As many of you who have been reading the comments to my post on Clint Ballard's BAP system have probably noticed, the inventor himself has weighed in with a pair of long replies. (Here and here.) A massive reply is forthcoming, but I first wish to take care of some housekeeping.
Ballard seems to take a rather dim view of this blog and its participants (at least where the BAP system is concerned), but then hopes that although we're probably incapable of rational discussion, we won't censor him. (An ironic request, as his website includes his responses to this blog (here and here), but without mentioning the blog or linking to my and others' critiques.) Now, as any long-time reader of this blog will acknowledge, I don't censor comments or commentators for disagreeing with me. (Fewer than five people have been banned from commenting in the 16+ months I've been at it, and it wasn't because of disagreement over content.) That said, getting banned is not impossible: I will oust individuals who are persistently belligerent or seem to deliberately misrepresent others' work. Here are some examples of the sort of thing I insist on avoiding if discussion of these matters is to continue on my site.
Ballard: Since this thread has material inaccuracies, thinly veiled personal attacks and even an example by the moderator with the intentionally derogative acronym of "CRAP", it is clear that there is a lot of animosity and downright hatred toward my BAP system. I doubt that a rational discussion is possible and I am used to that, but I will present FACTS for the unbiased reader to consider and hope it won't get censored. Of course, all the critics will accuse me of being irrational because I won't simply agree with 100% of what they say, even if they are accusing me of being disingenuous, that I am conducting tournaments that should be banned, etc.
First, I engaged in no personal attacks whatsoever; in fact, I (and several others) praised Ballard for putting up a substantial amount of his own money in support of his system. I'm deeply skeptical of that system - no "thin veil" there! - but the man himself was not attacked. As for Jacobs' comment, in which he labeled Ballard's insistence that the BAP system is a new pairing method rather than a rule change "disingenuous", I leave that discussion to the two of them. (But note that Jacobs also praises Ballard for his sincerity, his willingness to invest his time and money and calls him a gentleman.) So it's an extremely thin "attack" - and it's not attacks, plural.
Second, no one called Ballard "irrational" - I and most of the commentators merely disagreed with his proposal and its motivations.
Third, no one called for BAP events to be banned; objectors merely wished that they not be rated.
Another quote:
Also, saying that a white draw is the same as a white loss is also incorrect, though understandable error. BAP is not a zero-sum point system. The effect of white drawing has a 2 BAP change to the overall point pool relative to a white loss. White winning has a 3 BAP difference relative to a white draw. Black winning has a 2 BAP difference relative to Black drawing. Black drawing has a 3 BAP difference relative to black losing. If you are going to comment on BAP math, please use the correct numbers.
Who made that claim? I didn't and neither did any of the commentators; in fact, my argument against BAP based on the attractiveness of last-round bribes rests precisely on the fact that while White's score doesn't change with a loss or a draw, Black's most certainly does. My argument went like this:
Last round pairings:
1. White (17) vs. Black (18)
2. White (18) vs. Black (17)Given normal tournament prize structures, White on board 1 has good reason to take a dive, especially if he thinks he can't win. Only Black on board 1 has first place in his own hands; no one else can guarantee himself even a tie for first. (Board 1-White can't, because if both he and board 2-Black win, the latter gets it; board 2-White and board 2-Black can't, because Board 1-Black outscores either with a win.) The correct numbers were used.
More Ballard:
"indicating that the draw "problem" is not caused by GMs' nearly perfect understanding of the game" [DM:he's citing me here] This statement makes the implication that GM's have solved chess! Gee, I must have missed that announcement. Was it my imagination that Hydra DEMOLISHED Adams? One of the top 10 players in the world at the time, not prone to losing, got killed. The only draw was by agreement of the operators of Hydra, even though Hydra itself thought it was winning. Since Hydra is better than the GM's, shouldn't we have seen if it could find the win? So, with an actual result of 5.5/6 vs. Adams and maybe it should have been 6 out of 6, it boggles the mind that claims are being made seriously that human GM's have a nearly perfect understanding of the game.
I was summarizing Ballard's position here - I was making a statement that agreed with his! According to Ballard, a big reason why there are so many draws is that players are insufficiently motivated to fight for a win. If the problem was instead that GMs just knew too much, then computers, which play stronger chess than human GMs, would have an even higher percentage of draws. It's just the opposite, however, a point I summarized by saying that the problem is not caused by GMs nearly perfect understanding of the game (the antithesis of Ballard's view), precisely because their understanding isn't nearly perfect, or not close enough! That point could have been made more explicit, but there isn't anything else I could have meant in the original quotation:
Ballard offers a brief historical excursus recalling the days when draws were automatically replayed, notes that there are few draws in computer chess (indicating that the draw "problem" is not caused by GMs' nearly perfect understanding of the game)...
If my point (summarizing Ballard) wasn't to contrast computers with humans, with the presupposition that computers are stronger than we are, then the whole passage is a mystery.
So: If you wish to have a forum for your views here, then read others' objections with the same care you request for your own arguments. A little humor's fine, disagreement is perfectly okay, but misrepresentation isn't.
Related Posts (on one page):
- Is BAP Chess = Chess?
- The"BAP" System Revisited: A Prelude
I did not link to this site or include content of this blog because when I did that with another blog in the past, I was threatened with lawsuits for illegally using copyrighted material.
Jon Jacob's did make a thinly veiled personal attack. The moderator did create an example which abbreviates to CRAP. And the thread included more than one inaccuracy about BAP. I do not mean to sound belligerent and I honestly do not believe that I have misrepresented anyone else's work and I was just trying to set the record straight. Change "attacks" to "attack" and redact my paragraph where I thought the moderator was claiming GM's have a near perfect understanding of chess.
In the past, the reaction to BAP has been nearly universally hostile, so if I am overly sensitive it is due to this history and there have been many personal attacks on other boards. This board has actually been the most civil of all of them, so it really was just Jon Jacob that got me all bent out of shape. Sorry about that.
Jacobs did say "counting a draw as a loss for White", that's who made that claim.
On the last round pairings example, the one who has black with 18 points is the sole leader as that player achieved that out of 1 less possible point than the one who is playing white with 18 points. My point is that when one player is ahead of the other player in the last round, it is normal for the player who is ahead to be able to control his destiny. Why should anybody except the sole leader be able to control his destiny?
What BAP does is allows ANY of these four players to win the tournament outright simply by winning. There could be a sole winner with 21, sole winner at 20, sole winner at 19, and many possible ways to have more than one with the top score. This variety of possibilities in the last round is a good thing as normally if a player is half a point ahead, they can just draw and assure themselves a share of first. Much less possibilities for the audience to get intrigued by. What happens at the last round of the BAP tournaments that have been held is that none of the players can know with any certainity how many points they need to be safely in the money,so they all decide to play to win in the last round.
I totally admit I was dumb about misunderstanding your paragraph where you agreed with me. Sorry about that. Is that what you mean about me misrepresenting others? I will try to parse things better.
Did you use the Cunningly Reversed AP system to make fun of BAP or because you think that a point system that would encourage draws is bad?
Clint
The CR-AP doesn't refer to BAP, but to a different system, a sort of inversion of BAP. That said, I don't like BAP very much, but I am thinking more about it.
I think you're missing the point about my last round scenario. My complaint isn't that the poor 18 with White or anyone but the 18-pointer with Black can't win the event without help. It's that given a typical prize distribution with a significantly larger first prize, the odds of a thrown game go up significantly. Because of the color disparity, there will be on average fewer players who can guarantee first place with a win, which means the motivation to avoid a big first-place tie at the top will be greater, which encourages bribery. (Not that that ever happens in big chess tournaments, of course.)
Re copyrights, I appreciate your scruples, but providing links is legally unproblematic.
Doesn't it seem screwy to you that someone who draws six games - REAL games - in a six-round tournament should wind up tied with someone who loses five, but wins one game with Black? (Assume each faces the same quality opposition.)
If BAP is the inverse of CRAP, I can't take offense at that. I had assumed that you were lumping all different point systems together.
On the cheating issue, BAP doesn't address cheating as it assumes the players are honest as all point systems do. In the presence of cheating, I claim that any point system will be corrupted.
Even assuming that anybody who is the only person who can win will be guaranteed to offer a bribe and the opponent would be guaranteed to accept it, I don't understand the probabilities you used to conclude that "on average fewer players who can guarantee first place with a win".
Last round pairings:
1. White (17) vs. Black (18)
2. White (18) vs. Black (17)
In the above scenario, Black (18) is the sole leader. I think you understand this, so the comparable scenario using the 1867 point system is:
Last round pairings:
1. White (8) vs. Black (8.5)
2. White (8) vs. Black (8)
In the above scenario, we have Black on board 1 in the sole lead and the assumed cheating will also happen as a win would guarantee sole first. Notice that White (17) CAN win clear first with a win, so the odds of the bribe being accepted is probably comparable in both cases. I am probably missing something really obvious with your example, but all I can see is that if there is a sole leader in the last round he can control his destiny and if he wants to cheat and has a willing accomplice, BAP or no BAP, same result.
Ah, I think I understand your logic now on the assumption that BAP will increase chances of cheating by increasing the hard to resist sole leader playing against someone who can make more money accepting the bribe than playing to win. I think it is clear that a lot more people have a chance to win outright or at least tie for first with BAP. The large permutations make it nearly impossible to know the outcome and I guess if there is somebody who could guarantee a win to avoid all these permutations would be more inclined to bribe the white side. So, the key question is if the white player will be more or less likely to accept the bribe. I don't know. I was shocked when I found out that cheating is so rampant in chess. this is the other thing that prevents chess from being taken seriously as a sport. Cheating is like jay walking. Everybody does it, no big deal. It is expected to happen.
I have not worked out the probabilities of there being a sole leader in the final round with BAP vs. non-BAP. Have you? If we had:
Last round pairings:
1. White (19) vs. Black (18)
2. White (18) vs. Black (17)
Now, I think white would be much less likely to accept a bribe as he has a chance at clear first, just like black does. So, if the analysis is that if we have the leader playing black, cheating odds are increased a bit and if we have the leader playing white, cheating odds are decreased a bit. Wouldn't you agree it is unclear and could actually go either way?
Was there recent case law that allows linking, especially deep linking? Last I heard, only links to the main page was universally allowed, but if a website wanted to prevent someone from doing even that, they could have it removed. I know I have had several personal experiences with this, so without explicit permission to link to a site, I am very leery of doing so.
It certainly seems a bit strange if someone has draws in a 6 round tournament. The fact that this is even mentioned as a possibility is kind of the reason I came up with BAP. With current point system the odds of a typical player getting 6 draws in a row are 2.7%. So, in a 40 player field we can expect one player with such a result, using normal point system he ends up with an even score in the middle of the pack. Now, with BAP, if you can use my estimated 25% draw percentage, then the odds of a player with 6 draws in a row is I player out of 4096! So, as strange as this is, if one player out of 4000 who would have been in the middle of the pack normally, but ends up in the bottom half, is that such a big price to pay if there are some benefits? BAP isn't 100% roses, we do have to give up something to get something. I am personally willing to have such strange anomalies occasionally happen and since they are out of the money anyway, how big of a deal is it anyway? In the tournaments held so far, the prize winners have almost always gone exactly in the same order as traditional point system would have ranked players. I think there was one player that got a share of 3rd place who otherwise wouldn't have.
When I first saw the thread I noticed Jacob's error, but when I later was trying to find the exact quote I couldn't find it, so that is why I didn't quote it initially. However, it is there for all to see and the fact that BAP is not zero sum is true even in the last round. Whether this increases or decreases the odds of cheating is unclear to me. My conclusion is that the only way to eliminate cheating is to eliminate the cheaters, so the best I have come up with is a policy to ban players who have cheated, or who are involved in suspicious games from my tournaments. Legal to do for invitationals, problematic for Open tournaments. I think a much bigger cheating problem is the use of computers as they get smaller and smaller. What about the players that implant a single chip computer inside their shoulderblade? BAP doesn't prevent that. That is not a reflection on BAP, I hope you can agree to that point.
In response to the 12:39 am post:
I am very confused about this post. I am not sure if I can respond without risking being banned :)
I will try to present things logically in a very dry humorless way to minimize chances of being misunderstood.
Your CRAP system is where draws are worth two thirds a win, so it would certainly increase the draw percentage. However, I do not understand how you concluded that sharp players would get domesticated by the grind-lovers. Implicit in that conclusion is that the grind-lovers have a significantly higher draw percentage and the sharp players have a significantly lower draw percentage. If that is your assumption, does that mean Karpov at his peak was a sharp player? If memory serves me right, Karpov had one of the highest win percentages ever, by any player. I would actually think that Tal would have benefited from CRAP more than almost anybody else. Couldn't he have forced perpetual checks in a lot of games? CRAP might have the effect of increasing sharp play that ends up in perpetual checks. Aren't there quite a few opening lines that white can choose to go down if he wanted sharp tactical game with a very high probability of a perpetual check where if the opponent blunders he picks up a win?
When I first devised BAP I had a certain idea of what I thought would happen. However, my actual experience running these tournaments showed that BAP had a slightly different effect. Now, you think that less volatile grind lovers would suffer under BAP, but this contradicts one of your other predictions, namely that black has an unfair advantage far exceeding the advantage white has with the current system. At least I think you said that. I apologize in advance if you didn't make that claim. If the grind-lovers suffer when playing white, they would gain disproportionately more when playing black as black drawing has a 3 point effect on overall points while a white draw has a 2 point effect. As black, the grind lover happily starts grinding away full well knowing that it is a matter of time before white lets his dynamic nature overtake him and pushes for a win that is not there. Presto! Grind-Lover 3 and Sharp Player 0. As white, Grind Lover does the same and the sharp player learned his lesson and doesn't force the issue. Grind-Lover 3 and Sharp Player 1. with BAP, it is dangerous to make conclusions by analyzing only one color. It is not a zero-sum point system, so to have a semi-realistic prediction of what will happen, both sides of the equation needs to be looked at. Alternatively, you could ask me if the grind lover's suffer in the BAP tournaments that have been held. If you did, I would answer that one BAP tournament was won by a player most would call a grind-lover who played the London as white.
Positional chess is supposed to be based on the tactical underpinnings or future tactics that will arise, so I don't think BAP penalizes players who have a more positional style. Karpov would certainly do fine in a BAP tournament against players of his strength. I think we can agree that neither white, nor black has a forced win from the starting position, or at least nobody has published the 32 piece tablebase yet. My feeling is that the point of playing chess is to try to win the game. Not that draws are worthless, but the goal of chess is to win. If we can agree on that as common ground that we all play, study, etc. chess in order to win more, then the only question regarding the point system becomes:
Which point system encourages winning more, BAP or 1867?
I predicted BAP reduces the draw percentage significantly. It did. I predicted, white would play on in positions they couldn't win, white ended up playing harder than normal!. I predicted the draws that we do have will still be interesting. They have been.
Skeptics have predicted a whole host of things that have not come true, like players will change how they play. They haven't. White has no incentive to fight for a draw and would just resign games rather than play on for a draw. Nobody has done this.
The things that have happened with BAP tournaments are that players who drew disproportionately suffered in the standings, but it had no effect on prize money and since the rating system hasn't changed, no effect on ratings. What it did do I think is positive. In the subsequent BAP tournaments, the exact same players that had disproportionately more draws didn't repeat that. They improved their play and played on in positions they were better in and converted it to a win a lot more than originally. These are some of the local masters in the NW, not class players. BAP is not designed for class players, other that to get a feel for what it is like to play master level chess. There are just so many positions that have small enough advantages, it takes a master to convert them, but only if they are motivated to do so.
In any single game BAP can be brutally unfair. A player can play a brilliant game end up with a fantastic memorable draw and get 0 points, but he did hold his opponent to 1 point. A football team that fights valiantly and loses to a last second field goal, they get 0 points. Somebody has to win and somebody has to lose.
In a single tournament, BAP will lower a player's ranking if they have a disproportionate amount of draws. They are out of the money anyway and if they can't learn to win, they won't ever win prizes at master tournaments. BAP actually accelerates the process for players to learn how to win as without BAP, they might never feel the need to learn.
In a sport, it is expected that both teams will play hard 100% of the game. It is expected that nobody will cheat. It is expected that only one side will win. BAP brings that level of a black and white result to chess. The tradeoff that needs to be made to the game are mostly minor negatives versus a giant positive. BAP still has problems,but those problems are universal and not a reflection on BAP. There are certainly nightmare pairing scenarios that are possible with a BAP tournament and there is the need for an extra round or two with BAP tournaments to get the same resolution in a swiss. Now that is a valid complaint about BAP, but the fact that BAP removes the odd round swiss tournament color bias is compensation for the extra rounds. Since all players play an equal number of white and black games, regardless of what bias exists for black, all players play with no overall biasing at all. 0% overall bias for 100% of the players. In contrast, current swiss tournaments with an odd number of rounds have nearly 100% of the players with a 25% bias for or against them in the last round. Nightmare pairings are also very possible with normal swiss tournaments.
So, I am glad finally somebody is actually engaging me in a real debate about the merits of BAP. Thank you for that. BAP isn't perfect, but it is an improvement over the current point system if we want to encourage chessplayers to learn how to win chess games.
I know 140 years of tradition is hard to part with, it would be almost like admitting the possibility that Einstein might have been wrong about some things.
If BAP reduced the GM draw percentage to 25% and made every draw the fighting draws that we prefer over the lifeless ones would you change your mind? What if it turns out that positional players benefited as much or more than tactical players?
Clint
This contains an illogical element, depending on how CB defines blunder. Since Steinitz we know, that we only can win thanks to a mistake of the opponent. Hence our task is to seduce him to make one. As knowledge, understanding and technique increases/improves, the likelihood of mistakes at top level decreases.
So, if CB wants chess without mistakes, he hopes for a situation with 100% draws - exactly the opposite of his aim with the BAP-system.
This is not a personal attack - I wish him all the luck with his tournament. If it works in practice - and that's all what counts - I'll be convinced. It was the same with the Sofia rules: initially I did not like them, but now I have to admit that there is no reason for my dislike. I hope the same will happen with the BAP-system, but until then I preserve the right to remain sceptical.
Under the 1867 system, the expected score of a player of unknown strength after 2 rounds is 1 point. This can either occur by A) two draws or B) one win and one loss. Playing style A is more likely to play with the draw "in hand" when possible, whereas playing style B is willing to take chances.
Of course, a player who adopts style A also takes the "chance" that a player who adopts style B will overextend and lose the game. Thus it might be so (and it seems to me) that all else being equal, style A (the "grind-loving" player) is preferred to style B by the 1867 system.
I don't know if that conclusion is problematic or not. However, I *do* believe that it is the players' right to decide what system they play under, BAP or 1867, and would be most upset if this matter could not be decided by majority vote of the players or some other fair means.
As regards the BAP system itself, I fail to see the reason to give Black more points for a win or draw than White; is the game itself really that biased? As opponents' colors vary for each player it would seem that a strong player could "grind" his equals with Black and pummel his inferiors with White. Certainly pairings this inequitable would never occur, but the huge disparity (3 vs. 2 for a win, 1 vs. 0 for a draw) means that pairings would almost always be unfair: I fail to see how anything other than a Double Round-Robin would be totally fair to all the players. Just my opinion, but hopefully someone can make
rhyme orreason of it.By blunder, I mean a move that gains nothing, but loses something significant, eg. dropping a pawn for no compensation, or not making a move that had to be made to save the game.
It is quite possible to lose a game without making a blunder, especially to the so-called grind player. In computer eval terms, losing 0.02 pawns every move will leave you down a pawn after 50 moves and a lost endgame. It is not clear that a move that loses 0.02 eval is even a mistake.
Also, the statement that "As knowledge, understanding and technique increases/improves, the likelihood of mistakes at top level decreases" is certainly true, but in absolute terms the error rate of the best human players is still very high.Just look at any non-trivial endgame and compare it against a tablebase. The chances of a move being made that is not equivalent to the best move is quite high, even if it is Kasparov as he does not have tablebases loaded into his brain.
Now, imagine a 32 piece tablebase. What human will be able to play perfect chess against that? What are the odds of a move being made by the world champion that is not the best move or equivalent to the best move? I claim, quite high in a lot of situations.
My theory is that chess that is being played today by top GM's is in many cases totally unsound if it were played against a 32 piece tablebase. If that is the case, then that means that virtually every game between GM's would have a forced win in it.Even without such a tablebase, Hydra is able to outplay all humans at OTB time controls.
What I have seen in the BAP tournaments is that the the draw percentage goes up when the playing strength goes below around 1800. The reason is that these players are not able to convert the advantages they have into a win. As the players get stronger, the draw rate goes down for a bit, but then starts going up somewhere around 2300 to 2400. At this strength the players are able to convert the advantages that the lower rated players can, but they just don't get many games with that much of an advantage. At this point and above, the draw rate just keeps going up and up and up.
My other theory is that at around the 2800 ELO level, something similar happens as what happens at the 1800 level. The advantages that the under-2800 can't convert to a win are now enough for the >2800 players to win with. This is why we see the reigning world champion win against the 2600 players who are not making any blunders.
Clint
I would fully expect that any tournament that is to be conducted under BAP be announced as such, so if a player does not want to play using BAP, they just don't bother playing in the BAP event.
The goal of all non-double round robin tournaments is to find the player that would have won a double-round robin had there been time to play one. No pairing system is anywhere close to perfect. All pairing systems have nightmare scenarios. However, since it isn't practical to play full double-round robins, we need to make do with compromises.
You probably won't be surprised to find out that I have experimented with alternates to the standard swiss, beyond just the BAP color balancing. One that is quite promising is based on the basketball playoffs, where the top player plays the bottom player, etc. So during the first part of the tournament we have pretty predictable results and this rewards the players with the high ratings. The middle players are very close though so anything can happen. After a few rounds like this, the field is whittled down to the contenders. If this is small enough, then they can play a round-robin, single elimination, double elimination, etc.
The swiss tournament was first played in 1895, so I also feel that it is time for some improvements in that area also.
As to the reason for the seemingly disproportionate points given to black, the reason is that black has a harder time scoring points. At the recent GM Slugfest Qualifier that had A-players, experts and masters, black scored around 63% of the total points. This is significantly more than the 55% score that white scores using the 1867 system. However a very important thing to realize is that this 55% is for GM players. The 2100+ players at the Qualifier scored 55% as black and 45% as white, so the biasing in this one event was the same magnitude as the 1867.
This is why I feel so strongly that BAP will be less biased for black than 1867 is for white at the GM level. The percentage of points scored by black under BAP is expected to decrease as the playing strength goes up (above 1800). Since the percentage is around 63% to 65% for 1800 to 2000, dropping to 55% around 2200, it is reasonable to expect it to come in lower than 55% for GM's. It probably won't drop to the 45% that 1867 does, but that is a good thing.
I am researching the white vs. black wins of the strong players to provide a bit more background on this.
Clint
A very important point is that I did not do any adjustment for the opponent's strength, so this data is only for a sanity check.
I put in 4 different point systems, the current one first used in 1867, BAP, BAP2 and BAP3. For each point system I calculated the ratio that the player got relative to their opponents for both black and white. One thing that stands out is that with the 1867 point system, the ratios for white is in a pretty narrow range that is 50% to 70% more for white. If we take this as face value, it says that Kasparov is 50% better when he plays white as when he plays black and so are all the other players?? Clearly, it makes a lot more sense if black is just more difficult to play and that explains why the same players as white consistently outperform themselves as black. Since Kasparov is Kasparov no matter what color he plays, a point system that shows Kasparov at roughly the same strength with either black or white would be an improvement over the 1867 point system.
The biasing in favor of white is consistent regardless of the player's style. Of the new point systems, BAP3 is clearly superior based on this small amount of data. I divided the difference between the white and black ratio by the sum of the ratios to get a normalized biasing. Not super precise, but close enough for a quick approximation. This ratio is surprisingly consistent for all the players:
Fischer 0.20
Capablanca 0.20
Kasparov 0.26
Karpov 0.30
Anand 0.24
Tal 0.21
Smyslov 0.21
Larsen 0.18
J. Polgar 0.25
With Tal and Smyslov having the same ratio it is a good sign that this factors out style differences. The ratio with BAP is biased in black's favor a bit more than twice as much, so based on a static result assumption, BAP would seem to be biased far more for black than white is currently. However, when the point system is changed and games are played under it, the result distribution is expected to change, possibly dramatically. BAP is calibrated with the assumption that the draw percentage will be around 25% and that white will win twice as much as black, eg. 50% vs. 25%. Real data is needed to prove or disprove it.
BAP2 is a variation where a black win is set to be the same as a white win, eg. 2 points. BAP2 does reduce the black biasing that black has, but it is still significantly higher than 1867 white biasing. Of course, until we know what the draw percentage and the white win vs. black win ratio is, we cannot know which point system is more balanced.
BAP3 is an clear improvement over 1867. BAP3 is where the values for a win are reversed so that a white win is worth 3 and a black win is worth 2. This simple change to BAP creates some very interesting results:
Fischer +.08, 63% reduction
Capablanca -.22, 10% increase
Kasparov -.09, 67% reduction
Karpov -.02, 94% reduction
Anand -.07, 72% reduction
Tal -.13, 38% reduction
Smyslov -.16, 26% reduction
Larsen +.20, 12% increase
J Polgar +.23, 9% reduction
With the only increase in biasing being in the 12% range and the rest being reductions in biasing, with Karpov's case an amazing 94% reduction, BAP3 is a clear winner. Before we get too happy with it, the static model assumption is used here, so it is not clear if games played with BAP3 will have this distribution, but if minimizing biasing is the goal BAP3 is very promising. BAP3 is also the only point system of the 4 that has both positive and negative biasing. This lends further weight to BAP3's promise, especially as the biasing for or against white does not seem to be based on a player's style:
J. Polgar +.23, Larsen +.20, Fischer +.08, Karpov -.02, Anand -.07, Kasparov -.09, Tal -.13, Smyslov -.16, Capablanca -.22
Whether a player gets a white bias or black bias appears to be random and not a factor of their playing style.
With the 1867 point system, it says that a player is 50%+ better when they play white as when they play black, but since they are the same player, this is silly. With BAP3, the following are the ratios of the players by color:
Fischer 4.17 times better as white, 3.58 times better as black
Capablanca 3.18 times better as white, 4.95 times better as black
Kasparov 2.87 times better as white, 3.41 times better as black
Karpov 2.18 times better as white, 2.26 times better as black
Anand 2.10 times better as white, 2.41 times better as black
Tal 1.88 times better as white, 2.45 times better as black
Smyslov 1.67 times better as white, 2.29 times better as black
Larsen 1.78 times better as white, 1.18 times better as black
J Polgar 1.49 times better as white, 0.93 times better as black
BAP3 dramatically narrows the differences these players are with white vs. black. It makes a lot more sense that Fischer was 4.17 times better than his opponents as white and 3.58 times better as black, vs. the 1867's 3.34 times as white vs. 2.21 as black.
I think the above ratios are a good indicator of how good the players were with the openings of each color. Curiously Larsen was a lot stronger as white and this could be due to his unorthodox openings that he was very familiar with, but his opponent's were not. Capablanca's significantly lower performance as white as compared as black could be a hint of the player he could have been had he spent a lot of effort on openings for white. His 4.95 performance as black is by far and away the highest value of any of the others analyzed and I doubt I will find anyone that will do much better than 5 times the score of opponents when playing black.
How you do as white is a function of your opening preparation, but your performance as black is more indicative of innate chess talent. While you can certainly prepare openings for black, white dictates the opening a lot more than black. So, ranking these players by innate chess ability, we get the following ranking:
Capablanca 4.95
Alone at the top in a class by himself. Best player of all time and would win chess960 with incredible results.
Fischer 3.58
Kasparov 3.41
These two would be tied for first in a class by themselves, if it weren't for Capablanca.
Tal 2.45
Anand 2.41
Karpov* 2.26
Smyslov 2.29
The "ordinary" world champion category. Certainly amazing to score more than twice as many points as black than opponents. Now, the games used went to 2002, which includes Karpovs non-world champion strength games, so I expect that if only his games are used from his peak performance he would join Fischer and Kasparov.
Larsen 1.18
J Polgar 0.93
The "ordinary" super-GM that scores as many points as black as their opponents.
To do this right, a opposition strength normalized database needs to be used and also it would make sense to factor in a player's strength relative to their peak.
So, BAP3 appears to be better at determining a players strength than 1867, by a significant amount. Let's see how BAP3 does to the draw percentage.
White win 3 points
Black win 2 points
Black draw 1 point
White draw 0 points
Relative to BAP, white will want to win 50% more. However, it could lead to overpressing as even a 33% chance of winning is enough to score 1 point on average. Overall effect is 4 points.
Black gets 2 times as many points as drawing as compared to three times for BAP, so there is less incentive for black to play for a win.
If white is in a worse position, the overall value of saving the game and drawing instead of losing is only 1 point. This cuts in half the value of saving a draw.
The value for black saving a draw is 4 points, so this is 33% more incentive than with BAP.
The value for black converting a win instead of drawing is 1 point which is half of BAP.
white convert better position: 3 BAP vs. 4 BAP3
white saving worse position: 2 BAP vs. 1 BAP3
black convert better position: 2 BAP vs. 1 BAP3
black saving worse position: 3 BAP vs. 4 BAP3
white incentive to win: infinite BAP vs. bigger infinite BAP3
black incentive to win: 300% BAP vs. 200% BAP3
What BAP3 has over BAP is that it further increases white's desire to win, but BAP already has that at maximum level, so this is not really a valuable gain. What it gives up is that black's will to win is reduced significantly. So while BAP3 appears to be a good point system for determining player strength, it is not as good as BAP as far as reducing the expected draw percentage. While in practice it could have a lower draw percentage than BAP due to white overpressing, without errors the lower incentive for black to win leads me to believe a draw percentage of around 40% will result. Pure guesswork, but I am probably the world's leading expert on the effect of different point systems on the results of chess games at the master level :)
So, what to do with BAP3? It seems to be such a valuable metric. The answer is that BAP3 should be used as the rating system!! Of course, the resistance BAP has created for its use just with pairings and prizes makes it impossible for any new point system to determine ratings, but BAP3 appears at first study to be far superior to the 1867 system. After all, does it makes sense that 60% of your rating is based on how you do as white and only 40% based on how you do as black? That is how the current system is setup. A player's rating is 60% how they do as white and 40% how they do as black.
Capablanca best all time player? has the table of data, I couldn't get it to post here.
Clint