07-29-2010, 05:58 AM
I have written this guide to improve understanding of Pokemon probability mechanics. It's really quite simple if you have a good brain for maths. If you don't, then I'm afraid you might find the later calculations confusing.
This guide has been divided into sections of scenarios (not all possible scenarios will be calculated, only likely ones) and will get more advanced as you progress. All formulas have been simplified as much as I thought would be appropriate.
When using Flinch formulas, remember to multiply before you substract.
Key
/ = Divide
A = Move accuracy in decimals (0.8 = 80%)
F = Flinch rate of move in decimals
P = Probability to hit
O = Opponent's move accuracy in decimals
S = Accuracy modifier stage in decimals (-1 stage = 0.75 = 75%)
Lower than 100% Accuracy
This is the simplest to calculate out of all the scenarios. The formula is:
A = P
When calculating probability 1 means that the event is certain, because 1 = 100%. For example, if you used Stone Edge, the calculation would be:
0.8 = 80%
It's as simple as that.
Confusion/Tangled Feet/Infatuation
Confusion, Tangled Feet and infatuation are perhaps the second easiest to calculate. Infatuation is the status given by Attract, Cute Charm, etc. The formula is:
A / 2 = P
Confusion and Tangled Feet both effectively half you original chance to hit. However, if the move used has lower than 100% accuracy, it is important to factor that in too. For example, if you are confused and are using Stone Edge, the calculation would be:
0.8 / 2 = 0.4 = 40%
So you have 40% chance to hit.
Confusion and infatuation
These statuses effectively quarter your original chance to hit. The formula is:
A / 4 = P
Broken down
A / 2 / 2
Confusion halves your chance of hitting and infatuation halves that to a quarter. For example, if you are confused, infatuated and are using Stone Edge, the calculation would be:
0.8 / 4 = 0.2 = 20%
Broken down:
0.8 / 2 = 0.4
0.4 / 2 = 0.2 = 20%
So you have 20% to hit.
Paralysis
Paralysis is also easy to work out. The formula is:
A x 0.75 = P
Paralysis lowers your chance to attack by 25%, so you're left with 75% of the chance you originally had. For example, if you are paralysed and are using Stone Edge, the calculation would be:
0.8 x 0.75 = 0.6 = 60%
So you have 60% chance to hit.
Snow Cloak/Sand Veil
Snow Cloak/Sand Veil is pretty much similar to paralysis. The formula is:
A x 0.8 = P
Snow Cloak and Sand Veil both decrease your chance to hit by 20%, leaving you only 80% of your original chance to hit. For example, if you are attacking a Snow Cloak activated opponent and using Stone Edge, the calculation would be:
0.8 x 0.8 = 0.64 = 64%
So you have 64% chance to hit.
Paralysis and confusion
All you need to do to calculate this is combine the effects of paralysis and confusion. The formula is:
A x 0.375 = P
Broken down:
A / 2 x 0.75 = P
Confusion divides your original chance to hit by half and paralysis further lowers that by 25%. Ultimately, you are left with 37.5% of your original chance to hit. For example, if you are paralysed, confused and are using Stone Edge, then the calculation would be:
0.8 x 0.375 = 0.3 = 30%
Broken down:
0.8 / 2 = 0.4
0.4 x 0.75 = 0.3 = 30%
So you have 30% chance to hit.
Paralysis, confusion and Snow Cloak
All you need to do is combine the effects. The formula is:
A x 0.3 = P
Broken down:
A / 2 x 0.75 x 0.8 = P
We know that paralysis and confusion gives you 37.5% of your original chance of hitting. Snow Cloak gives you only 80% of the 37.5%, so that's 30%. For example, if you are paralysed, confused, are attacking a Snow Cloak activated opponent and are using Stone Edge, then the calculation would be:
0.8 x 0.3 = 0.24 = 24%
Broken down
0.8 / 2 = 0.4
0.4 x 0.75 = 0.3
0.3 x 0.8 = 0.24 = 24%
So you have 24% chance to hit.
Flinch
Flinch is a bit more complicated in itself. Let's assume that the opponent is faster throughout flinch calculations for the benefit of this guide. Remember to do O x F first, not 1 - O. The formula is:
(1 - O x F) x A = P
Your opponents flinch move accuracy is multiplied by the move flinch rate is taken away from one to give your chance of avoiding flinch. Your move accuracy is also factored in. For example, if your opponents' Serene Grace Togekiss uses Air Slash and you try to attack using Stone Edge, the calculation would be:
(1 - 0.95 x 0.6) x 0.8 = 0.344 = 34.4%
So you have 34.4% chance of hitting.
Flinch and paralysis
This is where you might start losing track. The formula is:
(1 - O x F) x A x 0.75 = P
First of all, you calculate what your chance of avoiding flinch is, then your accuracy in relation to that and then you add the paralysis effect in. For example, if your opponents' Serene Grace Togekiss uses Air Slash and you are paralysed and are to attack using Stone Edge, the calculation would be:
(1 - 0.95 x 0.6) x 0.8 x 0.75 = 0.342 = 25.8%
So you have 25.8% chance of hitting.
Accuracy modifiers
Stages of accuracy (source: PsyPokes):
6 = 3
5 = 2.67
4 = 2.33
3 = 2
2 = 1.67
1 = 1.33
0 = 1
-1 = 0.75
-2 = 0.6
-3 = 0.5
-4 = 0.43
-5 = 0.38
-6 = 0.33
What is meant by accuracy modifiers are moves such as Sand-Attack and Flash. The counterpart are evasion modifiers, but they have been banned from standard play. The formula is:
S x A = P
Basically, the accuracy modifier is multiplied by your move accuracy. For example, if you are -2 stages in accuracy and are using Stone Edge, the calculation would be:
0.6 x 0.8 = 0.48 = 48%
So you have 48% chance to hit.
Just for fun calculations
These scenarios will almost never be seen during battles but are still possible. Not recommended for those with minimal maths knowledge. No "Broken down" sections.
Flinch, paralysis and confusion
All you need to do is work out how much flinch will affect you, then apply the status effects. The formula is:
(1 - O x F) x A x 0.375 = P
This will give you a very rare chance to attack and only Pokemon such as Jirachi and Togekiss can use this well. For example, if your opponents' Serene Grace Togekiss uses Air Slash and you are paralysed, confused and are to attack using Stone Edge, the calculation would be:
(1 - 0.95 x 0.6) x 0.8 x 0.375 = 0.129 = 12.9%
So you have 12.9% to hit.
Paralysis, confusion, infatuation and Snow Cloak
This gives even a lower chance to hit. The formula is:
A x 0.15
Only Froslass is likely to achieve this. For example, if you are confused, paralysed, infatuated, attacking an opponent with Snow Cloak activated and are using Stone Edge, the calculation would be:
0.8 x 0.15 = 0.12 = 12%
So you have 12% chance to hit.
This article is finished, but if you think more scenarios or information should be added, then please say so. Any questions are welcome.
This guide has been divided into sections of scenarios (not all possible scenarios will be calculated, only likely ones) and will get more advanced as you progress. All formulas have been simplified as much as I thought would be appropriate.
When using Flinch formulas, remember to multiply before you substract.
Key
/ = Divide
A = Move accuracy in decimals (0.8 = 80%)
F = Flinch rate of move in decimals
P = Probability to hit
O = Opponent's move accuracy in decimals
S = Accuracy modifier stage in decimals (-1 stage = 0.75 = 75%)
Lower than 100% Accuracy
This is the simplest to calculate out of all the scenarios. The formula is:
A = P
When calculating probability 1 means that the event is certain, because 1 = 100%. For example, if you used Stone Edge, the calculation would be:
0.8 = 80%
It's as simple as that.
Confusion/Tangled Feet/Infatuation
Confusion, Tangled Feet and infatuation are perhaps the second easiest to calculate. Infatuation is the status given by Attract, Cute Charm, etc. The formula is:
A / 2 = P
Confusion and Tangled Feet both effectively half you original chance to hit. However, if the move used has lower than 100% accuracy, it is important to factor that in too. For example, if you are confused and are using Stone Edge, the calculation would be:
0.8 / 2 = 0.4 = 40%
So you have 40% chance to hit.
Confusion and infatuation
These statuses effectively quarter your original chance to hit. The formula is:
A / 4 = P
Broken down
A / 2 / 2
Confusion halves your chance of hitting and infatuation halves that to a quarter. For example, if you are confused, infatuated and are using Stone Edge, the calculation would be:
0.8 / 4 = 0.2 = 20%
Broken down:
0.8 / 2 = 0.4
0.4 / 2 = 0.2 = 20%
So you have 20% to hit.
Paralysis
Paralysis is also easy to work out. The formula is:
A x 0.75 = P
Paralysis lowers your chance to attack by 25%, so you're left with 75% of the chance you originally had. For example, if you are paralysed and are using Stone Edge, the calculation would be:
0.8 x 0.75 = 0.6 = 60%
So you have 60% chance to hit.
Snow Cloak/Sand Veil
Snow Cloak/Sand Veil is pretty much similar to paralysis. The formula is:
A x 0.8 = P
Snow Cloak and Sand Veil both decrease your chance to hit by 20%, leaving you only 80% of your original chance to hit. For example, if you are attacking a Snow Cloak activated opponent and using Stone Edge, the calculation would be:
0.8 x 0.8 = 0.64 = 64%
So you have 64% chance to hit.
Paralysis and confusion
All you need to do to calculate this is combine the effects of paralysis and confusion. The formula is:
A x 0.375 = P
Broken down:
A / 2 x 0.75 = P
Confusion divides your original chance to hit by half and paralysis further lowers that by 25%. Ultimately, you are left with 37.5% of your original chance to hit. For example, if you are paralysed, confused and are using Stone Edge, then the calculation would be:
0.8 x 0.375 = 0.3 = 30%
Broken down:
0.8 / 2 = 0.4
0.4 x 0.75 = 0.3 = 30%
So you have 30% chance to hit.
Paralysis, confusion and Snow Cloak
All you need to do is combine the effects. The formula is:
A x 0.3 = P
Broken down:
A / 2 x 0.75 x 0.8 = P
We know that paralysis and confusion gives you 37.5% of your original chance of hitting. Snow Cloak gives you only 80% of the 37.5%, so that's 30%. For example, if you are paralysed, confused, are attacking a Snow Cloak activated opponent and are using Stone Edge, then the calculation would be:
0.8 x 0.3 = 0.24 = 24%
Broken down
0.8 / 2 = 0.4
0.4 x 0.75 = 0.3
0.3 x 0.8 = 0.24 = 24%
So you have 24% chance to hit.
Flinch
Flinch is a bit more complicated in itself. Let's assume that the opponent is faster throughout flinch calculations for the benefit of this guide. Remember to do O x F first, not 1 - O. The formula is:
(1 - O x F) x A = P
Your opponents flinch move accuracy is multiplied by the move flinch rate is taken away from one to give your chance of avoiding flinch. Your move accuracy is also factored in. For example, if your opponents' Serene Grace Togekiss uses Air Slash and you try to attack using Stone Edge, the calculation would be:
(1 - 0.95 x 0.6) x 0.8 = 0.344 = 34.4%
So you have 34.4% chance of hitting.
Flinch and paralysis
This is where you might start losing track. The formula is:
(1 - O x F) x A x 0.75 = P
First of all, you calculate what your chance of avoiding flinch is, then your accuracy in relation to that and then you add the paralysis effect in. For example, if your opponents' Serene Grace Togekiss uses Air Slash and you are paralysed and are to attack using Stone Edge, the calculation would be:
(1 - 0.95 x 0.6) x 0.8 x 0.75 = 0.342 = 25.8%
So you have 25.8% chance of hitting.
Accuracy modifiers
Stages of accuracy (source: PsyPokes):
6 = 3
5 = 2.67
4 = 2.33
3 = 2
2 = 1.67
1 = 1.33
0 = 1
-1 = 0.75
-2 = 0.6
-3 = 0.5
-4 = 0.43
-5 = 0.38
-6 = 0.33
What is meant by accuracy modifiers are moves such as Sand-Attack and Flash. The counterpart are evasion modifiers, but they have been banned from standard play. The formula is:
S x A = P
Basically, the accuracy modifier is multiplied by your move accuracy. For example, if you are -2 stages in accuracy and are using Stone Edge, the calculation would be:
0.6 x 0.8 = 0.48 = 48%
So you have 48% chance to hit.
Just for fun calculations
These scenarios will almost never be seen during battles but are still possible. Not recommended for those with minimal maths knowledge. No "Broken down" sections.
Flinch, paralysis and confusion
All you need to do is work out how much flinch will affect you, then apply the status effects. The formula is:
(1 - O x F) x A x 0.375 = P
This will give you a very rare chance to attack and only Pokemon such as Jirachi and Togekiss can use this well. For example, if your opponents' Serene Grace Togekiss uses Air Slash and you are paralysed, confused and are to attack using Stone Edge, the calculation would be:
(1 - 0.95 x 0.6) x 0.8 x 0.375 = 0.129 = 12.9%
So you have 12.9% to hit.
Paralysis, confusion, infatuation and Snow Cloak
This gives even a lower chance to hit. The formula is:
A x 0.15
Only Froslass is likely to achieve this. For example, if you are confused, paralysed, infatuated, attacking an opponent with Snow Cloak activated and are using Stone Edge, the calculation would be:
0.8 x 0.15 = 0.12 = 12%
So you have 12% chance to hit.
This article is finished, but if you think more scenarios or information should be added, then please say so. Any questions are welcome.