[Competitive] Evasion

[eishiba]

What is the maximum amount of evasion a Pokémon can have? I'm playing a hack of Pokémon crystal kaizo where i am facing level 127 mons. So I'm going to resort to evasion garbage. My Typhlosion has kept smokescreen the entire time since it came in handy time and time again. I'm going to give it double team as well.

 

[Corveone]

The equivalent to your opponent's Accuracy being at 33%. Accuracy & Evasion formula works in a way that each successive boost will be less effective, with the first boost allways being the best one:

Default = 0%
+1: 3/4 = 25%
+2: 3/5 = 40%
+3: 3/6 = 50%
+4: 3/7 = 58%
+5: 3/8 = 62.5%
+6: 3/9 = 66.6%

So in theory it goes from dodging 1 out of 4 attacks to dodging 2 out of 3. Although in a Kaizo game... well, don't be surprised if you still take half of the attacks even at +6 😀

 

[Devalue]

Brings it down slightly more from Corveone's numbers with Bright Powder. Is not familiar with Crystal Kaizo. Assumes the same Generation 2 mechanics.

T = Move * Accuracy * Evasion - Bright Powder

Uses a value of 0 to 255 for the move. Assumes a 100% accurate move, so 255. Plugs that in.

T = 255 * Accuracy * Evasion - Bright Powder

Assumes just Double Team (or just Smokescreen) for this. Technically uses very similar, but slightly different accuracy numbers in Generation 2 for accuracy/evasion. Only moves the needle by a hair at most and not at all at times against Corveone's numbers. Goes like this:
0: 100/100
+1: 75/100
+2: 60/100
+3: 50/100
+4: 43/100
+5: 36/100
+6: 33/100

Sets Bright Powder at 20 also. Compares the resulting number against a random number between 0 and 255. Hits if the random number equals T or less. So, the final numbers for +6 evasion and -0 accuracy (assuming correct calculations and no rounding mistakes):
0: 235/255 = 92.16%
+1: ((255 * 75 / 100) - 20) / 255 = 67.16%
+2: ((255 * 60 / 100) - 20) / 255 = 52.16%
+3: ((255 * 50 / 100) - 20) / 255 = 42.16%
+4: ((255 * 43 / 100) - 20) / 255 = 35.16%
+5: ((255 * 36 / 100) - 20) / 255 = 28.16%
+6: ((255 * 33 / 100) - 20) / 255 = 25.16%

Benefits fully from both accuracy lowering moves AND evasion-boosting moves in Generation 2, unlike later generations. So, with +6 evasion on your Pokemon, -6 accuracy on the enemy Pokemon, and Bright Powder: ((255 * 33 / 100 * 33 / 100) - 20) / 255 = 3.05%.

May not be practical to reach those numbers in-game, though. Why?

1. Obtained Bright Powder from transferring Mewtwo or a legendary bird from Generation 1 to 2. Will likely not happen. Doubts a Kaizo hack to give you access to easier evasion hacks too.

2. Makes no sense to bring every opposing Pokemon's accuracy down. Will probably take more damage setting up 6 Smokescreens than using offensive moves and knocking the enemy out. Spoilered the math below.

Spoiler: Math

Assume no Bright Powder. Already made it to +6 evasion too. Will also say your Pokemon is slower. Takes four enemy attacks if you use three offensive moves, for example.

Refers to these numbers for hit chances:
-0 Accuracy: 33%
-1 Accuracy: (255 * 33 / 100 * 75 / 100) / 255 = 24.75%
-2: (255 * 33 / 100 * 60 / 100) / 255 = 19.8%
-3: (255 * 33 / 100 * 50 / 100) / 255 = 16.5%
-4: (255 * 33 / 100 * 43 / 100) / 255 = 14.19%
-5: (255 * 33 / 100 * 36 / 100) / 255 = 11.88%
-6: (255 * 33 / 100 * 33 / 100) / 255 = 10.89%

Case A: Taking four enemy attacks at +6 evasion, -0 accuracy

Odds of dodging four enemy attacks: (1 - .33) ^ 4 enemy attacks = 20.15%

Case B: Smokescreening six times, then using three offensive moves. Will get attacked ten times total.

Odds of dodging all ten enemy attacks: (1 - .33) * (1 - .2475) * (1 - .198) * (1 - .165) * (1 - .1419) * (1 - .1188) * ((1 - .1089)^4): 16.1%

20.15% > 16.1%. Stands a better chance of dodging all attacks by using three offensive moves, while slower, than using Smokescreen first.

Naturally asks when it would be beneficial.
(1 - .33) ^ 5 versus (1 - .33) * (1 - .2475) * (1 - .198) * (1 - .165) * (1 - .1419) * (1 - .1188) * ((1 - .1089)^5)
= 0.1350125 versus 0.1434454

Arrived at that sooner than expected. Will be more likely to take a hit if you will be attacked five times before you faint the opponent.

Would have been quicker to simulate this rather than math it out, but whatever. Simplifies the question of "at most one hit" too.

Short answer: Are you going to take four or less attacks at +6 evasion? Go offensive. Any more than that? Smokescreen x6. Specifies this result for not getting hit once, not expected damage taken.