Epic Perfect World

Critical Hit Rate (%)

Offline mikeyjamez

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Hi All,

This is my attempt at making a contribution to the community by sharing my observations on critical hit rates (%). For all the statistics nerds; the critical hit rates follow a binomial distribution. This explains why people with 50% crit rate can still not do critical hits after hitting the target 5 times. 

In this post I will;
  • Outline the likelihood (probability) of the number of critical hits at the varying crit rates after hitting a target five (5) times. 
  • Use theoretical base damages that decreases by 25 points for every % increase in crit rate.  
  • I will show the probability of total damage outputs after having hit a target five (5) times using the theoretical base damages. 

Note that;
  • Five (5) hits were used to accommodate maximum number of hits per second for APS classes and it would be enough for DPH and DPS classes.
  • Base damages per class differs and is the reason a theoretical number is used just to simulate how the process works. 
  • GOF critical hits were not accounted for but ought to be considered for melee classes when considering total damage dealt. I neglected this because I created the model primarily for my psychic.
  • The distribution of critical hits is the same for all classes. 

So let's get into it. 

80% Critical Hit Rate

Critical hit chance (P)80%
# of hits (N)5
E(X)4
VAR(X)0.8
Base Damage4250
Critical hit damage8500

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
00%                     21,250.00
11%                     25,500.00
25%                     29,750.00
320%                     34,000.00
441%                     38,250.00
533%                     42,500.00

70% Critical Hit Rate

Critical hit chance (P)70%
# of hits (N)5
E(X)3.5
VAR(X)1.05
Base Damage4500
Critical hit damage9000

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
00%                     22,500.00
13%                     27,000.00
213%                     31,500.00
331%                     36,000.00
436%                     40,500.00
517%                     45,000.00


60% Critical Hit Rate

Critical hit chance (P)60%
# of hits (N)5
E(X)3
VAR(X)1.2
Base Damage4750
Critical hit damage9500

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
01%                     23,750.00
18%                     28,500.00
223%                     33,250.00
335%                     38,000.00
426%                     42,750.00
58%                     47,500.00


50% Critical Hit Rate

Critical hit chance (P)50%
# of hits (N)5
E(X)2.5
VAR(X)1.25
Base Damage5000
Critical hit damage10000

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
03%                     25,000.00
116%                     30,000.00
231%                     35,000.00
331%                     40,000.00
416%                     45,000.00
53%                     50,000.00


48% Critical Hit Rate

 
Critical hit chance (P)48%
# of hits (N)5
E(X)2.4
VAR(X)1.248
Base Damage5050
Critical hit damage10100

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
04%                     25,250.00
118%                     30,300.00
232%                     35,350.00
330%                     40,400.00
414%                     45,450.00
53%                     50,500.00


45% Critical Hit Rate

Critical hit chance (P)45%
# of hits (N)5
E(X)2.25
VAR(X)1.2375
Base Damage5125
Critical hit damage10250

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
05%                     25,625.00
121%                     30,750.00
234%                     35,875.00
328%                     41,000.00
411%                     46,125.00
52%                     51,250.00


40% Critical Hit Rate

 
Critical hit chance (P)40%
# of hits (N)5
E(X)2
VAR(X)1.2
Base Damage5250
Critical hit damage10500

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
08%                     26,250.00
126%                     31,500.00
235%                     36,750.00
323%                     42,000.00
48%                     47,250.00
51%                     52,500.00


38% Critical Hit Rate

Critical hit chance (P)38%
# of hits (N)5
E(X)1.9
VAR(X)1.178
Base Damage5300
Critical hit damage10600

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
09%                     26,500.00
128%                     31,800.00
234%                     37,100.00
321%                     42,400.00
46%                     47,700.00
51%                     53,000.00


35% Critical Hit Rate

Critical hit chance (P)35%
# of hits (N)5
E(X)1.75
VAR(X)1.1375
Base Damage5375
Critical hit damage10750

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
012%                     26,875.00
131%                     32,250.00
234%                     37,625.00
318%                     43,000.00
45%                     48,375.00
51%                     53,750.00


32% Critical Hit Rate

Critical hit chance (P)32%
# of hits (N)5
E(X)1.6
VAR(X)1.088
Base Damage5450
Critical hit damage10900

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
015%                     27,250.00
134%                     32,700.00
232%                     38,150.00
315%                     43,600.00
44%                     49,050.00
50%                     54,500.00


30% Critical Hit Rate

Critical hit chance (P)30%
# of hits (N)5
E(X)1.5
VAR(X)1.05
Base Damage5500
Critical hit damage11000

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
017%                     27,500.00
136%                     33,000.00
231%                     38,500.00
313%                     44,000.00
43%                     49,500.00
50%                     55,000.00


28% Critical Hit Rate

Critical hit chance (P)28%
# of hits (N)5
E(X)1.4
VAR(X)1.008
Base Damage5550
Critical hit damage11100

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
019%                     27,750.00
138%                     33,300.00
229%                     38,850.00
311%                     44,400.00
42%                     49,950.00
50%                     55,500.00


26 % Critical Hit Rate

Critical hit chance (P)26%
# of hits (N)5
E(X)1.3
VAR(X)0.962
Base Damage5600
Critical hit damage11200

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
022%                     28,000.00
139%                     33,600.00
227%                     39,200.00
310%                     44,800.00
42%                     50,400.00
50%                     56,000.00


20% Critical Hit Rate

Critical hit chance (P)20%
# of hits (N)5
E(X)1
VAR(X)0.8
Base Damage5750
Critical hit damage11500

 
# of critical hits (X)Probability (Binomial Distribution)Total Damage Dealt
033%                     28,750.00
141%                     34,500.00
220%                     40,250.00
35%                     46,000.00
41%                     51,750.00
50%                     57,500.00


I hope this info will prove useful when trying to determine which stats to aim for. Thanks for reading.  
Dare to be different ^.^

Offline MMMMMMMMMMMM

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Offline mikeyjamez

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lol nerd


LOL! Best way to beat every1 is understanding game mechanics
Dare to be different ^.^

Offline BumleBee

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My iq too bad cant understand halp plz

Offline Masuta

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in short crit is nice



05.15♡

Offline Anselmo

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Offline mikeyjamez

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in short crit is nice
Don't be naive. Balance is important and at a certain point increasing crit rate makes no sense.
Dare to be different ^.^

Offline Saxysta

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Make Fudo cry and leave epw :3

(ノ`Д´)ノ彡┻━┻

Most importanly, take his account of >_<

Isora is mine

Offline Rikku

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this does not account for class balancing, which isn't public data.
:)

Offline Buffy

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Great post. I don't think it's appreciated enough ;--;