How long is an opening?

Before reading this post

The games in this analysis were lichess-annotated 3+0 and 3+2 blitz games from June 2023. More about the data can be found at the lichess open database. Players with more than 5 games on both time formats were chosen.

Deciding where the opening ends

Assume there is a random game. We have the x-axis as Move Number and the y-axis as Time Spent.
Maybe the game might look something like this.

I am making some assumptions here.

• Opening prep ends before move number 30.
• Players take more than 5 seconds to think after their opening prep.

5 seconds might seem arbitrary but it is the top 25% quantile of Time Spent on a move.

Then we can rank these points inside the box. I chose the 5 highest seconds spent inside each box.

This is all normal and there seems to be no new idea. From here on I chose two approaches that ended up being similar.

• When players are done with opening prep, they spend more time on average in the middle game.
• We would want a scenario where the average time used before move X < average time of moves after move X: we would want this difference to be as large as possible
• If the average time used before move X > the average time of moves after move X, we should look for a data point earlier where the ratio average time after move X is larger.

First is the local approach. We can take the average time of 5 moves before and 5 moves after.
We can define ratio = Average time of 5 moves after the center / Average time of 5 moves before the center

The other approach is to take the average of all moves before the center. This time we will define the ratio to be the Average time of 5 moves after the center / Average time of all moves before the center. The definition of ratio is to somewhat future-proof for analysis with different time controls.

We can continue to do this for all different data points and choose the data point with the highest ratio.

Does Elo affect opening prep?

Given this definition of selecting where the opening ends, there is actually a visible difference between elo groups. The following graph was obtained using the first definition. I grouped players into 5 elo groups based on quantile.

The second approach also resulted in a very similar graph.

Conclusion

The length of opening prep seems to vary a lot based on Elo groups.

I also read a comment on making a dot plot of Elo and the last opening move number. There is a proportional relationship between those two.

The standard deviation of Move Number (which can be interpreted as the depth of knowledge across the openings you play?) is consistent among elo groups.

I apologize for the incomplete post.

Discussion and Future posts

I first wanted to make a post where I guide people through my approach. If there are any better ideas of how to decide where opening ends I would love to know. There are limitations to this study and approach as well. I will be trying out similar approaches to study the middle-game and end-game tendencies of players. Thank you for reading!