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### AuthorTopic: Win Probability Calculator  (Read 11808 times)

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#### rrenaud

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##### Re: Win Probability Calculator
« Reply #25 on: December 04, 2012, 12:57:37 am »
+1

More research:

A logistic distribution based ranking system that outperforms trueskill on the trueskill data sets.  (I skipped the math and only skimmed the paper).

http://jmlr.csail.mit.edu/papers/volume12/weng11a/weng11a.pdf

Quote
In fact, most currently used Elo variants
for chess data use a logistic distribution rather than Gaussian because it is argued that weaker players have signiﬁcantly greater winning chances than the Gaussian model predicts.

which is consistent with the exp(-x^2) dropping off faster than exp(-x).
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#### DStu

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##### Re: Win Probability Calculator
« Reply #26 on: December 04, 2012, 03:51:09 am »
+1

Really don't like that statement of wikipedia. Of course in the middle, they can be fitted to be quite similar, but  they behave differently quite soon at the edges.

Even the math discussions devolve into bickering about edge cases

1) If you don't care about the edge cases, it's not math.
2) Bayesian statistics is not an edge case, but the example explicitly given in the wiki article.

Note of course I'm not talking about rating systems here, I have no idea and not thought about what distribution would fit better in this context, if WW says it's logistic I would just believe it. I don't see any reason why it should be Gaussian, as I don't think you are in a regime for Central Limit Theorem here.

Edit: What come's next is not really well thought off:
If the remainings of my understanding of TS is right, I somehow think the model lacks a parameter anyway.  You have mean skill, ok, and the uncertainity of the system on you skill.  Somehow it's maybe reasonable to assume Gaussian on the uncertainity.  But the same distribution is also used to get the winprobabilities given mean and uncertainity (or?), and I don't see any reason why one should do that.
« Last Edit: December 04, 2012, 03:57:15 am by DStu »
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#### SirPeebles

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##### Re: Win Probability Calculator
« Reply #27 on: December 04, 2012, 07:30:42 am »
+2

Really don't like that statement of wikipedia. Of course in the middle, they can be fitted to be quite similar, but  they behave differently quite soon at the edges.

Even the math discussions devolve into bickering about edge cases

1) If you don't care about the edge cases, it's not math.
2) Bayesian statistics is not an edge case, but the example explicitly given in the wiki article.

Note of course I'm not talking about rating systems here, I have no idea and not thought about what distribution would fit better in this context, if WW says it's logistic I would just believe it. I don't see any reason why it should be Gaussian, as I don't think you are in a regime for Central Limit Theorem here.

Edit: What come's next is not really well thought off:
If the remainings of my understanding of TS is right, I somehow think the model lacks a parameter anyway.  You have mean skill, ok, and the uncertainity of the system on you skill.  Somehow it's maybe reasonable to assume Gaussian on the uncertainity.  But the same distribution is also used to get the winprobabilities given mean and uncertainity (or?), and I don't see any reason why one should do that.

It was a joke.  You were literally discussing the edges in the snippet I quoted.
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#### WanderingWinder

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##### Re: Win Probability Calculator
« Reply #28 on: December 04, 2012, 08:21:34 am »
0

Note of course I'm not talking about rating systems here, I have no idea and not thought about what distribution would fit better in this context, if WW says it's logistic I would just believe it. I don't see any reason why it should be Gaussian, as I don't think you are in a regime for Central Limit Theorem here.

To clarify here, I'm not saying that logistic actually fits better necessarily (though every study I've seen done says that it does....), I'm saying that if you have no data and were making a wild guess by pulling a distribution out of thin air, you might well pick logistic, and there's more reason to pick logistic than gaussian. Having said that, what you *actually* want to do of course is going to look at the data available and seeing what both has some logical reasoning behind and very importantly actually fits the data.

To jump off of this, does anyone have some technical skills and/or knowledge of the isotropic data to be able to grab the results of a bunch of games from a given time period? (What I am looking for is ID player 1, ID player 2..., ID player N, and number of points scored by each. Rating would be nice if possible. Dates of game being played would be even nicer. Chronology of games played would be nicest, but probably overkill. And actually I only care about 2 player games here, but I ought to be able to filter that myself). I would like to do some statistical testing if possible....

#### DStu

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##### Re: Win Probability Calculator
« Reply #29 on: December 04, 2012, 08:54:41 am »
+1

It was a joke.  You were literally discussing the edges in the snippet I quoted.

It was too early to understand jokes.
Quote
To jump off of this, does anyone have some technical skills and/or knowledge of the isotropic data to be able to grab the results of a bunch of games from a given time period? (What I am looking for is ID player 1, ID player 2..., ID player N, and number of points scored by each. Rating would be nice if possible. Dates of game being played would be even nicer. Chronology of games played would be nicest, but probably overkill. And actually I only care about 2 player games here, but I ought to be able to filter that myself). I would like to do some statistical testing if possible....
Do you want to give some names and get the stats for them, or do you want to get all the IDs for all players in a given time?
« Last Edit: December 04, 2012, 08:57:45 am by DStu »
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#### ipofanes

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##### Re: Win Probability Calculator
« Reply #30 on: December 04, 2012, 09:15:32 am »
0

It's odd really.  I know logistic functions well from teaching so many semesters of differential equations, but I never used them elsewhere when I was a student, nor do I ever use them in my research.  I hope that some of you use this stuff, and that it's more than just a contrived plaything for my students.

Next time you can tell your students that the logistic function is used day in day out in statistical analysis. Don't now anything about TrueSkill but the rehashed Elo number uses the logistic distribution: http://en.wikipedia.org/wiki/Elo_rating_system#Implementing_Elo.27s_scheme

Also, genetic linkage: http://en.wikipedia.org/wiki/Genetic_linkage#LOD_score_method_for_estimating_recombination_frequency
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#### Kirian

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##### Re: Win Probability Calculator
« Reply #31 on: December 04, 2012, 11:33:48 am »
0

Highlight the OP text,

Quote
Hey, I was bored and I'm a huge nerd so I made a series win probability calculator in excel. It's still mostly functional in google docs and open office if you don't have excel.

Just plug in each player's mean skill and who goes first. Also you can adjust the first turn advantage parameter.

And then bring your cursor to the right.  You should get the attachment from chrome.

Got nuttin'.  Weird.

Edited:  Ohhhhhh.  You meant click-and-drag to the right.  That's quite a bit difference.

Also, genetic linkage: http://en.wikipedia.org/wiki/Genetic_linkage#LOD_score_method_for_estimating_recombination_frequency

Since I'm not seeing the word logistic in there, are you willing to explain how OD/LOD is related to the logistic function?  I did linkage analysis for about a year and a half and always simply treated it as a Bayesian probability analysis.  (Granted, the word Bayesian isn't in that article either, which makes me less than impressed with that WP article).
« Last Edit: December 04, 2012, 01:10:41 pm by Kirian »
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#### DStu

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##### Re: Win Probability Calculator
« Reply #32 on: December 04, 2012, 12:08:50 pm »
0

Since I'm not seeing the word logistic in there, are you willing to explain how OD/LOD is related to the logistic function?  I did linkage analysis for about a year and a half and always simply treated it as a Bayesian probability analysis.  (Granted, the word Bayesian isn't in that article either, which makes me less than impressed with that WP article).

Without clicking the link:
It's still Bayesian, you just have different underlying distributions in your model.
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#### Kirian

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##### Re: Win Probability Calculator
« Reply #33 on: December 04, 2012, 01:04:20 pm »
0

Since I'm not seeing the word logistic in there, are you willing to explain how OD/LOD is related to the logistic function?  I did linkage analysis for about a year and a half and always simply treated it as a Bayesian probability analysis.  (Granted, the word Bayesian isn't in that article either, which makes me less than impressed with that WP article).

Without clicking the link:
It's still Bayesian, you just have different underlying distributions in your model.

OK... I think I see what it is.  Doing genetics work I didn't really think of there being a "distribution" per se.  I guess the distribution is a distribution of [recombination frequency](x, y) over all pairs (x, y)?  But I can only imagine that would be exponentially distributed.
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#### Watno

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##### Re: Win Probability Calculator
« Reply #34 on: December 04, 2012, 01:07:27 pm »
0

So happy i chose not to take the Intrdoduction to Proability Theory lecture.
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#### WanderingWinder

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##### Re: Win Probability Calculator
« Reply #35 on: December 04, 2012, 01:27:21 pm »
0

It was a joke.  You were literally discussing the edges in the snippet I quoted.

It was too early to understand jokes.
Quote
To jump off of this, does anyone have some technical skills and/or knowledge of the isotropic data to be able to grab the results of a bunch of games from a given time period? (What I am looking for is ID player 1, ID player 2..., ID player N, and number of points scored by each. Rating would be nice if possible. Dates of game being played would be even nicer. Chronology of games played would be nicest, but probably overkill. And actually I only care about 2 player games here, but I ought to be able to filter that myself). I would like to do some statistical testing if possible....
Do you want to give some names and get the stats for them, or do you want to get all the IDs for all players in a given time?
I need all the IDs - can be names, can be some ID number, I don't know what iso gives. But if I want to make an overall good system, I need all of them, not just some players. Or at least all with over some minimum threshhold of games.

#### DStu

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##### Re: Win Probability Calculator
« Reply #36 on: December 04, 2012, 01:57:49 pm »
0

It was a joke.  You were literally discussing the edges in the snippet I quoted.

It was too early to understand jokes.
Quote
To jump off of this, does anyone have some technical skills and/or knowledge of the isotropic data to be able to grab the results of a bunch of games from a given time period? (What I am looking for is ID player 1, ID player 2..., ID player N, and number of points scored by each. Rating would be nice if possible. Dates of game being played would be even nicer. Chronology of games played would be nicest, but probably overkill. And actually I only care about 2 player games here, but I ought to be able to filter that myself). I would like to do some statistical testing if possible....
Do you want to give some names and get the stats for them, or do you want to get all the IDs for all players in a given time?
I need all the IDs - can be names, can be some ID number, I don't know what iso gives. But if I want to make an overall good system, I need all of them, not just some players. Or at least all with over some minimum threshhold of games.
And probably you want the results of the match of ID1 vs ID2, or just the (relative) number of wins of ID1?
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#### WanderingWinder

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##### Re: Win Probability Calculator
« Reply #37 on: December 04, 2012, 02:00:53 pm »
+1

It was a joke.  You were literally discussing the edges in the snippet I quoted.

It was too early to understand jokes.
Quote
To jump off of this, does anyone have some technical skills and/or knowledge of the isotropic data to be able to grab the results of a bunch of games from a given time period? (What I am looking for is ID player 1, ID player 2..., ID player N, and number of points scored by each. Rating would be nice if possible. Dates of game being played would be even nicer. Chronology of games played would be nicest, but probably overkill. And actually I only care about 2 player games here, but I ought to be able to filter that myself). I would like to do some statistical testing if possible....
Do you want to give some names and get the stats for them, or do you want to get all the IDs for all players in a given time?
I need all the IDs - can be names, can be some ID number, I don't know what iso gives. But if I want to make an overall good system, I need all of them, not just some players. Or at least all with over some minimum threshhold of games.
And probably you want the results of the match of ID1 vs ID2, or just the (relative) number of wins of ID1?
I don't understand your question. I want the results of every game, most preferably in this format:
ID1                ID2                         Number of wins for ID1
dummy1         dummy2                  1
dummyA         dummyB                  0
dummy2         dummyA                  0.5

etc. etc.

#### DStu

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##### Re: Win Probability Calculator
« Reply #38 on: December 04, 2012, 02:08:10 pm »
0

It was a joke.  You were literally discussing the edges in the snippet I quoted.

It was too early to understand jokes.
Quote
To jump off of this, does anyone have some technical skills and/or knowledge of the isotropic data to be able to grab the results of a bunch of games from a given time period? (What I am looking for is ID player 1, ID player 2..., ID player N, and number of points scored by each. Rating would be nice if possible. Dates of game being played would be even nicer. Chronology of games played would be nicest, but probably overkill. And actually I only care about 2 player games here, but I ought to be able to filter that myself). I would like to do some statistical testing if possible....
Do you want to give some names and get the stats for them, or do you want to get all the IDs for all players in a given time?
I need all the IDs - can be names, can be some ID number, I don't know what iso gives. But if I want to make an overall good system, I need all of them, not just some players. Or at least all with over some minimum threshhold of games.
And probably you want the results of the match of ID1 vs ID2, or just the (relative) number of wins of ID1?
I don't understand your question.
Obviously you don't need to, because you nevertheless answered it...
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#### rrenaud

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##### Re: Win Probability Calculator
« Reply #39 on: December 04, 2012, 02:14:03 pm »
0

This used to have a data set of size 1.2 million with player names, winning margin, and the kingdom supply.

http://forum.dominionstrategy.com/index.php?topic=20.msg438#msg438

The dataset link isn't going to work now, but I can find some other place to put the data if you'd actually use it.
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#### Kirian

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##### Re: Win Probability Calculator
« Reply #40 on: December 04, 2012, 04:39:59 pm »
0

This used to have a data set of size 1.2 million with player names, winning margin, and the kingdom supply.

http://forum.dominionstrategy.com/index.php?topic=20.msg438#msg438

The dataset link isn't going to work now, but I can find some other place to put the data if you'd actually use it.

How big is the dataset?  If it's <~30MB, I can host it.
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#### ipofanes

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##### Re: Win Probability Calculator
« Reply #41 on: December 06, 2012, 06:51:49 am »
0

Also, genetic linkage: http://en.wikipedia.org/wiki/Genetic_linkage#LOD_score_method_for_estimating_recombination_frequency

Since I'm not seeing the word logistic in there, are you willing to explain how OD/LOD is related to the logistic function?  I did linkage analysis for about a year and a half and always simply treated it as a Bayesian probability analysis.

You can transform the term such that the only factor depending on the random variate, R, is (theta/1-theta)^R, and there you have the logistic term.

Quote
(Granted, the word Bayesian isn't in that article either, which makes me less than impressed with that WP article).

There is a straightforward frequentist interpretation of the LOD score. The customary -3 limit for the lod score directly corresponds with a test level, I am currently to dumb to calculate which one.
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