It seems to me that if they spread out from each other, so a predator could only eat one in every bite, any single fish is safer because it’s less likely to be that single one, whereas if they’re huddled together and the predator can gobble ten at a time, the likelihood for any single fish being eaten in a bite is 10x higher.
I understand if the optics of a school are designed to look big and maybe scare off predators, but it’s always been phrased to me as if the “game theory” for a single fish makes it safer to pack in with others.
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Suppose you are a predator fish trying to eat a fish in a school. You match your approach to intersect its path and are reacting to its changes in direction. You are faster so you are going to catch it.
But before you can bite it you lose track of it, confusing it for a different one. This other fish is already moving in a different direction, dodging a different way. There is no time to react because they started that movement before you even focused on them. By switching your attention to a different fish it is like your prey instantly changed its movement, something you just can’t follow.
Normally of course you are unlikely to lose track of a single fish in this way, but if you clump a bunch of fish into a chaotic ball then it is very likely.
Each of the prey fish can focus on avoiding the predator, but the predator can’t keep track of any specific fish to follow its dodge. This creates an imbalance that reduces the rate of success of the predator.
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