"Why Do I Always Get Black Against Titled (Stronger) Players?"
Monday, August 23, 2010 at 2:48PM This weekend I played in a strong open swiss tournament and was in the running for first, but lost in the last round to GM Ben Finegold. He had White, but that wasn't really a factor: I got a perfectly good position out of the opening, and only mistakes in the ending cost me the game. Still, it would have been nice to have White, and I've heard many players lament that they "always" get Black against titled or significantly higher-rated opponents.
It's likely an exaggeration and a bit of a selection effect (they "forget" when they're White, but each Black game confirms the "always" narrative), but I think there's something to it. To the extent that there is some truth to it, the lamenter should probably stop complaining. Here's why. Aside from the luck of something like a first-round pairing against a strong player, you'll have to do some winning to play them. Now, the question is this: other than in cases where you're overwhelmingly stronger than your opponents, are you likelier to win your games when you're White, or when you're Black? With White, naturally. Let's say you're likely to face a big gun in round 4 of a tournament, when you're 3-0. If you've had two Blacks, you're less likely to have gone 3-0, even if you were a favorite in all your games. It's a lot easier to have done it with two Whites. But then, guess what? You're due for Black against the big gun!
This probably holds for the round 3 situation as well. Let's assume you're in the top half of the draw, but not a top player yourself. In round 1 you're probably going to beat whoever you're playing, and in round 2 you'll get a more challenging opponent, but one you're a moderate favorite against. If you had Black in round 1, then you're more likely to win in round 2, but to suffer in round 3 with Black against a very good player. If you've got Black in round 2, then you might win and succeed, but your chances of getting nicked go up as well.
If all this is correct, then the reason the lamenter should cease his song of woe is simple: if he weren't due for Black in their game with the better player, he would have been less likely to face the better player in the first place. (And note the irony: his previous opponent may have been a victim of the same sort.)
Hopefully someone will (or maybe already has) worked out the math of the situation, but this seems like a plausible account of why non-top seeds will more often wind up with Black in the big games with the favorites in open swisses in the mid-to-late rounds.
[Note: Comments are again possible, but I will moderate them before they appear. Other solutions are being considered, so stay tuned.]
Reader Comments (20)
I really don't know much about pairing Swisses, but isn't there something about how the higher rated player gets white if you are both due white? This being the case, it's probably not entirely an illusion that it seems that you get more Blacks against higher rated players.
No, there's no such rule. What is a rule is that the higher-rated player gets the color he's due in case of a color clash (all else being equal), but that's true whether he's due for White or Black.
Oh yeah, that's right, I just remember it that way because I got Black once against a higher rated player when we were both due White, which goes along with your observation that there is a perception about how you remember when you were "slighted".
At the US Open Rd1 white against a 1300 black against a 2200 rd3 black against an 1800 rd4 black against a 2200. Nope, its not selective memory. I keep statistics. Not only do I managed to get black in 65%!!! of my games. I actually have an extreme number of blacks against high rated players. This in fact makes my 50% score against experts much more impressive (i'm rated 1900) when you consider that actually I have black 75% of the time against them! In fact one of the worst records I have is against a certain expert who has beaten me 6 times to my beating him 2. However.... all 8 games I had black. That is correct, I have never ever had white against this person.
In a local tournament about a year ago, I had a third round encounter with a FM. I'd beaten a 2100 in the first round and could've/should've won the second round until my mind decided to mess up in the endgame. The master had a slow start and I was paired against him. I was due for the white pieces, but so was he and he outrated me by a 'mere' 400 points; I got black and had to defend the Ruy Lopez, did pretty well with the Modern Steinitz until I got totally creamed after delaying my queenside counterplay for too long.
I know very little about tournament schedules (and try to keep it that way), but someone told me after the third game if I'd won my second game, I would have avoided the FM; highly original advice: "Just win your games."
According to my fellow blogger Jonathan B, you are more likely to scalp a stronger player when you have black:
http://streathambrixtonchess.blogspot.com/2008/11/scalps.html
I've beaten two IMs in serious games. Each time I had black.
Sorry, but I'm not sure that makes sense! If players more often had black when they were playing titled players, then the titled player would (by definition) have white more often (than black). However, I'm pretty sure the titled player is going to get black half the time, and white half the time (in fact, the rule about the higher player getting the colour he is due makes this even more likely).
Without having gone over the mathematics, it may be possible that, if you fall within a particular rating group (for a particular Swiss event), you are more likely to play the titled player when you have white (for the reason you give). However, I think it is more likely that some people (simply through random variation) get black more often against titled players, and they are the ones who complain, while the ones who get white more often just smile quietly.
Here's an excellent resource if anyone wants check historical data from tournaments: http://chess-results.com/
There you can find pairings for all rounds for dozens or hundreds of tournaments.
I had a quick look at Philadelphia Open 2010: http://chess-results.com/tnr32277.aspx?lan=1
Top 12 players (starting rank) seem to have nicely alternating colours, and I can't see that they enjoyed white against weaker opponents more often than black. But this is only one tournament, and in order to get some real information someone should take a larger sample of tournaments and do some statistical analysis of the issue.
My guess is that it's purely selective memory.
@Steve: Good points. (But read on!) Clearly the top boards, like everyone else, are going to have approximately the same number of games with each color in the long run. And when top boards play each other, when one has White the other has Black, so there's not going to be any overall disparity there to be "made up" against lower-rated players. Further, when the top players play their early-round games, there too the number of games with each color will be approximately equal.
But I don't think these completely correct points refute the argument I was making, which I should state a bit more precisely for clarity's sake. If a player is significantly lower-rated, it doesn't matter very much what his color is going to be: he's overwhelmingly likely to lose. And if the players are close enough in rating, then while it matters in the context of a given game, the fact that the players are basically peers suggests that over time, their color balance will equalize. My target is games between players with about a 100-200 point rating difference: close enough that the game should be competitive, but distant enough that colors will, statistically, make a pretty big difference. I'm assuming that if the rating difference is less than 100 points or greater than about 200 points (or maybe a little more), one has no business whining about getting Black against higher-rated players, either because the player isn't much higher-rated or because the distance is too great to make much difference.
Here are some numbers, in case someone wants to run a Monte Carlo simulation. (These are roughly based on old USCF calculations.) If the rating difference is 400 or more points, the higher-rated player should be expected to win a four-game match 4-0. If 300 points, then 3.5-.5; if 200, then 3-1; if 100, then 2.5-1.5. Suppose further that if you're White, it adds 50 points to your rating and if you're Black, it takes 50 points away. (So there's a 100-point net difference.) Thus in a game between players 100 points apart, it's either a coin flip or a big 3-1 advantage for the higher-rated player, depending on the colors.
So suppose an 1800 must beat a 1700 to get a game with the local hero, a 2000 player. If he has Black, it's a coin flip, and half the time he'll get to play the expert in the next round and half the time the 1700 will go through. If he has White, we'll expect him to make it through to the expert 75% of the time. Let's say this scenario happens four times with each color. That means our 1800 will twice end up with White against the expert, but three times end up with Black against him. (And thus he whines!)
That's the logic of the argument. Now, the complication - and this is where we need some math and/or substantial data - is that there are other games going on too, and maybe (although I'm initially inclined to doubt it) the overall picture will somehow negate the previous reasoning. Hopefully someone will work this out!
The opposite is also possible, at least it happened to me once: At a Dutch blitz tournament with preliminaries and finals, I ended up in a group where half of the field was 200-500 points higher-rated than me *, and the rest had roughly comparable ratings. By strange coincidence (what else?), I had 6 whites and 1 black against the much stronger players, and 1 white vs. 6 blacks against the "beatable" ones. I slightly complained because I think my final score would have been better with a different color distribution. On the other hand, I have only myself to blame for not using the chances I got against two FMs - which I may not have had with the black pieces.
Bottom line: In round robins, a weak player may have better chances to get white against strong opposition. How common are such (blitz) events in the USA?
* Some of the strongest players may have deliberately avoided the A-final (with several GMs) to earn prize money in the B group!?
Back in the day I wanted to know why I got three Blacks in 4-round tournaments so often. I would usually get Black, White, Black, Black, the last two rounds usually against higher rated opponents. Eventually it dawned on me that it was always the same tournament director. Also, it was always friends of his that benefited by winning the class prizes I could never quite win after playing up 500 ratings points in the last round, with Black, while the other person playing for the prize always got to have White against someone rated less than either of us.
The lesson learned was to either become very good friends with the tournament director or quit playing in his tournaments. I stopped playing in his tournaments. Given that he directs a great many of the tournaments in my area it effectively meant that I gave up tournament chess for many years. Sometimes it really is a conspiracy.
@ Dennis, I’m not so sure that there is so much math to work out; the local hero should be due to have white 50% of the time and Black 50% of the time. And if the rule is that the higher rated player always get the color he is due, then he will get white 50% of the time and so will the 1800 player (in your example).
[DM replies: This comment doesn't address my point. The question isn't whether a player will, on average, get one color more than another. The answer to that question is obvious: he won't. Fortunately, that isn't at all what I was asking. Rather, my topic is whether two opponents a certain range apart (say, 100-200 points, with the higher-rated player at or near the top of an open Swiss-system tournament) are likelier to have a color imbalance against each other. Maybe the answer to that question is also no, but if it is it's not for the trivial reason that everyone is supposed to alternate colors every round.]
This discussion is about the lower rated player complaining about having to play black against a stronger player. In the case of the penultimate round I think the higher rated player is also complaining about having white against the low(er) rated opponent! That's because they would have expected to win with black anyway, and then in the final round they now are going to be black.
The point is that you can put a spin on it both ways. Of course which color you are against which player matters, but it goes both ways.
I think the best point was when DM pointed out how you're more likely to win your previous round with white, and if you had black the previous round you wouldn't be having this "problem" of being in contention to win and also being paired up with a strong player playing black. So this effect of lower rated players having black against stronger players at the end of a tournament is not necessarily a bad problem to have. It's like having the "problem" of paying tons of taxes on lottery winnings! That's a bit of an exaggeration, but the point remains.
My argument is too simplistic and it might not be correct, but it certainly addresses the point.
You made a calculation which shows that when a lower rated player meets a much higher rated player, then it is more likely that he has won with white in the round before. Therefore you infer that he then is more likely to get black when he meets the higher rated player. But that is only half of the story; the higher rated player would - say in round 6 - be due to have black half of the time. So even if the lower rated player was supposed to have black in 60% of the cases, he only will get black in 50% (as the higher rated player will get the color he is due).
On the other hand, you can argue that a lower rated player is more likely to meet a much higher rated player, if the higher rated player have lost in the round anterior, and this is more likely to have happened if he had black, and so he is more likely to have white against the lower rated player.
But actually, I don’t think it is so straightforward.
Pobody,
Ok, that's much clearer than the first time around. Your argument is that in it doesn't really matter what happened in the lower-rated player's previous round, in terms of colors, because the higher-rated player will always (or practically always) switch, making it a 50-50 proposition.
That makes sense, but I still think the argument of this post survives. Here's why. Let's say the top player is the top seed and the lower-rated opponent is the tournament's second seed. In that case, there won't be a color clash (they'll have started with opposite colors and continued that way throughout the tournament), and then my argument runs through the way I detailed it in the previous comment. On the other hand, suppose the lower-rated player is the third (or lower) seed. In that case, unless it's simply impossible to avoid a clash, the directors will pair him with a different but still stronger opponent - and that pairing situation will also fall under the conditions mentioned in my previous comment.
There may be a fly in the ointment, but I don't think we've found it yet!
@Pobody: I think the flaw in your argument is that you only consider one stronger opponent for the (previously) successful lower-rated player, but in practice the pairing software has several to choose from. Let's say that, in a given round of a Swiss open, eight GMs and two FMs still have a perfect score. For the GMs, this comes down to "business as usual" - they generally beat 'fishes' with either color - and four of them are due to play black in the next round, four should get white. The FMs most likely had an extra white an earlier rounds, hence they will face a GM opponent who is due to play white (four to choose from, rather irrelevant that there will be four others playing black in the same round).
Of course, if they always match a player who is due to have black with a player who is due to have white them your argument must be true.
[DM: Of course they always try to - this is a basic rule of pairing.]
Anyway, I think that the argument is better to make from the point of view of the stronger player in the matchup (as he will get his color in case of a color clash).
As most players score better with white than black, then it must follow that it is much more likely to get white after a loss, and even somewhat more likely to get white after a draw. And when a average player, who plays a good tournament, get to meet a top player late in the tournament, then it is more likely that the top player hasn’t won in the round before and thus it more likely that the top player is due to have white.
Actually, this is similar to your argument.
Since Dennis' theory actually sounded plausible to me, I tried to find some way to measure if the "Monokroussos effect" really exists. I assumed that, if a person is indeed more likely to face a stronger opponent if he had white in the previous round, and therefore he is more likely to play black against a stronger player in the next round, this effect must be quantifiable. So that means, if the rating difference in the subsequent round is bigger, it's more likely that the weaker player had some "help" by having white in the previous round. So all there was left to do, was to see if there's a connection between rating difference, and the color that the stronger player has. (I hope I am making sense so far... )
I took a database, filtered out all the games where both players have a rating > 2000, and where the PGN text contains [EventType "swiss"]. After that, I broke it up in groups with rating differences, and calculated the percentage where the stronger player had white. The surprising results:
rating difference (number of games) %white has the higher rating
1 - 100 (160197) 49,8%
100 - 200 (163689) 51,2%
200 - 300 (71629) 51,6%
300 - 400 (23274) 52,1%
400 - 500 (6407) 52,6%
500+ (1144) 52,0%
Not only does it confirm the assumptions, it even looks linear! I decided to test again, this time filtering out all the games from a round 1 or 2, take games only later than the year 1970 to correct for unreliable ratings, and where both players have a rating of 1800+. I assumed this should make the effect even more apparent, and it does:
diff (#games) %white higher
1 - 50 (56321) 49,3%
51 - 100 (76510) 50,2%
101 - 150 (74953) 51,2%
151 - 200 (53641) 51,7%
201 - 250 (31574) 52,3%
251 - 300 (17219) 52,2%
301 - 350 (8604) 53,3%
351 - 400 (4108) 54,0%
401 - 450 (2009) 55,2%
451 - 500 (964) 55,2%
501+ (710) 54,3%
I assume that the Monokroussos effect is even stronger than these numbers suggest, because of a couple of problems with my database:
1) not all the ratings are actual ratings, but a lot of them are estimates,
2) it includes youth tournaments, hence more unreliable ratings,
3) I found out that I have slightly more games from round 4 than round 3, and I don't think they can all be explained by a bye in round 3, so I assume some prior filtering has been done.
If someone has a database with a number of swiss tournaments, where -all- the actual ratings are known, and that include -all- the games of those tournaments, the results would be much more accurate, and significant.
Note that the number of games where the rating difference is less than 50 points is surprisingly small, I assume this is because of the nature of a swiss tournament, where a win or a loss make the opposition in the next round a great deal stronger or weaker.
I assume that the 49.3% in the table is actually the exception that proves the rule: since the stronger player will probably win with the white pieces, he would bounce back up in the tournament standings, and meet a player who is only slightly weaker this time, and have black again. The players at the top of the standings can't have white all the time, and since it seems they are playing white against a much weaker opponent, they should have the black pieces against the other players. So in a way, that small percentage makes up for the high percentages further down the table. Anyway, I didn't expect to see that at all, but it makes some sense.
Several people have asked to see my game. It will probably show up on ChessVideos.tv in a few weeks, but as a rule I'm not interested in presenting my games on here, for several reasons. One basic reason is that I don't like helping my future opponents prepare - the purpose of my blog is not to help me lose future games.
Excellent answer, PdV!---I was going to write that this test should be doable with databases. Did you mean to say you filtered /in/ games with EventType "swiss"? And filtered /out/ games with both players 1800+?
One other tweak involves how many tournaments follow strictly the "higher player alternates color" rule and have an odd number of rounds, rather than toss for color in the last (odd) round. If the top-rated player starts with White in Round 1, chances are ey will get white in Round 5. Does your looking at Rounds 3-4 already subtract out this effect?