While testing 100% strats I realized that the ultra ball detour in Pyrite Cave might be applicable to Any%. Here's what I've found so far:
The ultra ball detour takes 44-45 seconds of time, about 8 seconds more than an average turn against Twan (about 36 seconds).
Using the Gen 3 catch rate formulas, yoloing great ball on Meditite should have a 35% success rate, and yoloing ultra ball should have a 47% success rate. As a result the average great ball fight takes about a quarter of a turn longer than the average ultra ball fight. This would mean that the average time loss from grabbing the Ultra Ball should be 18 seconds.
But this 18 second time loss comes with a solid benefit - using more than 3 balls against Twan is an almost guaranteed death between running out of balls to throw and taking too much damage from hi jump kick or shadow rush or getting confused from confusion. About 27.5% of runs that make it this far should "die" to Twan just from using more than 3 great balls. Only 15% of runs at this point would die to Twan if ultra ball is used. This means that the 18 second average time loss almost halves the chance of dying in the fight. This is also ignoring the death scenarios where you die from damage, which would further increase the safety improvement from grabbing ultra ball.
So in Theory, grabbing ultra ball should double the safety of the Twan fight and lose 18 seconds of time on average. This is what I observed testing the two procedures:
Great Ball: 4 first turn catches, 1 second turn, 1 third turn, and 4 deaths
Ultra Ball: 6 first turn catches, 1 second turn, 1 third turn, and 2 deaths
Much more testing would need to be done to verify this tradeoff, as runners have experienced deviations from expected catch rates in the past.
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