This study, modified from its original version published May 12th , 2009, is cited in Mike Hart’s Chess Strength and the Power of the First Move.

Introduction

One project from my Harvard Master's of Business graduate study program may of interest to your readership. The purpose of the project was to demonstrate the use of statistical tools and methods to address practical problems. My husband, Michael Hart (a former USCF Master (2242) from Massachusetts) posed three chess-related questions:

1. Does the player with White win more often than they lose for both Grandmasters (GMs) and Club Players?
2. Are Club players as likely to win or draw when playing White as compared to GMs?
3. Are the results (percentage wins, losses and draws) for the person with White associated with the skill level of the players, provided the players are evenly matched? I used data from ChessBase 10 and analyzed the results from 250 random, representative games by competitors with player ratings from 1605-1625 as well as 507 additional games by players with ratings from 2595 - 2605. I have labeled these groups "Club Players" and "GMs" respectively for simplicity.

Per the request of the CH editor, the details of the statistical analysis methods used have been removed (available upon request); instead the focus of my summary herein is on the conclusions.

On Question 1: We see from Table 1 that "Club Players" had 179 decisive games (94 wins and 85 losses as White) out of the 250 games played. From a statistical perspective, it proves difficult to reject the hypothesis that White holds any consequential advantage for this class of players. The win rate of the decisive games was only 52.5% (= 94/179). Detailed statistical analysis using the One-Proportion Z-test on the data in Table 1 shows that the 95% confidence interval of the win rate is 45.2% to 59.8%. To determine, with confidence that White holds an advantage that meets suitable statistical criteria requires an analysis of a much larger number of games, perhaps an analysis of 2500 games or more. (By comparison, note that flipping a coin 180 times results in a 95% confidence interval of 77 "heads" to 103 "heads". In our case, we got 94 wins out of 179 trials, very much akin to flipping a coin)

The analysis of the "GM Class" yields a different result. The data strongly indicates that the percentage of wins for "GMs" is NOT 50%. Based on the 507 outcomes analyzed, the win rate of the decisive games was 62.4% (= 128/(128 + 77)) which implies the true win rate of the decisive games for GMs is between 56% and 69% (the 95% confidence interval using Chi-squared methods). To refine the true win rate confidence interval further requires an analysis of a much larger data set.

On Question 2: Table 1 shows the "Club Player" decisive game win rate was 52.5% while for the GMs the decisive game win rate was 62.4% or a difference of 9.9%. Detailed analysis using the Two-Proportion z-test indicates that the 95% confidence interval for this difference is 0.1% to 19.8% which again can be narrowed down by considerably expanding the number of games analyzed. Regarding the number of draws in each class, the Club Players had 28.4% (= 71/250) while the GMs had 59.6% (= 302/507). This difference is 31.2 % with the 95% confidence interval of the true underlying differential drawing rates of GMs relative to Club Players to be 24.1% to 38.2%.

On Question 3: The distribution of outcomes for each class of players with the White are statistically quite different based on a Chi-squared analysis of the results shown in Table 1, primarily due to the increased drawing probability of the GM class when GMs have White, followed by the lower losing probability when GMs have White. Although the rate of losing with the White pieces for GMs is reduced from that seen from the losing rate of the Club Player class with the White pieces, this is of lesser statistical significance in reaching this conclusion.

1.1 DISCUSSION

Based on these results, I conclude that the distribution of outcomes of a chess game (percentage wins, draws and losses) is clearly associated with the class level of the players involved (provided the ratings of the opponents are comparable). Whereas White seems to be advantageous for GMs (they win far more often than they lose), such an association is not evident for Club players (who are nearly as likely to win as to lose even when they can make the first move). This study also shows that based on the 507 GMs played and 250 Club Player games played, statistically speaking, one can say with a high degree of confidence that GMs are far more likely to draw than the Club players, with the 95% confidence that the true difference in drawing rates between these two groups ranges from 24% to 38% supporting that statement. The increased drawing rate for the GMs is probably a sign that when GMs sit down at the chessboard, it is more difficult for them to actually win the chess game against another GM than is it for the club player to do so against another club player.