Drawing Rates in Chess Pt.2 - Levelling Up!
“If you are interested in improving, think of a draw offer as an offer to remain ignorant of what you would have learned in the remainder of the game.” - Dan Heisman
When I did part 1 of this blog, I was looking at how the time control affected the likelihood of a player drawing a game of chess. I used Grandmaster level games to do this, and found that as expected, the longer the time control, the more likely you are to draw. Also, at the GM level, the time control made little difference to the overall score for White and Black, just the proportion of draws that were played.
But, not all players are Grandmasters. There are only around a thousand GMs amongst hundreds of thousands of FIDE rated players, and many more casual players on top of that. So, what about those of us who are not masters?
Does the skill of the player affect their likelihood to draw, or to hold an advantage as White?
Again, the seemingly obvious answer would be yes. This could be because at the lower levels, a greater number of decisive mistakes are made (such as dropping a piece, missing a checkmate etc.). These mistakes are almost never made in the professional level (I say almost), and even if they were to lose just a pawn at some point; often the player a pawn down in material would be able to hold the draw. But is there a straight correlation between a player's rating and their likelihood to draw?
To test this, I looked at the first Millionaire Chess Open tournament, held in October 2014 in Las Vegas. The big money (including a $100,000 1st place prize in the Open section) attracted big names like Ray Robson, Yu Yangyi and eventual winner Wesley So (the second event was won by Hikaru Nakamura). But with prizes up to $40,000 in the lower rated sections, it also attracted players of all ratings, all hoping to cash in on the huge purse on offer.
The time control was the same across all sections for that first event: 40 moves in 2 hours, followed by 30 minutes for the rest of the game with a 5 second delay from the start. (For MC2, the Under sections were changed to 40/90', G/30', d/5", meaning that the couldn't be compared as evenly.) This meant that the results could be compared fairly as they were played under the same conditions. The players were also split into 6 sections: Open, Under 2200, U2000, U1800, U1600 and U1400. This split in ratings allowed me to compare the results between the ranges reasonably well.
So, here are the results of the games in each section, graphed accordingly:
From what we can see, there is a difference in draws between the lowest and highest section. But there were more draws in the U1400 than the U1600. If draws are supposed to be more likely the higher rating you go, why is this not the case here?
Simply put, it could be that players at the U1400 level don’t have the ‘skills’ to finish off their opponents in an endgame where they should have a decisive advantage, whereas 1600 players are able to convert a winning endgame. And according to one famous historical player, it’s no wonder:
“The hardest thing in chess is to win a won game.” – Frank Marshall
And indeed, there is a lot of truth in this statement. Think of this for instance: In an even middlegame, both players are most likely looking for ways to break through for a win and not immediately thinking about a draw (there may be exceptions, for example when a player only needs a draw to secure a tournament win). But, if one player has an advantage (e.g. a piece up), the opponent is likely to be looking for drawing chances to save the game (such as a perpetual check or a stalemate trick). So, if you’re winning, you’re looking to finally checkmate your opponent (via a middle-game attack or simplifying to a won endgame), but you have to watch for any swindles your opponent could make. So you could say that there is more pressure on a player with an advantage, because they quite literally have more to lose!
Another reason why the draw percentages do not follow the pattern for those 2 sections is that often, lower skilled players do not resign until they are well and truly lost (e.g. a queen down), or do not resign at all! Because there are more moves being played until mate, objectively there are more opportunities for the player with the winning endgame to make a mistake and blunder away the win. Unfortunately, the PGN for the games in the lower sections were not available online, so I couldn’t look at the games to either prove or disprove this theory.
(A little side note, at my old school club, there was a KQ vs K endgame, and the player with the queen ended up stalemating his opponent in what was otherwise an easily won game. This was amongst two lower skilled players, and there was no clock in the game with no time pressure. So, it can happen!)
Aside from the U1400 section, the draw rates seem to rise steadily from U1600 through to the Open section. One measure of correlation, PMCC (often abbreviated to r), puts the correlation at 0.900 between the rating sections and the rate of the draws. The PMCC result is measured between 1 and -1, and where the closer to those extremities it is, the higher correlation the data set has. So the measure of 0.900 shows that there is a very strong positive correlation between the draws and the ratings of the players, which means that when the ratings of the players increase, the rate of the draws between the players also increases (which is clearly true).
(That bit is quite technical; if you don't understand what the PMCC is, there really is no need to worry )
So we’ve looked at the draws for each player; but what about the scores for White and Black? Does the White first-mover advantage carry through the rating ranges?
The first thing that surprised me here is that in the U1400 games, Black players scored better than White! Why is this? One explanation is that in that skill range, players are unable to capitalise on their advantage as White. It is generally thought that for less skilled players, the colour pieces you play as has very little effect on the outcome of the result, and this is a most likely the reason for this.
But one possibility for any ‘anomalies’ is that for each section, there were only 200-300 games played (with the exception of the Open, which had 532 games). This is a relatively small number compared to the tournaments I used in my previous blog; which had around 700-1,000 games in each section. So, this could also be down to the fact that simply, there isn’t enough games to get a solid conclusion.
At the time I was starting to draft this article, the World Open was in full swing, in Arlington, Texas. This event had over 200 participants in some of the sections, which were split by rating in an almost identical way to Millionaire Chess (the only differences were that there was also a U1200 and an Unrated section). The time control for most of these games was also very similar (40/120', G/30', d/10", the only difference being a 10 second delay instead of the 5 seconds used in Millionaire Chess). So, I took the results from that tournament, and did the same thing to see if the results were similar (huge thanks to shaun for pointing me towards the result page!):
Once again, we get a general increase in the number of draws from one section to another, with a similar number of draws to Millionaire Chess. But again, with the scores for White and Black, there seems to be less of a pattern in the lower sections. In the U1200 section, White scored over 57%; which is much higher than the 52-55% range that a lot of the results for the scores lie in. Compared to previous results, this is quite a large anomaly. Players as White in the U1400 section also scored worse than 50% like in Millionaire Chess, although both of those results could be down to co-incidence (for the U1400, 1-2% is a small margin of difference).
Generally, you can see the score for White increases as the ratings of the players increase, and this is most probably because the higher rated players are simply better at holding onto that first-mover advantage that the player with the White pieces has, and they can make it count through the middlegame and eventually into the endgame. This is why top grandmasters sometimes employ 'drawing weapons' in games where they take Black, in order to take out the first-move advantage for White and go for a draw (the Berlin Defence in the Ruy Lopez is an example, having been extensively used in many World Championship matches).
So, in conclusion, the higher rated you are, the more likely you will score well as White, and also the more likely you will draw your game (making those victories harder to come by).
But if you keep following Dan’s advice at the top of the article, and learn from your games, you never know, you could become one of those top rated masters one day…
* Ratings in the Under sections were paired using their USCF ratings. For Millionaire Chess, those with a FIDE rating had their rating converted using USCF = FIDE + 60. More about the rating rules used by Millionaire Chess can be found on their website here.