BTH calculations

[the1within0]

Hey, I'm not sure how to get this question answered. I've been messing with all the formulas for the games today, and if I understand things correctly, a weapon's BTH% will add BTH/101 percent to the accuracy. Now when I look at the calculations on UltimateAQ.com, they don't agree with my numbers, and I'm wondering who is in the wrong here. For example The "Liquid Fire" gun has 0 BTH%, and so 6.634 is the damage with no stats and the 0% BTH. That means the accuracy is 6.634/10.000 = 66.34%. Now my calculations agree with that. Now for a weapons such as the "Hotshot Sword", the BTH% is 5% and The No Stats calculation is 8.436. That means the accuracy is 8.436/10.5=80.34% accuracy. That's 14% better for a 5% BTH... I just picked two weapons, same with the "Super Pzycho Sabre (50)" with a 95.4% accuracy. I'm using my own Excel spread sheet to try to calculate everything, and well, I just want to know am I missing somethign big, or if there really is an error in the website. Thank you for any help.

The1within0

[Denzera]

Hi there,

Your formula is not, strictly speaking, correct. the accuracy, or Chance-to-hit, of a weapon, is given by:

CTH = ( 102 + WEAPON_BTH + STAT_BTH - MONSTER_DEF ) / 101

(for normal attacks. special attacks ignore stat BTH). And the full-accuracy expected-damage formula is:

ED = CTH * RATE * HITS * [ BASE + ( (STAT_DMGBONUS + RANDOM) / 2 ) ]

Where RATE is either the normal or special rate in question (there's a distribution so each one has a probability), and HITS is the number of times that particular hit type strikes (only applies to special attacks). STAT_DMGBONUS only applies to special attacks for certain weapons, not all.

You can choose to ignore stats for both of those calculations, and ignore BTH for the Chance-To-Hit calc, however you like... but those are the formulae.

What formulas are you using that give you those numbers?

-D

[the1within0]

Well, I believe I am using those same equations. I was attempting to reverse the calculations on ultimateaq to compare their answers with mine, so when I said accuracy I was referring to Chance To Hit %. I admit I was not clear how I was doing things, and I'm sorry ;) I'm having trouble trying to match up my numbers to the websites. So I will go over exactly how I'm doing it, and then compare.

Legend
-------
No Stats, No BTH = NN
No Stats, BTH = NB
Max Stats, No BTH = SN

Let me start with the Bludrut Blade.
NN = (5 + 35)/2=20.0
Agreed
NB WEP_CTH = (102+WEP_BTH(0)+STAT_BTH(0)+ARM_BTH(0)-MON_DEF(35))/101 = 66.34%
NB = WEP_CTH(66.34%) * (NN(20.0)+STAT_BON(0)/2) = 13.26
Not 17.624. Which means the WEP_CTH would be 17.625/20.0 = 88.13%, suggesting I'm missing 22 BTH% (Calculation not shown)
STAT_BON = 175/8 = 21.875 rounded up to 22
SN = (NN(20.0)+STAT_BON(22)/2) = 32
Agreed
I'm not even sure where to start with Full Accuracy. It says Stats and BTH. I'm Not sure what stats are used to calculate the STAT_BTH, but the equation is Round(STR/16 + DEX/16 + LUK/20) Which at 175 gives me 31, Making CTH 100% and I see that doesn't agree, so I'll stop there

And then Viking Sword
NN = (3+12)/2=7.5
Agreed
NB WEP_CTH = (102+WEP_BTH(0)+STAT_BTH(0)+ARM_BTH(0)-MON_DEF(35))/101 = 66.34%
NB = WEP_CTH(66.34%) * (NN(7.5)+STAT_BON(0)/2) = 4.98
Not 6.609, a CTH of 88.12%
SN = (NN(7.5)+STAT_BON(22)/2) = 18.5
Agreed

My only guess for why I'm getting different results for the NB case is I'm missing a 22 STAT_BTH, but stats should be zero.

As you can tell, I tried to pick the simplest of weapons because it would appear the errors are seen even on those weapons.

A 100% Special Rate Weapon, Liquid Fire
NN = (4+16)/2 = 10.0
Agreed
NB WEP_CTH = (107+WEP_BTH(0)+SPECIAL_BTH(0)-MON_DEF(35))/101=71.29%
NB = WEP_CTH(71.29) * NN(10) = 7.129
Not 6.634. Which means the WEP_CTH = 66.34%, suggesting a difference in 5 BTH% (Calculation not Shown)
SN = (NN(10).0)+STAT_BON(22)/2) = 21.0
Agreed

My Best guess here is that 102 is used instead of 107. I got 107 from the Master List of Game Formula [Updated 10/25]

I would like to apologize for taking so long to reply, Things have been very busy. I greatly appreciate you working on this with me. Thank you for your response.

[Denzera]

OK, a couple things I think can resolve the discrepancy:

1) Our calculations assume a LUK of 0, even when full stats is used. Most players, even if they have pumped dex or str, do not pump luk in the same way. (note that we need to alter these calcs to assume a new max of 200).

2) Previously, the no-Stats-use-BTH version included a stat bonus in the CTH. This is what created the "hidden 22 BTH" that you identified - it was ceil( (STR/16) + (DEX/16) + (LUK/20) ), which comes out to 22. Given the representations of "no stats", I have to consider this a bug. It has now been fixed.

3) The stats used in Full Accuracy include the CTH stat formulas (i.e. ceil( (STR/16) + (DEX/16) + (LUK/20) ) for Melee, dex for Ranged, Int +Dex for magic), and the stats random damage bonus. Here, this might be easier to understand:


switch ($weap['dtype']) {
case 'Melee':
$nr_statbonus = ceil($pstr / 8);
$ns_bth = ceil(($pstr / 16) + ($pdex / 16) + ($pluk / 20));
$edef = $emelee;
break;
case 'Ranged':
$nr_statbonus = ceil(($pstr / 16) + ($pdex / 16));
$ns_bth = ceil(($pdex / 8) + ($pluk / 20));
$edef = $eranged;
break;
case 'Magic':
$nr_statbonus = ceil($pint / 8);
$ns_bth = ceil(($pint / 16) + ($pdex / 16) + ($pluk / 20));
$edef = $emagic;
break;

}


So, that's where i'm getting it from.

3A) Even if you use 31 as your BTH stat bonus (i.e. assuming luk=175), you shouldn't get 100% CTH, it should be about 97%:

(102 + 0 + 31 - 35) / 101
= 98 / 101
= 97.03% accuracy

4) You are correct that the 'base' number for CTH is 102 rather than 107. This is not an error. Suikoman has indicated that the formula is listed on the forums as 107 because most weapons (although not all!) get a +5 BTH on their special attack, in addition to the amount listed for the weapon. Thus for casual purposes it's best to start off with 107 and not worry about whether this particular weapon gets the +5 or not. On UAQ, suikoman has set the special BTH as distinct from the normal BTH and it reflects actual reality, i.e. the older weapons don't have a +5 but the new ones do, and that's just factored into the value.

So don't trust the master list of game formulae on this one.

5) Rounding. For your reference, the following apply:

- Random damage stat bonus rounds up
- stat BTH rounds up
- CTH calculation does not round prior to the hit check on an attack
- in-game, the final damage dealt is rounded to nearest, but...
- ...for our purposes for average expected damage, we just round to 3 decimal places, since it's an average, not a final value

--------------------

So, once you incorporate all of that, do your numbers agree with ours?

Thanks for going over this with me. I've hoped for a while that someone else was around and was checking my numbers.

-D