR 3.0 player beating a PR 7.0 player is >= 95%?
Why am I asking?
I'm interested in assessing the luck and skill components.
If we consider a 7 as an average player, and assume that the world's
best play at around a 3, and if we consider 95% + as "almost certain",
then it seems a useful measure -- "How long do we need to make the
matches such that the world's best are almost certain to beat the
mediocrities?"
Thanks for your help.
Paul
A don't think a PR 7 player exactly qualifies as a mediocrity. That was the error rate of many world-class players before the bots came along.
Having said that, and just guessing here, I'd peg it at about a 1000-point match. (And if forced to bet I'd take the over.)
When I played regularly against XG, I was always disappointed to perform
worse than a 7.0. I think I'm stronger than a 7.0 but I don't know.
So I'm assuming that I'm a mediocrity myself.

Paul
Bradley K. Sherman
2020-06-17 12:41:13 UTC
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Post by Paul Epstein
What is the minimum match length required so that the probability of
a PR 3.0 player beating a PR 7.0 player is >= 95%?
...
13

--bks
Tim Chow
2020-06-18 15:32:06 UTC
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Post by Paul Epstein
What is the minimum match length required so that the probability of
a PR 3.0 player beating a PR 7.0 player is >= 95%?
There's not enough data to answer this question with any confidence.

However, don't let facts stop you. Let's go ahead and take two commonly
used heuristics as the gospel truth:

1. Rating difference is a linear function of PR difference; in particular,
a 3 PR difference is about 100 Elo points.

2. https://bkgm.com/faq/Ratings.html#rating_formula

Then if you go to some site with a rating calculator---

http://www.netadelica.com/bg/fibscalc.html

---you'll find that the answer to your question is about 400. Even better,
you can program up the formula yourself and calculate the match length to
4 decimal places.

---
Tim Chow
Paul Epstein
2020-06-18 17:12:27 UTC
Permalink
Post by Tim Chow
Post by Paul Epstein
What is the minimum match length required so that the probability of
a PR 3.0 player beating a PR 7.0 player is >= 95%?
There's not enough data to answer this question with any confidence.
However, don't let facts stop you. Let's go ahead and take two commonly
1. Rating difference is a linear function of PR difference; in particular,
a 3 PR difference is about 100 Elo points.
2. https://bkgm.com/faq/Ratings.html#rating_formula
Then if you go to some site with a rating calculator---
http://www.netadelica.com/bg/fibscalc.html
---you'll find that the answer to your question is about 400. Even better,
you can program up the formula yourself and calculate the match length to
4 decimal places.
400 fits quite well with my intuition. I would probably have guessed 100.

Thanks.

Paul

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