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## Re: [Bug-gnubg] match winning chances

 From: Michael Petch Subject: Re: [Bug-gnubg] match winning chances Date: Tue, 13 May 2008 10:41:29 -0600 User-agent: Microsoft-Entourage/11.4.0.080122

On 5/13/08 9:06 AM, "Thomas Koch" <address@hidden> wrote:

That is exactly what I am searching for. Thank you very much. I suppose that even with a biased cube error rate I will get pretty good results. The rating difference D must be D = R_favorite - R_underdog, right?
Now that you are thinking about recalculating the values submitted by Kees van den Doel, how about integrating the formula into GnuBG? I think that would be quite handy and appreciated by most users!
Thanks for your efforts and good luck with the calculations. I am looking forward to the reviewed formula!

No problem.  Yes, you are correct - the ratings difference is R_Favorite - R _Underdog.

Kees’s calculations are currently computed and displayed in individual match statistics (Not in the player records or relational database). The Match favorite (MWC) is also displayed but it happens to be displayed and computed with a slight twist. If you open up an individual SGF file (Or create a new one), and analyze the match and look at the output you will see something like:

MontyBackgammon      mpetch
Overall Statistics:
Error total EMG (MWC)                      -2.432 (-19.198%)      -2.145 (-13.032%)
Error rate mEMG (MWC)                     -12.2   ( -0.096%)     -10.2   ( -0.062%)
Snowie error rate                          -6.0   ( +0.000%)      -5.3   ( +0.000%)
Actual result                          +50.00%              -50.00%
Luck based FIBS rating diff.           -19.13
Error based abs. FIBS rating          1912.9               1930.5
Chequerplay errors rating loss         126.2                114.1
Cube errors rating loss                 10.9                  5.5

------

Of particular interest are 3 lines.  Actual Result, Luck adjusted result , and Luck based FIBS rating diff.

The “Actual Result” simply means that BEFORE the first roll was thrown in the match MontyBackgammon and mpetch were assumed to be 50/50 favorites.
The “Luck Adjusted Result” is a % of MWC that is gained or lost after a variance reduction is applied across all moves and decisions to factor out luck.
The “Luck based FIBS rating diff.” is the Ratings difference between the two players.

Okay so how does all apply to what you are interested in. From this information how do you determine the MWC (With luck factored out)? Its  quite simple (But maybe not obvious). You take the “actual result” for a player and add it to “Luck adjusted result” for the player. Do the same for the the player and Voila you have you chances of winning the match (This is an estimate of course, and results can be off for shorter match lengths <= 3). For longer matches its usually pretty good.

So in this example we take Monty’s actual result of 50% add his Luck adjusted result of –2.13% and get 47.87% MWC
To get my MWC we take my Actual Result of 50% and add my luck adjusted result of +2.13% and get 52.13% MWC.

Which means of course after  luck is factored out I was estimated to be a 52.13% to 47.87% favorite in the match.

The ratings Difference can be positive or negative. The plus or negative only says which player was the underdog or the favorite. In this case it shows –19.13 under Monty. Which means the ratings difference between the 2 of us was 19.13 and that Monty was the underdog. Had it shown +19.13 under Monty it would have meant he was the Match favorite.

I have very little experience with Player records, but noticed this information isn’t displayed (or whether these values are even stored). Not sure this was by design or not.

Mike