A critical look at critical hit rate!

[KFCrispy]

i'm putting together a spreadsheet of stats using estimated level 61 values... with maxed Heavy Damage/Sharp-shoot skills and a Killer Rune, it turns out Hugo actual beats out Yuiri! this list doesn't use Chief's Hat (which can be equipped to a whole bunch of characters including Hugo and Yuiri)
i'm using the S2 formula for critical hit rate which is (SKL+LUK)/32. i assume this formula is used for the 2x dmg critical hit formula, and that 3x crits are enabled only by the Heavy Damage skill--my guess is that the % given in the skills chart for 3x crits is the actual chance getting a 3x critical hit once the critical is confirmed.

Critical hit rates with maxed skills, no Killer Rune/equipment/Medal
Yuiri 16.85 (Yuiri has a permanent Killer Rune so it's included)
Hugo 12.23
Chris 12.19
Sgt. Joe 11.88
Viki 11.30
Thomas 11.28
Lilly 11.08
Cecile 11.03
Juan 11.03
Borus 10.68
Melville 10.59
Fubar 10.45
Belle 10.42
Shabon 10.42
Jacques 10.41
Duke 10.41
Yumi 10.15
Hallec 10.06
Kenji 9.98
Queen 9.90
Viki (sm) 9.78
Mel 9.47
Yuber 9.29
Rico 9.13
Aila 9.13
Sanae Y 9.13
Franz 9.13
Leo 9.13
Nash 8.93
Emily 8.91



Critical hit rates with maxed skills and Killer Rune, no equipment/Medal
note: Cecile and Hallec drop from the list because they lack free rune slots
Hugo 17.46
Chris 17.40
Sgt. Joe 17.09
Viki 16.95
Thomas 16.92
Yuiri 16.85
Lilly 15.81
Fubar 15.68
Belle 15.63
Shabon 15.63
Juan 15.44
Borus 15.25
Melville 15.00
Kenji 14.98
Duke 14.98
Jacques 14.82
Viki (sm) 14.66
Yumi 14.56
Mel 14.20
Queen 14.12
Rico 13.70
Aila 13.70
Sanae Y 13.70
Franz 13.70
Leo 13.70
Yuber 13.26
Wilder 13.24
Mua 13.24
Dupa 13.24
Sharon 13.24
Futch 13.24
Nei 13.24
Augustine 13.24
Beecham 13.24
Salome 13.24
Ace 13.24
Samus 13.24
Toppo 13.24
Bazba 13.24
Nash 12.92
Emily 12.81

I ended the list with Emily because she's such a highly rated character and has B+ in Heavy Damage, but her critical hit rate is actually not so great. of course, she's still very good because of the number of attacks she pulls off. there are some surprising things, like Kenji, Thomas, Cecile, Mel, and Fubar don't have heavy damage skills but their stats put them near the top. when you have those high stats to give you a high base critical hit rate, the Killer Rune is much more effective.. others who need the Heavy Damage and Sharpshoot skills to match them don't get that same boost by the Killer Rune.
Sgt. Joe's another surprise. i knew he gets crits often, but i didn't think he was one of the best!

EDIT: I found a problem with my calculation for Yuiri... she is now lower than before :/


Chief's Hat
It may be counter-intuitive to give a Chief's Hat to characters who don't have the Heavy Damage skill, but you'll notice that the boosts from B to B+ to A to A+ are all only 3% gains. The largest gains are actually going from no skill to E and A+ to S - both are 5% increases. However, it is still beneficial to raise one's Heavy Damage to B+ or higher because it introduces the deadlier 3x damage chance.

[Punkaiser]

To continue KFC's work, I'd like to add another approach to make it clearer to see why characters like Emily gets us to feel like she critical hits alot although her base cri % is only 9% (or 0.09)

Subjects to look at this time are Emily and Yuiri.

<1> Emily:
Supposes she could successfully land 8 hits on her attack round then:
- Probabilité for her to get 1 critical hit from her 8 swings= 8x 0.09= 0.72= 72%
- For her to get the 2nd cri hit from 8 swings, it requires the 1st to occur and then she has 7 swings left to count on. Then
the chance for her to get 2 cri hits from 8 swings = 0.72 * (7*0.09)= 0.45=45%
- same logic, to get her 3rd cri from 8 swings, it requires 2 swings to occur before that and she has 6 swings to count.
Chance to get 3 cri hits from 8 swings then = 0.45* (6*0.09) =0.24=24%
-....chance for 4cri hits= 0.24*(5*0.09)= 0.11=11%
-....chance for 5cri hits= 0.11*(4*0.09)= 0.04=4%
-....chance for 6cri hits= 0.04*(3*0.09)= 0.01=1%
-....chance for 7cri hits= 0.01*(2*0.09)= 0.002= 0.2%
-....chance for 8cri hits= 0.002*(0.09)=0.0002= 0.02%

Conclusion:
Everytime Emily performs her 8 swings, she has an effective critical % as:
72% to get one critical hit out of 8 swings
45%: 2 critical hits
24%: 3 critical hits
11%: 4 critical hits
4%: 5 critical hits
1%: 6 critical hits
0.2% : 7 critical hits
0.02%: 8 critical hits

<2> Yuiri:
Suppose she could successfully hit 2 times:
With her base cri %= 17%=0.17
- Chance to get one critical hit out of 2 swings= 2* 0.17= 0.34=34%
- same logic above, chance to get both of her attacks to be critical hits= 0.34*0.17= 0.06=6%

Conclusion:
Yuiri has an effective critical % as:
34%: one critical hit
6%: 2 critical hits

...for the other characters...

[KFCrispy]

nice way to break it down. since we're seeing so many hits every time she attacks, you see criticals fly by left and right and end up thinking she's got auto-crit or something. i'd really like to put an equally high level Thomas up next to Lilly or Yuiri, all with Killer Runes, and see if they are really getting about the same crit rate or if Lily/Yuiri actually get a lot more - that would confirm how the skills boosting critical hit rate are working the way we expect here or in a completely different way.

[Punkaiser]

Imo, taking Chabon and Juan into test would be the best choice since those two have many suitable points for this experiment.
like both can reach 6 swings without title(more swings, easier to tell how often they cri hit), and both have almost same critical rate after skill then shabon doesnt have any heavy damage skill while juan reaches the max grade, both are speedy to act first in battle =>way easier to test.

[KFCrispy]

update: my stat calculation for Thomas is flawed. so yeah, better to compare Shabon and Juan...

[ninjaluc79]

Isn't the critical hit rate from Suikoden 2 like this?

(SKL + LUK/2) / 16

[KFCrispy]

yes a months ago someone said the correct critical hit equation in Suikoden 2 halves LUK, so it favors SKL. (and he also pointed out SKL is used for multi-hits instead of SPD in that game as well). and we only have that Suikoden 2 calculation to apply to all the other games, because we haven't seen any official information about the critical hit formula for other games.

i can redo the calculations at some point, but i haven't felt the need