How some common material imbalances affect your win-rate

I was curious exactly how much the various material imbalances help you win chess games.

I couldn't find a good answer, so I pulled the last 100 million Lichess games, determined what material imbalances were involved in each game, looked at how
often people would end up winning that game, and bucketed the results by Elo
range.

These were all the imbalances I tested:

• Being up a "clean" pawn/bishop/knight/rook
• Having the only bishop pair
• Trading a minor piece for 3 pawns
• Being up "the exchange" (trading a minor piece for a rook)
• Being up two minors for a rook
• Being up two rooks for a queen

I looked at all of these for the elo ranges 0-800, 800-1000, 1200-1400, 1600-1800,
2000-2200, and 2200+.

If you want to test your intuitions, it might be worth spending a minute or
two to think about what you would expect to see in the data, before scrolling
to the results.

Personally this is sort of what I assumed I'd find:

1. Imbalances would matter a lot less at lower Elo ranges than higher Elo ranges
2. There would be some imbalances that are useful at a lower Elo
   range, and bad at a higher Elo range. For example, maybe the bishop pair is
   actually a detriment at the lower Elo ranges because people struggle so much
   with defending against knights, and likely you're going to end up blocking
   in one or both of your bishops if you don't know how to handle them.

Findings

Here are the full results in infographic form, it might help to click on it to see it in full-screen:

Being "up" two rooks for a queen is actually generally a disadvantage

This was very surprising. Even at the higher levels, having two rooks for a queen is generally a signal that you're slightly more likely to lose, not win. It's more pronounced at the lower elo ranges, but it's still a <50% winrate in 2200+ Elo games.

Advantages are surprisingly stable across Elo ranges

I thought there would be huge differences across Elo ranges, and there's definitely some trends by Rlo, but it's not as extreme as I had thought.

This is particularly surprising to me with the more minor advantages like being up a pawn, or more theoretical advantages like being up the bishop pair. Even at lower Elo ranges like 1200-1400, you're 4-5% more likely to win if you have the only bishop pair. 1200 Elo players don't know how to take advantage of having the bishop pair, and yet it helps them win all the same, about the same amount it helps 2200 players in fact. There's something sort of fascinating about these helping you win regardless of whether you really know how to handle them.

Lower Elo ranges struggle to use two minors against a rook

A 1000-1200 Elo player is only about 8% more likely to win when up two minors for a rook. A 2200+ player is 35% more likely to win with the same advantage.

Clearly there's a certain amount of skill needed to take advantage of this imbalance.

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