Controlling more space hasn’t always been universally accepted as an advantage. World Champion Emanuel Lasker would deliberately accept cramped positions to provoke his opponents into reckless aggression. Bobby Fischer and Garry Kasparov, two of the greatest of all time, both made the King’s Indian Defense a mainstay of their opening repertoire. In the King’s Indian, Black accepts less space initially in the hope of launching a counterattack later on.
It’s only with the dominance of computers that space has really taken its place in the pantheon of positional advantages. Computers LOVE space. They can’t get enough of it. The King’s Indian Defense? Total garbage, according to the computers. Black has less space, simple as that. It’s probably for this reason that the King’s Indian has fallen out of favor among the world elite, although there are some stalwarts who stick with it and seem to do alright.
More space means more options, in particular more mobility for the pieces. One classic move is to use that greater mobility to switch the front of battle at a crucial moment, swinging from one side of the board to the other when opponent’s pieces are too cramped to react. More space also means more territory to defend, more tender bits exposed to the enemy. A successful “squeeze” therefore requires a delicate touch, controlling the position for many moves without slipping up.
It’s easy to see then why computers do so well with extra space. They’re better at leveraging the extra options space affords and they’ll never accidentally let a piece drop off. For a human, the extra blunder risk of having more pieces exposed for many moves starts to add up; for a computer, there’s nothing to add up, because they don’t blunder.
I started to wonder if, below some rating level, having more space is an advantage at all. Maybe below a certain level of skill, the added risk of dropping a piece outweighs the greater mobility that space allows.
The challenge is how to define space. While the idea of space seems straightforward, it’s not obvious how to define it mathematically. After considering various options, I decided to go with the Stockfish definition:
Number of safe squares available for minor pieces on the central four files on ranks 2 to 4. Safe squares one, two or three squares behind a friendly pawn are counted twice.
To be honest I find this definition quite fiddly and not entirely convincing, but it’s battle-tested and the numbers it spit out in various positions I tested mostly agreed with my sense of space.
When the curtain is pulled back, it’s surprising how stupid the computer really is. It can calculate a lot moves, but at some point you have to stop calculating and evaluate a position, and the evaluations are surprisingly ham-fisted. Nonetheless, there’s no arguing with the results. Powerful search + simple evaluation function = very strong chess performance.
It’s also worth noting that the latest version of Stockfish doesn’t use this definition of space. The space feature, along with the rest of the evaluation function, has been torn out and replaced with a neural network. Basically, since no one can define space in a way that’s entirely convincing, we just let the computer figure it out, along with all the other positional features. This approach seems to work - it resulted in a stronger engine overall.
To test the effect of space at different levels, I grabbed 100,000 games from the latest lichess monthly database and looked at who had more space after 15 moves and how that correlated with the result of the game. To try to isolate the effect of space, I added a few additional restrictions:
Only blitz and slower time controls (no bullet)
Players within 200 ratings points of each other
Material equal after 15 moves
I then looked plotted space vs. average results for different rating tiers and fitted a line to the results. The greater the slope of this line, the bigger an advantage space would seem to be at that level.
Having more space proved to be an advantage at all rating levels: more space was generally associated with a higher average result. To my surprise, the advantage did not increase at higher rating tiers. In fact, if anything space seemed to be slightly more valuable at lower rating levels.
In conclusion, this analysis supports the idea that having more space is a real advantage: on average, controlling more territory on the board will give you a better chance of winning. Surprisingly, the advantage did not increase with the rating levels of the players. Having more space was an advantage at all levels.