Following up on my promise from two weeks ago, I have compiled and analyzed the data from the 2016 Sinquefield Cup. Before I begin, I tweaked one of the goals so that it would better serve the chess community. I had previously stated that I was going to use all 45 games from the tournament; however, since the second half of the tournament tends to have more games peter out to early draws after the players get a feel for who has a significant chance to win the tourney and who doesn’t, I decided to only use the first 25 games. Sure, it’s a smaller sample size, but the data will be more telling.

I have grouped the moves in such a way that they have more impact since players tend to also ask, “Which area of the game should I spend the majority of my time?” The groupings will be as follows: Moves 1-10, 11-15, 16-20, 21-30, and 31-40. As stated in my previous article here, I am only analyzing the first 40 moves because the number of games that go the distance is relatively few and time controls after the first 40 moves are not always constant. Before we move on to the data, some definitions: **Mean **is the average value of the elements in the set; **standard deviation** is the variance (I meant to use the square root of the given values, which is the actual standard deviation; what is shown now is the variance. When time permits over the weekend, I will try to edit these tables to show the correct values) in the data (the larger the standard deviation, the more spread out the data is); **standard error** is the standard deviation put into perspective based on the sample size. **Mean(x1-x2)** will show the mean time spent for each interval of moves. **AverageTotalTimeSpent(x1-x2)** will show the average total time spent during the interval of moves. All measurements of time will be displayed in seconds for consistency. For every move, the lowest and highest value were discarded in order to account for outliers.

Let’s start with moves 1-10:

The table shows the calculation used and the resulting values. The first three rows are move-specific, while the last two (in orange) are in regards to the whole interval. The mean time spent on the move increases throughout the interval, which is expected. The moves become less automatic as the game develops out of the opening. However, no more than two minutes was spent on any move on average for these first 10 moves. This is, once again, expected, since most games are still in “book” and the players know the moves they are playing by heart.

Moves 11-15:

Unlike in the previous table, the means here are not in perfectly ascending order. This denotes a couple things:

- The opening stage typically comes to an end around here since the times are not as low and not in ascending order
- Any difference or value that doesn’t follow a linear path is normal and purely due to the fact that it turned out that way, and there is no other explanation.

Just by comparing the mean times from this interval to the previous, it is easy to see that the players are already beginning to slow down at this stage. *Disclaimer: If your opening knowledge extends beyond this point, then, by all means, continue to play faster. This is merely a general guideline for the common opening. *It is also possible to see a steadily increasing value for standard deviation; this signals that at this point, the times spent per move are varying a great deal. This suggests that the typical middlegame begins around this point.

Moves 16 – 20:

Shockingly enough, the trend seems to be reversing at this point! The mean time spent during this interval is decreasing move-by-move. While the middle game might not be over yet, the data suggests that the most crucial part of the game is nearing its end. Once the players have cemented their plans, the moves begin to play themselves, and not as much thought is required. After all this, there seems to be one discrepancy: while the mean time is beginning to decrease, the total time spent is still higher than previously. This is most likely due to the fact that some games were still in their opening phase during the 11-15 interval, while all games were in the middlegame phase at this point.

Moves 21-30:

The trend continues with the mean time decreases steadily as the move count increases. Also, the standard deviation values are also beginning to stabilize after they were quite volatile in the previous intervals. These are likely due to the fact that some games are beginning to liquidate and, as a result, not as much time is being spent on moves as a whole. The inflated value for average total time spent is solely due to the fact that there are 10 moves in this interval as opposed to 5 in the last two sets. In reality, if they were all sets of 5, the average total time spent would be significantly lesser.

Moves 31 – 40:

This last set comes as no surprise that the mean times spent for moves in this interval are even lesser. For many of the games, the position at this point was at the endgame and not as much was being spent; specifically for the draws, the moves were basically being blitzed out. It is best to ignore the last column – the time retrieving software from this website couldn’t get those times for any game’s 40th move. However, the rest of the moves are still perfectly reliable. The standard deviation value is still steadily decreasing. Any odd calculations (like move 32) are, once again, purely due to the fact that it just happened that way, and there were no other significant factors in those specific results.

Now that we have an idea for how these grandmasters divided up their time based on the situation of the game and the move interval that they were at (important since they had to make the first time control in 40 moves), it is possible to look at all of the moves as a whole. For sake of consistency and lack of a need to waste space, I will not be presenting the whole set of data; that would just take up way too much space. However, in order to represent that data, I have created a couple graphs to depict the visible trends.

The bar graph here plots the move number against the average time spent on that move. The basic shape of a distribution can be visualized from this. The varying values that are encountered while nearing move 40 are due to the fact that fewer games reach that point, thereby leaving the mean values the chance to move drastically at the slightest change.

This graph uses the same set of data but utilizes a scatter plot of all of the means instead. The ability to fit a regression to this data aids in the visualization of this data. While the regression is not a perfect distribution, Excel does not allow distributions to be fitted to data, so a polynomial regression was the next best option. It is easier to visualize the relationship between the time in the game and the time spent per move with these graphs and it offers insight into the minds of grandmasters and how they manage their time while playing their games.

To wrap up, we can conclude that the majority of clock time should be spent in the middle game, and typically, long thinks should only be made while attempting to formulate a plan. Once a plan has been decided upon, it should not take as much time to make the moves on the board. For the most part, these results are reliable since they come from the world’s best players. There were a couple limitations in this study. The most important one was that there was a difference in the players in the tournament; sure, some of these players are known to play faster or slower than others. However, in the end, they are all around the same skill level and know equally well how to manage their time.

If time permits, I hope to be able to analyze the data even further so that I am able to provide more situational results instead of a generalized picture. If I am not able to, I will discuss another topic next time. I hope that the information presented today will help you in the future in managing your time wisely at the board. As always, thanks for reading, good luck in your games, and see you next time!