Is 99% enough?

We often measure ourselves by our peaks. We have a brilliancy, and we're happy. We get a draw (or even win!) against a titled player, and we're happy.

But chess is about consistency. If you play 10 games, the measure of how well you did is not about which game had your best move, or which had the coolest checkmate. It's about how you did against all of the players, cumulatively. If you played 9 out of the 10 games against players within 100 points of your rating, but you won the 10th game against a master, don't focus on that one. Did you score 3 out of 9 points in the 9 games? How often did you "overlook a tactical sequence", which sometimes is a nice way of saying "hang pieces".

If the answer is just once in the 10 games, then hey that's pretty good. Because basically every move you make, there is an opportunity to overlook something tactical. Play against a computer sometime, in what you think is a very tranquil position, and all of a sudden you'll realize that it is not so tranquil after all.

Even better - if you _think_ that you only overlooked a tactical sequence once, chances are good that this is not true. Your opponent just didn't take advantage. This is where computer analysis of your games comes in. Take a game that you might be proud of, and run it through a computer. (You'll get more out of this process if you analyze the game yourself first, but that's a subject others have written on extensively). You'll find lots of swings in the evaluation of the position, which translates to mistakes, overlooked opportunities, etc. Getting good at chess is about reducing these errors.

Which brings me to my main point. Is 99% good enough? What if you made a tactical error only 1% of the time. Turns out that this is not very good. At 33 moves a game, this means that you're likely throwing away one out of every three games. At 50 moves a game, it's one out of every 2. Chess players strive for much better than that.

One can even begin to quantify this. I know what a blunder is in the chess sense, but one has to quantify it so that the computer can measure it. Must be a move which causes the eval to change by more than some threshold (say 1.00 pawns), where it is meaningful to the game result. (If I'm up a rook for knight, and sacrifice back the exchange to get to a winning pawn ending, I don't really care if it wasn't objectively the strongest move.) So I begin to wonder - what is my blunder frequency? Is it below or above 1%?

Consistency is very difficult. Doing something rather repetitive again and again without making a mistake is rather against human nature. (It fits right in with what computers do best though.) But getting to be a strong chess player is all about consistency.

well put

Thought-provoking!  Thx 

Your logic on 99% not being good only holds if blunders follow a flat random distribution.  It's more likely that blunders arise from a player's specific weakness or lack of positional understanding. 

On a related note, I've always wondered how most well-trained pianists can sight-read through complex technical pieces (they've never seen before!)  with very few mistakes.

My guess is that it is because the composers weren't too creative. So it's as impressive as a chess player playing a game blindfolded. All the same patterns, plus you're more or less used to it.

I completely agree.  I identify consistency as a problem of mine at tournaments, and is something I'm interested in improving.

Like you said, don't be blinded by your brilliancies or good games.  My performance rating has actually be pretty consistent my last few tournaments, but I alone know what I've missed and what I saw, and whether or not it was consistent.  I also try to be very objective about my playing strength, paying attention even in club games to who played better, not just who happened to win.

I'm sure if there were a magic bullet we'd all know about it by now, but let me know if this sounds right... basically I think I just have to play in more tournaments and more long/serious games and cut down on blitz.

The funny thing is though, I'll miss tactics in a long game that I see in 3 minute bullet games because I get distracted long or deep thinks... or maybe I'm more willing to go with my gut and can start a sequence that looks promising without calculating it to the end (at tournaments I usually only go for sure things, which is probably another problem).

If the musical pieces are truly complex, then that would indicate that the composers were significantly creative, at least. I would say that the two fields (piano and chess) are very similar indeed, in this sense. When I started college, I was not a very good sight-reader and was afraid that I never would be. Now, 10-11 years later, I am an excellent sight-reader. It takes a great deal of training -- reading through droves of different pieces (akin to playing a great many games of chess) -- and pattern recognition: recognizing at a glance harmonies, melodic shape, harmonic scheme, feeling of pulse, and on and on. Of course, pieces that are extremely complex (like two irregular time signatures at once) or those that move at blinding speed (Prestissimo) are almost impossible to sight-read, and there will always be some pieces that even the greatest pianists cannot simply sit down and read.

So improving one's chess requires a great deal of consistency with pattern recognition as well, I think; and there will always be some truly deep positions that require sitting down and calculating (i.e. practicing), notwithstanding an immense pattern-recognition ability.

Blunder frequency depends on the level of opposition. One can easily mate a beginner without blundering anything, but Kasparov will make you blunder in every game.

My point is that the bread and butter of one's strength has to do with consistency against opposition of approximately equal strength.

I believe that this changes the higher the rating, though not for me. Grandmasters who play in weekend Swiss tournaments earn their living by consistently winning all games against people rated <2400. Think for a minute about how hard that is to do. If you're the "local" GM, such as GM Ivanov in Boston, then everybody knows you, they know your openings, and you have to win, with white, and with black, every time against everybody. So it's different for top level GMs. But for the rank and file, so to speak, it's all about consistency within 100-200 pts of your rating.

don't forget to account for your opponents consistancy because you may be 99% consistant but he must be less than you if not equal so its actually less than every 33 games 

Given the mathematical faux pas, the scientists among us are now eager to model blunders.  My bet is that one can predict a blunder centred around positions.  There will be a small flat-random component, but unless the rating is ~1200, it'll be <<10e-5 (0.001%).  

From there, you could have the core distribution of "strength of move" and then catagorize "innaccuracy," "mistake," or "blunder" in terms of standard deviations from the mean.

Ahhh man..... I need to start doing my actual job.  This would be beyond hilarious/ridiculous to model.  A case study would could be done with a player doing variations of the open Sicilian.

In general, rating is about consistency of performance. We can all look at our online chess and see where we're beaten someone ~400 points higher than us.  The best can have a bad day, but if you play that person 1000 times with the same knowledge (assuming you assimilate no new information after each game) you will, on average, get creamed. Having a rating of 1800 should mean that if the other player has a rating of 1800, the most likely outcome is a draw.  Defeat or victory comes when one player makes a mistake or has a non-as-advanced understanding of the position.

Nice. :)

99% I think it's unrealistic against an opposition corresponding to your level. Just look at the recent Topalov-Anand match and see how often even the best players miss decisive opportunities.

The topic you bring up ozzie is something I've always thought about, in fact I think I made a post (not as long) incidentally with the same general point as yours some time ago. Of course the 99% thing isn't supposed to be taken completely seriously as the math could never be that simple because of different ratings and play styles, etc, but it makes a good point.

One of the problems in my game is that I may play a well thought out game for 30-40 moves, but past then sometimes the position gets really tedious (partly because im tired, and sometimes the rest of the game is, unfortunately, based solely on taxing calculation), where in one game my opponent was down the exchange but had a strong knight (d4) and queen in my position, and my king was fairly open, so I basically had to defend and he could force a prepetual without too much difficulty if he wanted to but could still press and hope for a blunder. Anyway for such a long time I had to mechanically (like a computer, it would do great in this kind of position) look at every possible little mating net that could possibly form with a series of checks or something, and if I slipped just once it was over. I eventually did. There was no real strategy to it at this point, I basically just had to avoid falling into any mating net. Let's see, the game was about 60 moves, but it was decided on one blunder (there were plenty of mistakes thoughout the game on both sides, with the evaluation often changing, but as far as game losing blunders there was only one and it belonged to me). Over 98% accuracy, but it wasn't enough, and the tedious calculation eventually got to me. Honestly this kind of purely mathematical situation is not what I love about chess.

Yeah I know what you mean. The context for me is that I think I give away a game in the opening, every so often. It seems to be about 2 times within the past 15 games, which is actually a lot if you think about it. The opponents were around my level, so in some sense I would expect to get 1/2 for those points, which ends up being perhaps 8 or 9 FIDE points on my way to the FM title.

If I ever get there.

Speaking from my experience, I totally agree. These days I actually try to make sure I'm in good form, mentally and physically, as that can literally make a difference of hundreds of rating points sometimes, for me anyway.

In post game computer analysis, I've come to use the following:

- ?! means the move I chose differs in evaluation from the computer's choice by > 0.2 pawns

- ? for moves that differ by more then 0.5 pawns

- ?? for moves that differ by more then 1 pawn

- ! for moves which are not obvious captures and for which my move differs from the 2nd best move by more then 0.5 pawns

- !! for moves which are not obvious and when the evaluation differs from the 2nd best move by more then 1 pawn

This only leaves !? available and this is a hard comment to apply for me.  I use it sometimes when my move is worse then the computer in the 0.15 - 0.3 range, but when my move has a strong positional logic behind it, and I think perhaps the computer would agree if only I would give it more time to think.

On a side note, I think a more formal definition like this for "!" and "!!" would be great in that it would allow for objective annotation of games, and amateurs would be able to take pride in having played exclam worthy moves.  I imagine that this would improve the popularity of this great game.

Complicated.

Of course 99% is enough. It is even too much

The matter is that blundering probability should be calculated in a different way.

If you have 99% chance not to make a mistake every move, then your chance not to make a mistake in two (say, consecutive, but not necessary) moves is 0,99*0,99 (the chance not to mistake the second one provided you haven't mistaken the first one). It can easily be proven that your chance not to make a mistake in X moves will be 0,99^X.

So, for 40 moves your chance not to make a mistake will be about 0,669 = 67%. To reach 50% chance of making a mistake in a game, you will need to play about 69 moves (0,99^69=0,4998=50%).

And even if you make a mistake, your opponent should succeed to exploit it in order to win. Also, if he has already made a mistake, you should be in a better position (by definition, since your moves have been correct so far and you should have taken an advantage; it may turn out he won't be able to equalize).

That's it

Here are some more calculations that come to my mind:

If you have Y chance not to make a mistake per move, your chance for a mistakeless X move game is Y^X. If "mistakeless" includes "drawish" (you'll need a mistakeless opponent for that), then it may not be a win. If your opponent's chance not to make a mistake is Z, then his chance of a mistakeless X move game is Z^X. (Y and Z are fractions, i.e. 0,97.) The chance the X move game will be a draw is the chance you won't make a mistake provided your opponent won't too, or Y^X*Z^X=(Y*Z)^X (maybe with one tempo inaccuracy).

If you make a mistake, and your opponent doesn't: (1-Y^X)*Z^X wins for your opponent.

So, for a X move game, you have Y^X*(1-Z^X) chance for a win (you make no mistake and your opponent does), (Y*Z)^X chance for a draw (both you and your opponent make no mistake), and (1-Y^X)*Z^X chance for a loss (you make a mistake and your opponent doesn't).

I haven't included games where both players make a mistake in the result distribution, because I'm too lasy to think how to approximate their outcome Their part of all games is (1-Y^X)*(1-Z^X).

So, for 40 moves, with no mistake chances 99% for you and 98% (!) for your opponent, the W/D/L/? ratio is 37,08/29,82/14,75/18,35, or you win at least 37%, draw at least 30% and lose at least 15%.

If your opponent's no mistake chance is 95%, then the ratio is 58,30/8,60/4,25/28,85, or you win at least 58%, draw at least 9% and lose at least 4%.

Of course, all the above is rough approximation, but to have a more exact one, you'll need at first more exact output data (mistake chance), and that will be hard to determine.