Expected Value of Vortex - Let's End the Confusion

[ApocaLips]

I've seen a lot arguments recently undervaluing KF's vortex. Here's the math right up front to end this confusion. No more 'lol just block right.'

Here are some basic assumptions for the following math:
(1) We're assuming pure 50-50. This assumption disfavors Frost - KF players are usually good at understanding the psychology behind the coinflip mindgames. This includes the Rule of Three, for example. KF players can always fall back on being truly random and avoiding a thought process to their choices, but if they're in your head, you're screwed.
(2) You cannot react to b1 vs. f3. I haven't ever seen anyone back up this claim in the first instance, but even if they could, you can delay the b1 by a couple frames to avoid the fuzzy guard.
(3) We're ignoring other options that actually increase the chance to land a hit in certain situations. For example, if the opponent has <11% life, the mixup for the kill becomes F3/b1/throw, each requiring a distinct reaction. I also have a few mixups for clutch victories, but I'm saving them in case I show up to a major .
(4) Assuming second hit is f3 for simplicity. It's a 1% difference between the overhead and low.
(5) Assumes full health bar. If the opponent has less, the chance to kill rises drastically.
- Note that most of these assumptions disfavor Frost, so the payoffs are higher.

Here's the basic math
- 1st touch is an 100% chance
- 2nd touch is a 50% chance to deal an additional 37% damage - it's a 50/50.
- 3rd touch is a 25% chance to finish the kill. The third hit is contingent on the second succeeding, so the odds of it occurring are .5*.5 = .25.
- Cost is 2 meter - the last kill combo can be meterless. This is, of course, ignoring the meterless vortex.

Here's the expected payoff from various hits:

f3 (overhead): initial combo deals 37%
1(37) + .5(37) + .25(26) = 62% expected payoff
- 100% chance to deal 37%, 50% chance to deal 74% percent, 25% chance to kill

b1u3 (low): initial combo deals 38%
1(38) + .5(37) + .25(25) = 62.75% expected payoff
- 100% chance to deal 38%, 50% chance to deal 75%, 25% chance to kill

Raw slide: initial combo deals 28%
1(28) + .5(37) + .25(35) = 55.25% expected payoff
- 100% chance to deal 28%, 50% chance to deal 65%, 25% chance to kill

d2: initial combo deals 26%
1(26) + .5(37) + .5(37) = 53.75% expected payoff
- 100% chance to deal 26% for 1 bar, 50% chance to deal 44.5% for 2 bars


A few extra points:
- In every instance but starting with d2, the vortex has a 50% chance of exceeding its expected payout.
- KF requires a minimum of 3 touches to kill. The chance of not reaching the expected payoff in any of those 3 touches is only 12.5%. So if you're banking on blocking the vortex correctly to deny her the expected benefit, the odds are painfully stacked against you. In a more realistic match, it's going to take more touches, and the odds of guessing right on the first hit are even less likely.


Summary:
- We're not banking on KF's vortex to kill you in one touch. But we're sure as hell expecting it to hurt, and you can count on that.

 

[RunwayMafia]

Oh my...I love smart men.

 

[DJ L Toro]

I have issues. with how you approach probability. first, the assumption that you already hit with the first hit means your damage isnt payoff, it's just raw damage calculation. in a word, the first hit is no more guaranteed than the first hit in the 2nd or 3rd iteration. This is not a question of probability, it is simply a question of earning your first hit.

Secondly, the probability of the 3rd iteration itself is not .25, but .5. It is the gambler's fallacy to assume that the probability of guessing wrong is increased because of two correct guesses (or rather it is the inverse of the fallacy, but it still holds true). your analysis is more true if the discussion is being had from the end point (100%). In a word, all iterations are 50/50s, but a discussion of "how likely are you to do 100% damage in a single vortex" would be a more correct phrasing.

i agree with the summary

 

[ApocaLips]

I have issues. with how you approach probability. first, the assumption that you already hit with the first hit means your damage isnt payoff, it's just raw damage calculation. in a word, the first hit is no more guaranteed than the first hit in the 2nd or 3rd iteration. This is not a question of probability, it is simply a question of earning your first hit.

This is a calculation of the expected damage when you set up a vortex. When you start the vortex and get your first hit, all of the damage from the first rep is guaranteed - that's the basic premise of a combo.

If you want me to calculate the odds of landing a hit from the neutral, you're literally asking me to solve Injustice.

Secondly, the probability of the 3rd iteration itself is not .25, but .5. It is the gambler's fallacy to assume that the probability of guessing wrong is increased because of two correct guesses (or rather it is the inverse of the fallacy, but it still holds true). your analysis is more true if the discussion is being had from the end point (100%). In a word, all iterations are 50/50s, but a discussion of "how likely are you to do 100% damage in a single vortex" would be a more correct phrasing

...No.

(1) The gambler's fallacy pertains to single, non-contingent events. It gets its name from gamblers thinking they're more likely to succeed after successive failures.

(2) Yes, the probability of the second guess succeeding is 50/50 as a discrete event. But we're calculating the probability that you'll both get to the second 50/50 AND have it succeed. Since it's contingent on the first event, its chances of occurring are lowered by the chances of the first occurring.

But you used the word "fallacy," so you get partial credit according to the rules of the internet.

 

[@MylesWright_]

Oh my word lol