This post is dedicated purely to the Probability to Hit Formula.

B27 H0

Terms Used:[ul][li]PTH = Probability to Hit (NOT “Chance to Hit”/“Chance to be Hit”!)[/li]

[li]OA = Offensive Ability[/li]

[li]DA = Defensive Ability[/li]

[li]CH = Chance to Hit or Chance to be Hit[/li]

[li]CC = Chance to Crit or Chance to be Crit[/li]

[/ul]

Formulas:

```
PTH = (OA-DA+1275)/15
OA=(PTH*15)+DA-1275
DA=-(PTH*15)+OA+1275
CC=1-(90)/(max[100,PTH]))
PTH=90/(1-CC) [IF CH IS GREATER THAN 100, OTHERWISE PTH=CH]
Due to the rounding of CH and CC in Grim Dawn to the nearest tenth, expect errors no greater than 100.
There exists a relationship between OA and DA, each 15 OA/DA difference between you and the enemy will give 1 more PTH.
```

Unsimplified Formulas[spoiler]

```
PTH=((((OA*5)+7500)-(DA*5))/75)-15
OA=((PTH+15)*75+(DA*5)-7500)/5
DA=((PTH+15)*75-((OA*5)+7500))/-5
```

[/spoiler]

Example Usage of Formulas:[spoiler]

Lets say we want to find out how much OA this Gunman has. We already know four things:

## [ul][li]Our DA: 893[/li]

[li]CH: 91%[/li]

[li]CC: 1%[/li]

[li]PTH: 91 (We know this because CC is less than 10, so PTH = CH)[/ul][/li]We can just plug these numbers into the “OA” formula and we get 983 OA. That’s roughly how much OA the Gunman has.

Lets say we want to find out how much DA Moosilauke, the Chillwind has. We already know four things:

[ul][li]Our OA: 1689[/li]

[li]CH: 100%[/li]

[li]CC: 16.7%[/li]

[li]PTH: 108.04 [Since CC is greater than 10, use the PTH formula][/ul][/li]We can just plug these numbers into the “DA” formula and we get 1343.4 DA. That’s roughly how much DA Moosilauke, the Chillwind has.

[/spoiler]

Misses, Critical Thresholds, and Weights

This image may make it seem like that PTH and Crits are done by a percentage based system. [b]This is a lie[/b]. Crits, hits, and misses are done via weights. There are always at least 100 weights, and each PTH gives one weight that can hit or crit. There are 6 PTH Thresholds, and a sorta kinda one that I’m just going to call PTH Threshold 0.

PTH Thresholds

[ul][li]PTH Threshold 0: Less than 70 (Less than 1x Damage). X [This color represents a miss for uses later on][/li]

[li]PTH Threshold 1: 70 (1x Damage) X[/li]

[li]PTH Threshold 2: 90 (1.25x Damage) X[/li]

[li]PTH Threshold 3: 110 (1.5x Damage) X[/li]

[li]PTH Threshold 4: 130 (1.75x Damage) X[/li]

[li]PTH Threshold 5: 150 (2x Damage) X[/li]

[li]PTH Threshold 6: 170 (2.5x Damage) X[/ul][/li]

PTH Threshold 0: Less than 70 (Less than 1x Damage).

If your PTH is less than 70, any attacks that land will do (PTH/70)x less damage. So, if your PTH is 65, you will do 92.86% of a normal damage on a hit, or 65/70.

PTH Threshold 1: 70 (1x Damage)

Let us assume you have exactly 70 PTH. This means you have 70 weights that can hit, and 30 weights that can miss. To visualize this, let each “X” be 10 weights:

XXXXXXXXXX

The game then picks a weight at random, and you will do that amount of damage.

PTH Threshold 2: 90 (1.25x Damage)

So, for values between this threshold (90) and the next threshold (110), you will get a Critical. So, let us assume you have 100 PTH.

XXXXXXXXXX

Notice that we cannot miss anymore. If our PTH was 99, we’d have 89 Normal Hit weights, and 10 1.25x Crit weights, and 1 miss weight.

Also notice that at PTH=100, you have exactly 10% chance to crit. Pretty nice, eh?

PTH Threshold 3: 110 (1.5x Damage)

So now let us assume that we have 120 PTH. That would lead our weight bar to look like this:

XXXXXXXXXXXX

But wait! We have more than 100 weights! That’s right. We have 120 weights in our weight bar (remember that each X represents ten weights). Also notice that we have 90 weights on a normal hit, and 30 (20 1.25x, and 10 1.5x) weights to crit. This means that our Chance to Crit would be CC=1-(90/PTH), or in this case 25%! Let’s keep going!

PTH Threshold 4: 130 (1.75x Damage)

This time let’s assume a PTH of 140:

XXXXXXXXXXXXXX

Our Chance to Crit Formula tells us we have 35.7% Chance to Crit. Not too shabby, eh?

PTH Threshold 5: 150 (2x Damage)

Nothing too special here, let’s just continue what we’ve been doing. Let PTH=160:

XXXXXXXXXXXXXXXX

PTH Threshold 6: 170 (2.5x Damage)

Let PTH=200:

XXXXXXXXXXXXXXXXXXXX

The only thing to note is that since there is no PTH Threshold above 6, all extra weights are added on as a 2.5x damage multiplier.

Recap:

So let’s recap, did we notice anything significant?

Well, we noticed that when PTH=100, then CC=10.

We also noticed that at PTH=120, then CC=25.

Well, if you took a guess, you might be able to tell that [b]you can know when you broke a threshold by looking at how much CC you have[/b]. This might not sound like much, but if you know this, then you can know that at CC=47.1%, then you have just barely broken into PTH Threshold 6, and can get those juicy, oh so juicy, 2.5x Crits. Of course you will only have one weight in, so your chance of getting this particular Critical is only 1/170 or .0059% chance.

## Here are the CC% and what Threshold you’re in:

CC | PTH Damage Threshold

0.0% | 1 or less

1.0% | 2 PTH 90

18.2%| 3 PTH 110

30.8%| 4 PTH 130

40.0%| 5 PTH 150

47.1%| 6 PTH 170

Conclusion:

And that about concludes everything you need to know about the PTH formula. All information is from the Game Guide on PTH Formula. The reason I took the time to write this all down is solely because of Ninetrix and ex_cathedra, who didn’t understand how the formula worked. So you can thank them for their ignorance if this post helped you in some way

Special thanks to doublebuck, ex_cathedra, and gabfou for correcting and explaining my errors to me.

A very, very special thank you Grohuf for telling me repeatedly that I have an error. Thanks buddy!

Feel free to correct misinformation, suggest additions, or ask questions!