Eval Dilemma

[bob]

I'm poking around on a spreadsheet trying to make everything stick in my brain. Assuming I'm interpreting what Dr. Muller said correctly (dangerous assumption, I know)...

For 52% score vs 48% score:
Assuming 0% draws, it would take about 1228 games
Assuming 35% draws, it would take about 811 games

For very raw engines where the difference might be extreme, testing with 95% confidence interval still seems viable without a setup like Dr. Hyatt has. for example, going 25% vs 35% score would be more like 95 games for 95% confidence interval.

The problem is, most changes don't produce that kind of variation. Most will be one game in one hundred improvement at best, and you can't measure that with a thousand games... or even 10,000 games. Yet that is the way most improvements look. Also the way this calculation works is complicated by the fact that at longer time controls, the % of draws increases significantly...

[bob]

I guess some of you may have encountered this. It's somewhat annoying. I'm currently in the process of trying out some new things on my eval function. Let's say I have an old eval feature I'm going to denote as F1 and a new implementation of this eval feature as F2.

I have tested F1 against a set of opponents using a set of test positions in a blitz tournament.

I then replaced F1 by F2 but on some twist of fate I accidentally enabled F2 for the white side only and F1 for the black side. I tested it and it scored way higher compared to F1 in the same test condition. I said to myself, the new implementation works well, but then when I reviewed the code I found out that it was not implemented as I wanted to.

I then fixed the asymmetry bug and went on to implement the correct F2 feature. To my surprise it scored only between the F1 and the F1/F2 combination. Note that I have not tried F2 for white and F1 for black to see if it still performs well.

Now here's my dilemma, if you're in my place, would you keep the bug that performs well or implement the correct feature that doesn't perform as well?

I never accept bugs just because they are better. The idea is to understand what is going on, and _why_ the bug is making it play better (this is assuming it really is, which may well require a ton of games to verify) and go from there. Once you understand the "why" then you can probably come up with an implementation that is symmetric and still works well.

Since I do lack the resources to test them thoroughly I mostly rely on intuition. Since this one is so counter intuitive, I don't know what to decide. Well I guess I will just have to choose the right implementation even if it seems to be weaker in my limited tests.

You said that you knew it was too few games. But I do not think you knew the magnitude of games needed to come up with a conclusion. What Giancarlo was pointing out can be translated to: "Both versions do not look any weaker or stronger than the other". So, your test does not look counter intuitive.

To make a decision based only on the numbers of wins you had in your tests, is almost as basing it on flipping coins. The difference you got was ~10 wins on 240 games. You had a performance of ~33%. This is not the same (because you have draws) but just to have an idea, throw a dice 240 times and count how many times you get 1 or 2 (33% chances). Do it again and again. The number will oscillate around 80, but getting close to 70 or 90 is not that unlikely. This is pretty well established. The fact that you are using only 20 positions and 4 engines make differences even less significant (statistically speaking).

Miguel

I'm using 30 positions played for both colors, so 60 positions per opponent multiplied by four opponents equals 240.

I don't think that basing a decision from just 240 games is like basing it on flipping coins. What I know is that there is a certain difference in percentage of wins that you could declare if a version is better than the other if there error bar doesn't overlap.

For example I have a version with a performance of 2400 +-40 and I have another version with a performance of 2600 +-40. The upper limit of the first version is 2440 and the lower limit of the second version is 2560, they doesn't overlap so in this case I could say that the second version is better than the first version even if I only have a few hundred games.

It is just as random, in fact. I have a script I run on the cluster when I am testing. It grabs all the completed games and runs them thru bayeselo. It is almost a given that after 1000 games, the Elo will be 20-30 above or below where then 32,000 game Elo will end up. Many times a new change starts off looking like it will be a winner, only to sink down and be a no-change or worse....

If you play 10,000 games, and you look at the result as a series of wld characters, you can find all sorts of "strings" inside that 10,000 game result, that will produce results significantly different than the total.

1,000 games is worthless for 99% of the changes you will make.

[Gian-Carlo Pascutto]

In my opinion why the younger generation tends to surpass the old ones is that the younger generation is willing to learn something new while the old ones tend to stick to their old methods that might already be obsolete.

See Vincent, no need to worry

[diep]

Can you or anybody point me to how the error bars are calculated?

I think the rule-of-thumb Error = 40%/sqrt(numberOfGames) is accurate enough in practice, for scores in the 65%-35% range. (This is for the 1-sigma or 84% confidence level; for 95% confidence, double it.) For very unbalanced scores, you would have to take into account the fact that the 40% goes down; the exact formula for this is

100%*sqrt(score*(1-score) - 0.25*drawFraction)

where the score is given as a fraction. The 40% is based on 35% draws, and a score of 0.5. In the case mentioned (score around 0.25, presumably 15% win and 20% draws, you would get 100%*sqrt(0.25*0.75-0.25*0.2) = 37%. So in 240 games you woud have 2.4% error bar (1 sigma).

When comparing the results from two independent gauntlets, the error bar in the diffrence is the Pythagorean sum of the individua error bars (i.e. sqrt(error1^2 + error2^2) ). For results that had equal numbers of games, this means multiplying the individual error bars by sqrt(2).

To get a score difference of 30% (35% ==> 65%) that's so big, that if you add just 1 pattern to your evaluation with such a huge impact, that obviously we might hope that's not the 'average pattern' that you add.

More likely it is that you see a score difference of 1 point at a 200 games when adding just 1 tiny pattern.

Vincent

He was not talking about increases from 35% to 65%. The formula is valid if both score A and score B (from versions A and B) are within 35% to 65%. In other words, if score A is 48% and score B is 52%, you can apply the formula. If score A is 8% and score B is 12%, you cannot.

Miguel

If A scores 48% and B scores 52%, that's basically blowing 2 games with maybe in total just 2 very bad moves, as that can give a 4 point swing in total.

First of all odds these 2 bad moves were caused by the specific pattern is tiny. It could be some fluctuation or book learning or whatever effect.

So you really soon will conclude you need THOUSANDS of games for real good statistical significance. I'm going usually for 95%.

Vincent

Going from 50-50 to 52-48 is an increase of ~15 Elo points. Yes, you need thousands of games to make sure it is real with a good level of confidence.

Miguel

Additionally they have to be preferably on the hardware and time control you want to play tournament in.

Jonathan Schaeffer: "You have to test with what you play".

There seems to be a positive correlation of engine strength between short and longer time controls, based on some results published here and what you also can notice in the established rating lists.

So if you're lacking the time and resources to test with what you play, for example a tournament time control of 40/40 you can take a compromise by playing blitz games. There is a big probability that the result in blitz will correspond with its result in longer time controls, though there are some few engines that are the exception.

Well, you get lured by evaluation function.

For search several algorithm do no longer work very well in longer time controls which do in short time controls and vice versa.

Vincent

[michiguel]

I guess some of you may have encountered this. It's somewhat annoying. I'm currently in the process of trying out some new things on my eval function. Let's say I have an old eval feature I'm going to denote as F1 and a new implementation of this eval feature as F2.

I have tested F1 against a set of opponents using a set of test positions in a blitz tournament.

I then replaced F1 by F2 but on some twist of fate I accidentally enabled F2 for the white side only and F1 for the black side. I tested it and it scored way higher compared to F1 in the same test condition. I said to myself, the new implementation works well, but then when I reviewed the code I found out that it was not implemented as I wanted to.

I then fixed the asymmetry bug and went on to implement the correct F2 feature. To my surprise it scored only between the F1 and the F1/F2 combination. Note that I have not tried F2 for white and F1 for black to see if it still performs well.

Now here's my dilemma, if you're in my place, would you keep the bug that performs well or implement the correct feature that doesn't perform as well?

I never accept bugs just because they are better. The idea is to understand what is going on, and _why_ the bug is making it play better (this is assuming it really is, which may well require a ton of games to verify) and go from there. Once you understand the "why" then you can probably come up with an implementation that is symmetric and still works well.

Since I do lack the resources to test them thoroughly I mostly rely on intuition. Since this one is so counter intuitive, I don't know what to decide. Well I guess I will just have to choose the right implementation even if it seems to be weaker in my limited tests.

You said that you knew it was too few games. But I do not think you knew the magnitude of games needed to come up with a conclusion. What Giancarlo was pointing out can be translated to: "Both versions do not look any weaker or stronger than the other". So, your test does not look counter intuitive.

To make a decision based only on the numbers of wins you had in your tests, is almost as basing it on flipping coins. The difference you got was ~10 wins on 240 games. You had a performance of ~33%. This is not the same (because you have draws) but just to have an idea, throw a dice 240 times and count how many times you get 1 or 2 (33% chances). Do it again and again. The number will oscillate around 80, but getting close to 70 or 90 is not that unlikely. This is pretty well established. The fact that you are using only 20 positions and 4 engines make differences even less significant (statistically speaking).

Miguel

I'm using 30 positions played for both colors, so 60 positions per opponent multiplied by four opponents equals 240.

I don't think that basing a decision from just 240 games is like basing it on flipping coins. What I know is that there is a certain difference in percentage of wins that you could declare if a version is better than the other if there error bar doesn't overlap.

If the confidence value you obtain is not far apart from 50%, it is no much different from flipping coins. That is what you get with a difference of a handful of wins in 240 games. You mention in another post a difference of 3 wins. That was hint that I should better warn you no to put any weight on these type of results. That is exactly like flipping coins.

For example I have a version with a performance of 2400 +-40 and I have another version with a performance of 2600 +-40. The upper limit of the first version is 2440 and the lower limit of the second version is 2560, they doesn't overlap so in this case I could say that the second version is better than the first version even if I only have a few hundred games.

That is not the example you brought!

Miguel

[MattieShoes]

I used what Dr. Muller explained for calculating error bars earlier in the thread. I threw it into a spreadsheet with the formulas and plugged in different numbers of games until the 95% confidence interval flipped from false to true.

[MattieShoes]

The changes YOU are making don't make that sort of change -- You've been tuning your engine as long as I've been alive! By raw, I meant something like my engine, where I'm going from no pawn structure eval to simple pawn structure eval, and no null move pruning to R=2 null move pruning. Those probably made a 200 point difference alone.

Of course, now that they're implemented, you're absolutely right. I could double or halve the penalty for doubled pawns and I wouldn't be able to test whether it's better or worse with any sort of confidence. For all I know, it'd perform better with totally different piece values (it's using 100, 325, 333, 500, 980, which i plucked from thin air).

[MattieShoes]

In my limited experience, testing vs previous versions can be very misleading because they're too similar. A minor tweak could make the new version absolutely dominate the old version but it might do exactly the same vs other players.

[bob]

The changes YOU are making don't make that sort of change -- You've been tuning your engine as long as I've been alive! By raw, I meant something like my engine, where I'm going from no pawn structure eval to simple pawn structure eval, and no null move pruning to R=2 null move pruning. Those probably made a 200 point difference alone.

Of course, now that they're implemented, you're absolutely right. I could double or halve the penalty for doubled pawns and I wouldn't be able to test whether it's better or worse with any sort of confidence. For all I know, it'd perform better with totally different piece values (it's using 100, 325, 333, 500, 980, which i plucked from thin air).

None of that is going to make +200 Elo jumps. You will make steady progress, but as you add things, you are adding +5 or so, maybe +10 if you are lucky...

Null-move is a big one at +120, but there are not many others. It is the sum of the parts, and you will end up with _many_ parts, each worth a small elo gain.

[Edsel Apostol]

Can you or anybody point me to how the error bars are calculated?

I think the rule-of-thumb Error = 40%/sqrt(numberOfGames) is accurate enough in practice, for scores in the 65%-35% range. (This is for the 1-sigma or 84% confidence level; for 95% confidence, double it.) For very unbalanced scores, you would have to take into account the fact that the 40% goes down; the exact formula for this is

100%*sqrt(score*(1-score) - 0.25*drawFraction)

where the score is given as a fraction. The 40% is based on 35% draws, and a score of 0.5. In the case mentioned (score around 0.25, presumably 15% win and 20% draws, you would get 100%*sqrt(0.25*0.75-0.25*0.2) = 37%. So in 240 games you woud have 2.4% error bar (1 sigma).

When comparing the results from two independent gauntlets, the error bar in the diffrence is the Pythagorean sum of the individua error bars (i.e. sqrt(error1^2 + error2^2) ). For results that had equal numbers of games, this means multiplying the individual error bars by sqrt(2).

To get a score difference of 30% (35% ==> 65%) that's so big, that if you add just 1 pattern to your evaluation with such a huge impact, that obviously we might hope that's not the 'average pattern' that you add.

More likely it is that you see a score difference of 1 point at a 200 games when adding just 1 tiny pattern.

Vincent

He was not talking about increases from 35% to 65%. The formula is valid if both score A and score B (from versions A and B) are within 35% to 65%. In other words, if score A is 48% and score B is 52%, you can apply the formula. If score A is 8% and score B is 12%, you cannot.

Miguel

If A scores 48% and B scores 52%, that's basically blowing 2 games with maybe in total just 2 very bad moves, as that can give a 4 point swing in total.

First of all odds these 2 bad moves were caused by the specific pattern is tiny. It could be some fluctuation or book learning or whatever effect.

So you really soon will conclude you need THOUSANDS of games for real good statistical significance. I'm going usually for 95%.

Vincent

Going from 50-50 to 52-48 is an increase of ~15 Elo points. Yes, you need thousands of games to make sure it is real with a good level of confidence.

Miguel

Additionally they have to be preferably on the hardware and time control you want to play tournament in.

Jonathan Schaeffer: "You have to test with what you play".

There seems to be a positive correlation of engine strength between short and longer time controls, based on some results published here and what you also can notice in the established rating lists.

So if you're lacking the time and resources to test with what you play, for example a tournament time control of 40/40 you can take a compromise by playing blitz games. There is a big probability that the result in blitz will correspond with its result in longer time controls, though there are some few engines that are the exception.

That's not the issue. You are trying to decide whether A' is better than A, and that absolutely does not correlate well at different time controls, for many kinds of changes. Particularly with respect to things that significantly alter the shape of the tree, such as search extensions, reductions, etc. I have found some ideas that work better at fast time controls (small but significant improvement) but then fall flat on their face at longer time controls. Eval changes are less likely to do this but I have seen examples there as well where this also happens.

In my opinion, when you test the things that significantly alter the shape of the tree, you can make it consistent with the results on longer time control as long as you give enough depth to the blitz time control for the reductions, extensions to take effect. I mean if you only test with ultra fast time control that the average depth of the engine in the game is 5 then I think you could not trust it to determine improvements on the search. I think it must be at least depth 12. A solution is to play blitz but to make sure that the blitz time control is adjusted to have the engine at least an average depth of 12 in the game.

If only eval is being tuned I don't think that result in short time control would not correlate with longer time controls, though there might be some rare cases that will prove as an exception. I'm just curious what are these rare exceptions. Can you cite some examples? It would help the amateurs like me and the others as we became aware of it.