Postmortem scoring
The final game score, a 1, 0, or 0.5, is a very crude indicator of how well you actually played for the extent of the game. To determine whether you need to go over a win (or even a loss), use the postmortem score, or PMscore:
Where the numerator on the right is the number of moves that were not best moves, the denominator is the total number of moves in the game. This fraction is subtracted from 1.0 to yield a score between zero (none of your moves were best) and one (all of your moves were best). Rather than best moves, you obviously can be more flexible, adding a move to the numerator only if it is below some acceptable deviation from best (e.g., within 0.3 of best counts as best in the equation). We could make this more explicit in the equation, denoting the left-hand side PMscore(α), where α indicates what your threshold is for considering a move best.
Say you got a full point but your PMscore is a pathetic 0.1 because you played horribly but won with a swindle on the last move. Yes, getting such swindles is great, and you won, but there is lots of useful postmortem analysis to be done. Let the PMscore show you the truth about how good your play was!
Blogging has taken up way too much time today. Hence I've turned off comment moderation so your comments will show up without censorship until later tonight. :)
Where the numerator on the right is the number of moves that were not best moves, the denominator is the total number of moves in the game. This fraction is subtracted from 1.0 to yield a score between zero (none of your moves were best) and one (all of your moves were best). Rather than best moves, you obviously can be more flexible, adding a move to the numerator only if it is below some acceptable deviation from best (e.g., within 0.3 of best counts as best in the equation). We could make this more explicit in the equation, denoting the left-hand side PMscore(α), where α indicates what your threshold is for considering a move best.Say you got a full point but your PMscore is a pathetic 0.1 because you played horribly but won with a swindle on the last move. Yes, getting such swindles is great, and you won, but there is lots of useful postmortem analysis to be done. Let the PMscore show you the truth about how good your play was!
Blogging has taken up way too much time today. Hence I've turned off comment moderation so your comments will show up without censorship until later tonight. :)
posted by Blue Devil Knight at 10/24/2007 02:24:00 PM
17 Comments:
I can't resist.
Isn't best/total simpler than (1-nonbest/total)?
Assuming best + nonbest = total.
Anyhow, you can't tell how many nonbest moves there are until you've already been analyzing the game. In which case you've already been going over it, and may as well finish the job. Unless you're just relying on an automated computer analysis, which I rarely do.
Hey, what was I thinking?! Good modification. (For those who aren't tracking it, his equation will give the same answer, but is much simpler to understand and write out).
I was assuming Fritz or some other computer analysis (otherwise it would be hard to set the alpha level objectively).
OK, no more POSTS today but obviously I won't be able to resist comments.
I suck. Time to get back to work.
Hey wait, that's punishment. If I work I will get a bigger paycheck, so I should work.
Come on Blue. Once we've got used to a minimum of three profound posts per day, you don't really think we'll let you entertain yourself with such common things as sleep, bathroom visits or - Caissa forbid - work!
We want more, we want more!
In my defense for making the equation note I used the better simple version as the original in my comments to the previous post to Dean. Then when I starting making the image for this post I accidentally put #nonbest in the numerator, and realized that gave the wrong answer. Instead of putting best in numerator, I subtracted it all from one. Duh.
It has been some time ago that I have seen a subject being hammered flat in such short time. Only men seem to like such "discussions":)
There was a Chessbase article awhile back that I (and, I believe, dk) did a brief post on (well, dk's wasn't so brief ;) ) ANYWAY, looking at World Champions supposedly Capablanca was the most accurate player of all time measured against a computer using a formula similar to yours. I think they only looked at WC matches, though, which might be a distorting factor.
It seems like a pretty fair way to measure a game to me, but the weakness of the "strong version" is that "second-best" moves get marked off--I think the "more flexible" version is the best for below Master level. I've done deeper analysis than previously on my games from the Western States Open (first three are posted at the blog) and it seems that one can afford several second-best moves per game and do quite well (I was playing all 1700-rated opposition).
Of course if (in computer scoring language) you lose 0.3 per move for 5-6 moves in a row you're going to be in trouble. But, to sum up, avoiding those -1.0 to -3.0 (blunders) is enough, all by itself, to be a pretty darn good player!
Wow, all that verbiage for a truly hackneyed conclusion...
Yeah, but most chess positions are non-tactical, and the computer evaluation is only reliable in tactical situations. So this "best versus non-best" thing is not useful for pre-filtering.
War: yes, rigidly using best (setting alpha to 0) rather than setting alpha to .3 or something would be crazy.
Anon: the good programs are solid positional players. Try it out on one of the programs: see if it picks the positionally best move (of course if it sees a big tactic it will put that above getting a Knight outpost, but that's what it should do!).
warheit: Of course if (in computer scoring language) you lose 0.3 per move for 5-6 moves in a row you're going to be in trouble.
It depends if your opponent is also making mistakes of this magnitude, which is typical in amateur chess. This is one factor in why finding our weaknesses is so difficult. If you made each move 0.1 better your results would go through the roof, but the thread of your 0.1 - 0.3 mistakes is washed away by the mistakes of your opponent.
Wahrheit said: I think they only looked at WC matches, though, which might be a distorting factor.
Not in my case. No distortion -- I have a perfect record in WC matches.
BDK: Good idea, not the best implementation. I sum, from 0 to N (number of moves) the value of my move minus the value of the move expected from a player rated R. For R I use my current rating plus 200 points. If the sum is positive I did good! If negative I need to see why. Plug in different values for R and get different best moves and game evaluations! Patent pending.
Glenn: that sounds cool, but how can you determine the value of the move expected from a player with a certain rating?
:) me too, cutting back from blogging.
chess, chess, chess: let there be more chess, more chess study, more rest instead of blogging, more of less.
DK's Law of Dissimilars:
------------
the coefficient of big posts creation is inversely proportional to the amount of time availalbe for real chess time minus sleep + women + healthy diets, which can inhibit true chess performance short term, provided over N occassions the diet is not so quickly generated as to impare physiological functioning and thereby compromise cognitive functioning.
BDK: My comment was slightly tongue-in-cheek. But only slightly.
If you had a chess engine (say Fritz) that could have parameters tweaked to generate moves at a certain level of play (rating R) then it could evaluate your actual move and the move it would make for rating R and compare the value of those two to determine how you did versus that rating.
Fritz could then just calculate my estimated rating (averaging on a per move basis) for the game and report it along with other analysis.
Dude,
NERD ALERT. NERD ALERT.
Sorry it was called for. You should examine all your games, wins and losses to a certain degree.
A formula will get you nowhere, except perhaps as treasurer of the Tri-Lambs.
:P
PMD: I agree. See previous two posts. :) This was just making a point. Don't use the crude game score to decide. How can you know where you could have improved if you don't look at the game?
Post a Comment
<< Home