| |
BGonline.org Forums
"Easy" improvement to PR calculations
Posted By: Henrik Bukkjaer
Date: Friday, 12 April 2013, at 11:47 a.m.
Stick wrote, in another thread discussing complexity adjustments in PR calculation:
>> I wish bg could incorporate complexity of the position (the match) into obtaining a more meaningful PR.
It doesn't really have to be complex to be an improvement over the current PR.
I have earlier thought about this, but never really cared to write down or even make my ideas public, but here goes:
PR is calculated (more or less), by adding all the normalized errors, and divede by the number of non-forced decisions. A big improvement over the old ER that simply divided by the number of decisions (including forced).
The main improvement was, that you didn't get ridiculous low ERs when being steamrolled!
Now, if we look at the formula, we could simply refine the decision calculation further, and get to an even better PR.
A suggestion to start with could look like this:
For checkerplay:
Forced moves (where all possible moves result in the same equity):
0) None forced moves will count as any decision (0).Opening play (first two moves for each player):
1) Normal rolls count as .5 decision.
2) Doubles count as 1 decision.
From the bar:
3) A double from the bar, count as 1 decision.
4) A normal roll from the bar count as .75 decision if both dice can be played down.
5) A normal roll from the bar count as .5 decision if the move down is forced.
Contact play:
6) Doubles count as 1.5 decisions (if none of the four individual moves are forced).
7) Doubles count as 1.25 decision (if one of the four individual moves are forced).
8) Doubles count as 1 decision (if two of the four individual moves are forced).
9) Doubles count as .5 decision (if three of the four individual moves are forced).
10) Normal rolls count as 1 decision if not forced in any way.
11) Normal rolls count as .5 decision if one of the moves are forced.
Non-contact play (defined by true non-contact or both players at 13 or lower):
12) All rolls count as .5 decision.
Bear-off play:
13) Bear-off plays where only one of the moves are non-forced, count as .25 decision.
14) Bear-off plays where you can chose to take off two pieces (or 4 pieces for a double), without leaving any holes, count as 0 decision.
15) Bear-off plays where you can chose to take off two pieces (or 4 pieces for a double), count as .25 decision.
16) Other bear-off plays count as .5 decision.
For cube decisions:
I'm most confident about the adjustment for checkerplay, but I imagine that the count of cube decisions could be improved in a similar way:
Today there is a threshold for when a cube decision counts.
I suggest that instead of having a 0 or 1 count, a .5 decision zone is applied. I don't know the numbers of todays zone in XG, but say the number today is .300 error, I then suggest to have a 0.5 decision count zone ranging from .250 to .325
Furthermore - and this has not been given too much thought from my end - I suggest that in the following scenarios, the .5/1.0 decision count, is multiplied by the following factor:
1) In all non-contact play (defined like above), multiply by a factor of .75
2) If the cube at the current score will be taken as a dead cube, multiply by a factor of .75
3) For all fully live recube decision, multiply by a factor of 1.5
4) Maybe - I haven't thought this through - a multiplier could be used for lop-sided scores, say 1.25 if there are more than 5 points between the players.
---------------
Conclusion:
I'd imagine that this proposed enhancement of PR calculation would:
- Be relatively easy to implement in the current XG version (*1)
- Represent a noticeable and immediate improvement on the current PR calculation
- Make PR less result sensitive (*2)
- Get rid of the (indirect) bias towards agressive over conservative play, which hurts adjusting to weaker players more than it should. (*3)
- Be relatively easy to finetune through analysis of actual play - by catogorizing decisions in analyzed games, the weights put on the decision count could be adjusted.I hope that some of you guys who are strong in backgammon and errorrate theory, and mathematics, could review the idea and improve upon it. And I hope that Xavier could find time to try to implement something like the above in a beta version of XG, to test it.
Cheers,
Henrik(*1) Since no complex terms are introduced, no huge analysis are needed, and all catogories are objectively defined thus not needing any NN evaluations.
(*2) We still get lower PR when being crushed: Loosing is easier! I recon this is due to more partly forced moves coming off the bar, and a relatively higher amount of non-contact play after being blitzed, etc.
(*3) It is much preferred from a PR perspective to double early rather than late, and to make the same sized error taking a cube rather than dropping it - since that leads to many more easy non-contact decisions (more games being played to the end).
As for points (*2) and (*3), I've actually done some analysis to support my theory, and it showed that a player playing an error-rate of about PR 3-4, would get an overall lower error-rate by starting to make errors doubling a bit too early in near borderline decisions, and taking borderline passes. The higher the error-rate of the player, the more pronounced this effect will be. Likewise, making the opposite more conservative errors, hurt your PR relatively more.
| |
BGonline.org Forums is maintained by Stick with WebBBS 5.12.