Catch Rates of Poke Balls

[PTM]

The probability you calculated (17%) is the probability that you do NOT catch Azelf after throwing 34 Dusk Balls at it. 100% - 17% = 83% is the probability that you catch Azelf with 34 Dusk Balls.

Also, that percentage is a bit off. I'm almost sure that the value should be 'floored' before dividing by 256. That would give it a probability of 4.6875% of catching Azelf. If Azelf is asleep, the probability would increase to 8.59375%.

In the first case, the average number of Dusk Balls required to catch Azelf is 22. For the second case, it is 12. I don't know if this corresponds to what really happens.

EDIT: By the way, McGraw's formula would correspond exactly to Peterko's if he removed that [4 *] before the X, making it (X-2*Y)*A*B/X+1+S.

Yes I was aware of that it was a 17% chance that the pokemon would *not* be caught; I apologize if my word choice was ambiguous enough to prevent this from coming through.

I miscalculated originally using McGraw's formula (apropos the discrepency); for some reason I reused 145 as the min (should have used 1). This is what happens when you do basic math past midnight after pouring over mindless duskball spamming for hours while simultaneously studying random college history. Apparently this also leads you to formulate run-on sentences the day after.

 

[X-Act]

http://www.serebii.net/games/capture.shtml

This is where i saw the capture rate posted, and it should be 100 % accurate unless it has changed between generations...

There, the formula is B*(((C*(4*M-2*H))/M)+S+1)/256

B is the Ball Multiplier
C is the Catch Rate
M is the Max HP of the foe
H is the current HP of the foe
S is 10 if the foe is asleep or frozen; 5 if it is burned, poisoned or paralysed; 0 otherwise

This formula, although similar, is different to both McGraw's and Peterko's.

For the Azelf example, probability that a 1HP Azelf is caught by a Dusk Ball: M = 145, H = 1, S = 0, C = 3, B = 4 : 19.92% (!)

Probability that a 1HP sleeping Azelf is caught by a Dusk Ball: M = 145, H = 1, S = 10, C = 3, B = 4 : 35.55% (!!!)

For the first case, you should catch Azelf within 6 Dusk Balls; for the second case, within 3 Dusk Balls.

I have never caught an Azelf, but I don't think this is correct. These values seem too easy. Anyone having experienced catching an Azelf would like to comment?

 

[aquasuicune]

I'm just going to master ball azelf, but it has the same catch rate as Uxie, who I did catch.
1st time-28 dusk balls
2nd time-4 dusk balls
3rd time-30 dusk balls, 9 ultra balls, etc (struggle suicide)
4th time-1 quick ball.

Hope that helps.

 

[UnskilledBreed]

First time around I caught Azelf after throwing two quick balls (failed), and 12 dusk balls (which pretty much agree with the formula, since it wasn't at 1 HP, just in the red somewhere).

Combined, Uxie and Azelf didn't use up half of the 50 dusk balls I had predicted I would use.

 

[PaT2090]

so wait is Para/Poison/Burnt better or worse than Sleep/Freeze?

 

[X-Act]

so wait is Para/Poison/Burnt better or worse than Sleep/Freeze?

Worse.

 

[Reflect Suicune]

um yeah I spent days trying to catch azelf... 3, quick balls, 30+ dusk balls, and then timer balls until I catch it was pretty much the norm every attempt.

 

[Rolken]

B*(((C*(4*M-2*H))/M)+S+1)/256

This is the formula I always see, and it's just plain wrong; any pokemon with a catch rate >127 would be caught 100% of the time, which is obviously nonsense. Has anyone actually looked at the code or are people making this stuff up?

 

[Mario With Lasers]

I always capture Kricketots (255 Catch Rate) with just one Poké Ball.

 

[Generalmeng]

i throw 5 pokeballs and 2 great balls and i caught it with a nest ball(kircketots)??

 

[odnamrataizem]

From a Japanese site, it seems to me the catch rate formula has changed from GSC:

Rate = ((( MaxHP * 3 - CurHP * 2 ) * CatchRate * BallRate ) / ( MaxHP * 3 )) * Status

Status is 2 for Sleep and Freeze, 1,5 for others, 1 otherwise. If Rate evaluates to above 255, the Pokémon is automatically caught and the step below is entirely skipped.

Now this is where it goes psycho:

Probability = ( 1 048 560 / ( sqrt( sqrt( 16 711 680 / Rate )))) / 65 536

A random number is thrown against this every time before the pokéball shakes, and also before the final "click", hence the effective catch rate is actually Probability^4.

This is all ADV, though I'm assuming nothing has changed for DP.

 

[Deucalion2]

I caught Azelf first time with Quick ball on 100% health, no stat cond., and Uxie after 4 quick balls on ~60% health, paralysed. (I did that in one crit. hit Spark!)

 

[PTM]

In practice, it's basically impossible to intuitively "feel" what kind of percentage we should be expecting. I caught an Azelf at full HP on turn 1 with a Quick Ball once, yet I'm currently engaged in an hour long ball chucking fest. I've used up 69 duskballs so far; this guy has been at 1HP and para for the duration. Will update when he struggle-kills himself (which he will I'm sure).

Update:
As predicted, Azelf suicided his idiotic self (struggle). Final usage tally:
Duskball: 72
Timerball: 20 (all at max efficiency)
Quickball: 3 (first three turns, hoping I'd get lucky before switching to my usual strat of 1HP + para).

With the exception of the quiclballs, every ball hit him as he was at exactly 1HP (False Swipe ftw) and Paralyzed.

Conclusion: the system employed for catching pokemon is completely and fundamentally flawed. Honestly there is *no reason* whatsoever for capping Timerballs at 4x (the only reason I carry them is because they look cool and so I switch to them once they are at max efficiency); if they were capped at something like 10x then at least you'd be more or less assured of a catch after the 70th turn. In my opinion, if you don't kill yourself in real life after 60-70 mindless turns of wild pokemon ball chucking you deserve something. If at some point you throw 95 balls and fail to catch a pokemon at 1HP/para, that's a poor system. I'm thoroughly bothered by this, as you can tell.

 

[freaktron]

Do stat-lowering moves like Screech have any effects on the capture rate? Because in Diamond I tried using a Level 29 Skuntank that had Screech against Uxie and I found the Screeching to be a bit more effective.

 

[Mario With Lasers]

A random number is thrown against this every time before the pokéball shakes, and also before the final "click", hence the effective catch rate is actually Probability^4.

This is all ADV, though I'm assuming nothing has changed for DP.

I've made the calcs using Rate=255, and the Probability ended up as 0,999938966... So, the random number would be something between 0 and 1, right?

 

[PTM]

Do stat-lowering moves like Screech have any effects on the capture rate? Because in Diamond I tried using a Level 29 Skuntank that had Screech against Uxie and I found the Screeching to be a bit more effective.

I doubt it. I employed my usual strategy for catching Azelf during the magnificent 95 ball-run: this includes lowering his accuracy 6 levels so I can save myself money on potions.

 

[X-Act]

Japanese site

Rate = ((( MaxHP * 3 - CurHP * 2 ) * CatchRate * BallRate ) / ( MaxHP * 3 )) * Status

Probability = ( 1 048 560 / ( sqrt( sqrt( 16 711 680 / Rate )))) / 65 536

A random number is thrown against this every time before the pokéball shakes, and also before the final "click", hence the effective catch rate is actually Probability^4.

Let's use this for our Azelf example, shall we?

Probability of catching Azelf having 1 HP with a Dusk Ball:

MaxHP = 145, CurHP = 1, CatchRate = 3, BallRate = 4, Status = 1

Rate = ((( 145 * 3 - 1 * 2 ) * 3 * 4 ) / ( 145 * 3 )) * 1 = 11.9448.

Probability = (1048560 / ( sqrt( sqrt ( 16711680 / 11.9448 )))) / 65536 = 0.4652.

Hence, the probability of catching it is 0.4652 ^ 4 = 0.0468, or 4.68% (1 in 21 Dusk Balls).

If the same Azelf is asleep:

Rate = 23.8897, Probability = 0.5532.

Hence, the probability of catching a sleeping Azelf having 1HP left with a Dusk Ball is 0.5532 ^ 4 = 0.0937, or 9.37% (1 in 11 Dusk Balls).

This doesn't seem too bad.

 

[Deucalion2]

Would it be possible to test out Quick Ball cap? Because they are truly amazing. I'm sure they start at at least 5x, if not more.

 

[Xenesis]

A random number is thrown against this every time before the pokéball shakes, and also before the final "click", hence the effective catch rate is actually Probability^4.

Did I call it or did I call it? ^_^

So yeah, that's why catch rates are Hax in this game. ^_^;

 

[odnamrataizem]

So, the random number would be something between 0 and 1, right?

Actually between 0 and 65535. The real formula doesn't have the "/ 65536" part, I just did that because it's easier for us to look at percentages =P

 

[Azrael]

I like the uncovering of the math and such, but it just leads to what we've always known.

False Swipe it to 1 HP and sleep it, and throw lots of balls at it.

 

[Rolken]

Rate = ((( MaxHP * 3 - CurHP * 2 ) * CatchRate * BallRate ) / ( MaxHP * 3 )) * Status

Probability = ( 1 048 560 / ( sqrt( sqrt( 16 711 680 / Rate )))) / 65 536
A random number is thrown against this every time before the pokéball shakes, and also before the final "click", hence the effective catch rate is actually Probability^4.

Assuming all this is correct, it can be massively simplified. Make a slight round from 16711680 -> 16777216 and 1048560 -> 1048576 (both powers of 2 - I'm inclined to say that those are the real numbers and somebody screwed up somewhere, but who knows), and the second formula magically folds down to

Probability = Rate^(1/4) / 4

And if you plug in the "effective catch rate" of probability^4, you conveniently get

Effective Catch Rate = Rate / 256

So you might as well just dispense with all these equation steps and call it

Probability = (1/256) * (1 - 2/3 * CurHP/MaxHP) * CatchRate * BallRate * Status

Well, look at that... it's almost exactly the same as the original equation I called into question, just with an HP coefficient that actually works and status as a multiplier instead of a straight addition.

And if make certain assumptions, you can whittle it to

MinHP Probability (0-255) = CatchRate * BallRate * Status
MaxHP Probability (0-255) = CatchRate * BallRate * Status / 3

which is quite convenient for on-the-fly calculations!

 

[Rolken]

Well I did some testing, and I can verify with 98% confidence that if the above formulas are correct, Quick Balls have a 4x multiplier.

I gave the formulas a sanity check by tossing 50 ordinary pokeballs at untouched 255 catch rate pogeys. One would expect a 1/3 success rate, and I got 19/50 or 38% (with 14% margin of error); not exactly conclusive evidence, but demonstration that they can't be -totally- wrong.

I then tested Quick Balls by hurling them at untouched 45, 100, 150, 190, and 200 catch rate pogeys within the first 4 turns (west of Veilstone and in the garden). If Quick Balls have a 3x multiplier, then none of them should catch with 100% success; if 4x, then 190-200 should catch with 100% success; if 5x, then 150x should have 98% success. The results were as follows:

45 3/10
100 2/4
150 5/8
190 11/11
200 4/4

The odds of a 3x ball catching all of those 190/200s:
(190/256)^11 * (200/256)^4 = 1.9%

The odds of a 5x ball missing 3 of 8 is way below statistical significance. Ergo, barring some kind of weirdo fractional ball, it must be 4x.

 

[Deucalion2]

Really? Are you sure? They seemed to do miracles for me, like my full HP no stat Azelf caught in 1 quick ball. (yes, I'm going to brag about that all day). Maybe you should retest, to see if it may be 5x, and you just got unlucky.

 

[aquasuicune]

I'm not as confident in the pokeballs as I used to be. I did catch my Uxie at full health with one quick ball, but last night (yes, at night) I used three dusk balls and two quick balls on a weakened level 22 gligar before catching it with a fourth dusk ball. Gligar also has a catch rate of 60, while Uxie's is only 3.