Switch rate

[X-Act]

That's why AA's point that "2. The Pokemon being hit will lose if either the crit or the added effect happen, even if hit from full health." is important. In your Blissey example, the added effects are seldom important, maybe, so in that case you could just ignore it (i.e. putting AER = 0 in the formulae).

Flinching is important, but if you have just switched in, the opponent's move will never flinch (or will always flinch, so to speak, because you never attack in the turn you switch in). Since this is the switching rate formula, I don't think flinching is very relevant here. It might be relevant somewhere else, but not here.

 

[Steven718]

Honestly, I don't think a single formula exists for switching rates. Imo, it depends more on whether or not the opponent is a noob. Some obvious switch predictions can be backfired if the opponent decides to be stupid (thus accidentally getting the edge).

Can't assume that though, for example on NB I lead with Vaporeon, against Jolteon leads I always Surf knowing full well that 9 out of 10 times the jolteon is going to substitute predicting a switch, allowing me to survive the next tbolt easily and from then on I am going to win that particular matchup until either he switches, faints or gets a crit.

Predicting against obvious switch predictions causing them to backfire really can't be considered "newb" and "accidently getting the edge."

 

[Mekkah]

You know, there is such a thing as too much information.

I really appreciate all the work you guys put into this, but its rather pointless to point to an "OMG FREEZE J00 ARE HACK" n00b you would have beat anyway and say "this formula proves I'm right!"

There's no such thing as too much useful stuff, and this is definitely useful. You don't say "this formula proves I'm right" anyway - all you need to tell this idiot that sooner or later you would have gotten that "OMG FREEZE".

 

[TSPhoenix]

People seem to have the mentality that anything with a 10% effect chance should never happen, moves with 85% accuracy never miss and anything with less accuracy always misses. All this theory points out is how that mentality is not only silly but statistically flawed.

 

[Deck Knight]

There's no such thing as too much useful stuff, and this is definitely useful. You don't say "this formula proves I'm right" anyway - all you need to tell this idiot that sooner or later you would have gotten that "OMG FREEZE".

Personally I'd prefer to let the idiot stew in his own ignorance. This is the kind of thing I don;t feel needs a mathematical formula to go with it. If you use Fire Blast over Flamethrower you are making the assumption that the power will serve you better in a clutch situation than the accuracy, landing you a much needed KO.

Moreover this formula, as its assumptions state, is only useful for 3HKOs on wall switchins where any additional affect or crit is meaningful. Most of the time its irrelevant though.

Really, there's nothing this tells us that hasn't been common competitive knowledge since RBY. In fact, this was even more exaggerated in RBY since Freeze was essentially equivalent to a KOd pokemon, and CH's were tied to speed.

Maybe I'm just not getting it, but a switch rate of 11 or 5 isn't meaningful at all to me. The liklihood I'm going to switch anything into a 3HKO rather than sacrifice something to bring my wall in unharmed late game is minimal. If I do switch in, I usually want either A: impunity, or B: I'm essentially trying to create a stall war, where this formula is rendered meaningless.

I fail to see how it isn't simpler to just say:

Switch Rate = )ceil(100/Damage %)

Ex: Switch Rate = (ceil)100/40 = 2.5 = 3. That's your baseline.

Since Crits do double damage (4x with Sniper), if you want how many times you could switch into a crit, just divide by 2. If your number is 2 or less, You probably shouldn't switch in. Since Crits are statistically certain to happen after either 16(normal) or 8 turns (high CH), just subtract your initial (unrounded) number.

Switch Rate = ceil(100/Damage %) - ((100/((Damage%)(2)))/Turns to Crit Certainty.

Switch Rate = ceil(100/40 = 2.5) - ((100/80 = 1.25) 1.25/16 = .078. Switchrate = 2.5-0.078 = 2.42 = 3.

In other words, you're still statistically likely to be able to switch in 3 times on a normal hit. If it were something like Cross Chop you'd still end up with 3 in this instance, but the true value would be 2.34 times, not 2.42.

To adjust for leftovers, subtract 8 from the damage percent, subtract 12 for Poison Heal, Dry Skin, and Ice Body. For burn and normal poison, add 12, for toxic add 6. For SR and Spikes add appropriately.

You could even add in accuracy by multiplying your Base Damage number by that accuracy.

In other words:

Switch Rate = ceil(100/((Base Damage% * 1-MA) + (F + S) - (I + A)) - ((Base Damage% * 1-Acc)(CHM)/TtCC)

This reads:

Switch Rate is equal to the ceiling of 100 divided by the sum of base damage percent multiplied by 1 minus Move Accuracy plus additional field effects(Spikes, SR, Sandstorm), status(toxic, burn), and abilitity damage(Dry Skin in Sun) minus item(Lefties/Black Sludge) and ability recovery(Ice Body, Rain Dish). Then subtract the sum of Base Damage multiplied by 1 - move accuracy multiplied by critical hit multiplier (usually 2, 4 for sniper), which is then divided by the Turns to Critical Certaintly.

Ex: Spiritomb with Leftovers switches into a Weavile Night Slash that does 42% Base Damage. Stealth Rock is out.

Switch Rate = ceil(100/((42%+12%-6%)*1) - ((100/80%)*1)/8

Switch Rate = ceil(100/48 - 0.16

Switch Rate = ceil(2.08 - 0.16

Switch Rate = ceil(1.92. = 2.

Summary: Only do this once folks.

Freeze is a nuisance to account for primarily because it isn't a damaging effect. What I would do in that case is since you're usually going to be frosted over for 2 or 3 turns minimum, subtract that amount from the end value. If the answer is less than zero or one, be advised you're taking a huge risk.

I love you guys, but [log] isn't my specialty. Give me addition, subtraction, multiplication, and division plox. When I solve for something, I prefer to have the thing I'm solving for as one concrete value on the left side of an equivalency.

 

[X-Act]

Okay, so you claim that

Switch Rate = ceil(100/((Base Damage% * 1-MA) + (F + S) - (I + A)) - ((Base Damage% * 1-Acc)(CHM)/TtCC)

is simpler than

Switch Rate = ceil(-log(2) / log(1-(MA)(CH + AER - (AER)(CH))))

Furthermore, you say that "[log] isn't my specialty. Give me addition, subtraction, multiplication, and division plox." Well, then tell me how to solve the equation 2^x = 3 without using logs, please.

 

[Deck Knight]

Okay, so you claim that

Switch Rate = ceil(100/((Base Damage% * 1-MA) + (F + S) - (I + A)) - ((Base Damage% * 1-Acc)(CHM)/TtCC)

is simpler than

Switch Rate = ceil(-log(2) / log(1-(MA)(CH + AER - (AER)(CH))))

Furthermore, you say that "[log] isn't my specialty. Give me addition, subtraction, multiplication, and division plox." Well, then tell me how to solve the equation 2^x = 3 without using logs, please.

Well yes, considering that basically the extra letters after base damage can be encompassed into one value that anyone can plug in immediately with no effort, yes.

Not everyone wants to break out a scientific calculator to do logarythms to figure out, as dragontamer described it to me, "the point where the likelihood of hax is greater than or equal to 50%."

Mathematical simpletons like me don't feel like determining a fairly useless, impractical metric using advanced mathematics. Rather, the information I care about is not figuring out when haxation has representation, but how many times can I switch my counter or wall in before I get screwed. This is easily done with simple math by plugging in easily determinable variables. Base Damage of an attack can be obtained through Metalkid's Calculator. Field Effects are obvious, my formula was simply exhaustively categorized. If Stealth Rock is out, you take nuetral damage, and you have Leftovers, the answer is Base Damage + 6. adding in for crit rate is simple enough, double damage divided by mean turns to crit. I admit it isn't accurate to within a decimal, but this is pokemon. If you can switch in 16 times it is inconsequential (you wall something hard), if you can only switch in 4 or 5 the impact is not massive.

I like my math like I like my English. Short, sweet, to the point, and purposeful. We are not all math lecturers and/or gurus. The mathematical proof of hax may be an astouding achievement to you, and it is certainly a mathematical marvel, but its a roundabout way of answering what people want to know: How many times can I switch my wall or generic counter in before I get owned.

The beauty of my formula is that you can check the number of times you can switch in against any attack under any field condition, at full health or at 80% or at 60%. All you have to do is replace the initial 100 with 80 or 60, or whatever percentage your pokemon is at.

Whereas:

The main presumptions are:

1. The Pokemon being hit is hit while switching in.
2. The Pokemon being hit will lose if either the crit or the added effect happen, even if hit from full health.

Is useful only if you already know your pokemon is going to be 3HKOd, and at that point you don't need a formula to tell you if a CH or freeze happens you're toast.

Like I said, the mathematical proof is cool, but it isn't practical. Many situations are not 3HKOs or 4HKOs, and the limited nature and complexity of this formula makes it a poor metric for practical use.

As for 2^x = 3, I haven't done logarythms in a long time, if ever, and I don't see myself using them now. I'm a 2^2 - 1 = 3 kind of guy. I don't remember how to work a logarythmic function, all I can surmise is that since 2^1 = 2 and 2^2 = 4, the answer is roughly between the two. After trial and error, the answer I came up with is 2^1.585 = 3. I'm sure there's a more accurate and glamourous way to do it that goes out 6 or more decimals, but I'm here for pokemon, not advanced mathematics.

I'm not knocking you guys, I'm just saying there's a more practical way for those of us who aren't mathematical wizards to get similar information. I literally cannot figure out what the hell

General case: .5 >= (move accuracy)(1- ((1-crit rate)(1-added effect rate))^switch rate)

I'm supposed to plug into that area, nevermind the fact that I cannot translate this formula into a meaningful list of instructions. From what I read:

The general case is that 50 percent is greater than or equal to move accuracy multiplied by 1 minus the result of 1 minus the critical rate multiplied by 1 minus the added effect rate, taken to the switch rate power.

This is great if you know the switch rate, and absolutely blanking useless if you don't and don't feel like spending the time to figure out what power that needs to be to cause the rest of the equation to equal 0.5.

I may suck at logarhythms, but I know how to read. I do not follow how that formula got us to 11 from Garchomp Earthquake on Milotic. A formula is useless if the only people who can understand it and calculate it are its creators. Which is why I made this much tl;dr post. My favorite thing about mathematics is that you can take almost anything and simplify it down to where it's secrets are available to almost everyone.

That's why I made my formula, not to knock you guys or be the genius upstart, but because I was having the damndest time trying to figure out where the numbers came from, and wanted to see if I could make something more user-friendly.

 

[CardsOfTheHeart]

Well, Pokemon is basically a big numbers-crunching game (with some psychology); feel free to manipulate the numbers as often or as little as you like to get the information you want. This formula too much to take in for you? Don't use it. It's up to you. If you do understand, it's another tool in your toolbox of Pokemon understanding.

Hmm, there was something else I wanted to add here, but it just slipped my mind...

 

[obi]

What you are saying is akin to saying "I don't want to use a damage formula, I already know that if they have more attack, I take more damage." Someone could write a calculator for this just as easily as people write them for the damage formula.

It's also poor form to criticize a formula if you aren't familiar with the math used in it. Sure, you can say it's too complex for you to use, but to then go on and break down the formula seems kind of odd. X-Act used the 2^x=3 example specifically because

General case: .5 >= (move accuracy)(1- ((1-crit rate)(1-added effect rate))^switch rate)

The point is that you need logarithms to solve this. The reason his formula has log(stuff) in it is because that's how you solve for an exponent. You shouldn't first admit you don't understand the formula then say it's useless.

I guess I should take this time to explain just how logs works.

.5 ≥ (move accuracy)(1- ((1-crit rate)(1-added effect rate))^switch rate

For the sake of simplicity, I'm going to simplify a whole bunch stuff to just "x".

.5 ≥ x^switch rate

When you take the log of both sides, you get...

log(.5) ≥ log(x^switch rate)

Pretty simple, right? Well, a property of a log is that if you have a whole bunch of stuff raised to some power, and then take the log of that, then you get the log of a whole bunch of stuff times whatever power you had. So this means you have

log(.5) ≥ switch rate * log(x)

That's all a log does. Now you can easily solve for the switch rate by dividing both sides by the log of a whole bunch of stuff (x)

log(.5) / log(x) ≥ switch rate

Now, if you really want, you can rewrite this as

log(.5 ^ (1/x)) ≥ switch rate

 

[Insignia]

I agree in that many people abuse the word "hax" nowadays. One shouldn't be complaining about hax when a crit 1hko's a fully healthed Pokemon 30 turns into the game. In fact, one should be expecting it.

There may be counterpoints against this already, but I believe AA's switch rate calculations has a flaw. AA is assuming that if the defender switches less often than it attacks, the defender has the advantage. Likewise, a defender that switching more often than attack doesn't necessary mean the attacker has the advantage.

A defending Pokemon with Substitute generally has a lower chance of switch and the sub prevents a lot of hax. The defending Pokemon's attack is higher than switching in this case since the defender is most likely spamming sub and attacks while being immune to side effects and critical hits. However, losing 25% HP might be giving the defender the disadvantage in the long run.
Some Pokemon do not need to attack as often to make heavy impacts on the flow of the battle. It is ideal for Choice users attack as often as they switch because they are dealing heavy damage, causing the opponent to switch and avoiding damage. Though the choice user is obviously winning, Switch Ratio states that the two battlers are in a stalemate since attack and switch frequency are the same for both players. Also, serene grace abusers need only a few chances to cripple entire teams.