Freeze-adjusted damage

[lilith]

switching in snorlax on chansey is fun. getting frozen is not! i wanted to find a way to quantify this tradeoff - freeze-adjusted damage!

the catch: as with any vector, the magnitude depends completely on the metric. in this case, "damage" is a terribly limiting concept. but, it's still possible to do the most obvious thing and consider a freeze to be a OHKO and then take the average. of course, if you exceed a OHKO by a considerable margin, average damage becomes super meaningless. so let's not call a freeze 100%, but rather 100% of the opponent's current hp.

taking an average can be quite misleading with so much variance. but in a game that's fairly even / with no specific reasons to take less or more risks, it's not such a bad number to throw out when making decisions. unless recover is involved, and then it's sorta silly

anyway, i haven't started yet, and i just learned something cool:
switching in an unparalyzed half-hp snorlax in on chansey is less risky than switching in an unparalyzed full-hp snorlax. well umm. now it seems really obvious, but i'd never thought about it that way...

AverageHitDamage = (chrate*(chmax+chmin)/2) + (1-chrate)*(nochmax+nochmin)/2
AvgDamage = (1 - .25*user.paralyzed)*Accuracy*AverageHitDamage
AdjustedDamage = (1 - .25*user.paralyzed)*Accuracy*(.9*AverageHitDamage + .1*other.hp)

Jynx's Blizzard vs. Snorlax:
AvgDamage=35%
AdjustedDamage=41%
Paralyzed Jynx's Blizzard vs. Snorlax:
AvgDamage=26%
AdjustedDamage=30%

Chansey's Ice Beam vs. Snorlax:
AvgDamage=20%
AdjustedDamage(Snorlax at 50%)=23%
AdjustedDamage=28%
Paralyzed Chansey's Ice Beam vs. Snorlax:
AvgDamage=15%
AdjustedDamage(Snorlax at 50%)=17%
AdjustedDamage=21%

Starmie's Blizzard vs. Snorlax:
AvgDamage=25%
AdjustedDamage=31%
Starmie's Ice Beam vs. Snorlax:
AvgDamage=22%
AdjustedDamage=30%
Paralyzed Starmie's Blizzard vs. Snorlax:
AvgDamage=19%
AdjustedDamage=23%
Paralyzed Starmie's Ice Beam vs. Snorlax:
AvgDamage=16%
AdjustedDamage=22%

[t3h Icy]

Cool stuff, but not too surprising. If a Pokemon has more HP, it's more valuable than a low HP one, so Freezes are more "damaging" to the Pokemon.

However, I really like the idea of averaging damage in terms of percentage as it's a good way to show mathematically Ice Beam > Blizzard when both OHKO. It's of course obvious, but it's helpful when using code to calculate damage stuff.

Example: Starmie vs Snorlax (10%)
Surf's percentage average is 10%
Hydro Pump's percentage average is 8%

So Surf is better in that case which is easy to explain to a computer.

[lilith]

Jan 26, 2013 23:31:20 GMT -8 t3h Icy said:

Cool stuff, but not too surprising. If a Pokemon has more HP, it's more valuable than a low HP one, so Freezes are more "damaging" to the Pokemon.

However, I really like the idea of averaging damage in terms of percentage as it's a good way to show mathematically Ice Beam > Blizzard when both OHKO. It's of course obvious, but it's helpful when using code to calculate damage stuff.

Example: Starmie vs Snorlax (10%)
Surf's percentage average is 10%
Hydro Pump's percentage average is 8%

So Surf is better in that case which is easy to explain to a computer.

yes! unfortunately i don't know of any concise way to compare moves in non-ohko situations

over the course of one turn, i often like to check median damage so i know what i can trust to happen more often than not. but then there's that mess where summing N median damages isn't the same as the median damage after N turns, and then where none of those damages are accurate in ohko situations like you mentioned. then for some situations (highroll body slam vs hbeam), i also like percentiles other than the 50th (in this case, the 10th percentile). i guess an hp-aware calculator would also correctly report the average damage for the better move as higher here, though.

for multiple turns, even ignoring things like recover, combinations of different moves, and non-fresh pokemon, the simplest i can think of is to look at the probability to KO by turn N. combined with the opponent's probability to KO by turn N in a messy probability tree, i guess it could give a win% too. i guess there's not really one or two scalars that can describe "3 blizzards is a big bell curve centered at 3X plus a small bell curve centered at 4X and a smaller bell curve centered at 2X and even smaller bell curves at other multiples of X except for X where it's just a really small square wave". oh well. (but i kind of want to see that graph now... lol)

and there are so many other things to know! maybe what i secretly really want in life is to see a graph of the probability distribution for every outcome of a particular matchup (i.e. f(-50) would be the probability to lose the matchup while doing precisely 50%), possibly and/or a cumulative version of it (i.e. the probability to do at least 50% before dying).

and then with a discrete Z axis representing statused at the end or not statused. but what about quantifying ability-to-switch-out-if-it-looks-bad-before-dying-ness?

augh i'm going to be crazy forever aren't i.

and then recover users come in and ruin all the math too

T_T