# Analyzing the Investigator's combat on paper

### Investigator Playtest

Unfortunately I still haven't had a chance to see any combat for my Investigator in combat. Even if I do, it will be a small sample size. As such, I've decided to turn to spreadsheets to see what things I might uncover. Let me add a caveat that I haven't spent that much time on this. So it's entirely possible my formulas are wrong, or I'm overlooking some modifier. Please point these out if you spot them. It's taken me longer to write this up than it took to make the math model.

Also, I am ignoring the ceiling and floor effects of rolling a 1's and 20's and crit failures/successes

Goal: There are a number of questions I was looking to explore, but the first was what was the probability of getting extra damage from Studied Strike?

1. A matrix. The first thing I did was create a matrix. The columns represent WIS modifier (0,1,2,3,4) and the Rows were DEX. I created fixed boxes for NPC Will Mod, NPC Armor Class, PC Perception Proficiency, PC Weapon Proficiency, and the bonus from Study Subject.

2. My formula: (20-NPC Armor class + Dex Modifier +Study Subject Bonus + Weapon Proficiency+1)/20*(20-10-NPC Will Save +PC Wisdom Modifier+PC Perception Modifier+1)/20

Testing the formula:
By setting NPC AC to 1, PC weapon, and Subject bonus all to zero, I should get the probability of Study Subject working for all values of PC WIS for any given Will save. So let's test that with a 1st level Investigator against a Goblin Warrior (-1 level) with a Will save of +3.

I get (starting with a WIS of 10 and ending with 18) 65%-85. As we expect every point of WIS increased the chance of Subject working by 5%

Let's test this out loud. A +3 Will means I need a 13 to beat the goblin's Will DC. At 1st level, a WIS 10 Inv gets +5 on Perception Proficiency. So that means I need to roll an 8 or better. That's exactly a 65% I look over at 16 WIS and its' a predictable 80% Formula passes the first test.

Now, let's try it the other way, we give PC Perception a 9 and zero out Subject Mod and Will save (essentially what happens when Subject Study succeeds 100% and gives no bonus). With a PC weapon proficiency of 3 against an AC of 10, we see the DEX column starts at 70% and goes in 5% increments up 90% with a 18 DEX. And that all checks out. If I zero PC weap. Prof. It drops to 55%, which is what we'd expect.

For now, I'm proceeding like this mostly works. There is some wonkiness with the fact you succed on a 16 for an AC/Will DC of 16 hence the +1's at the end. I'm also ignoring the 1's and 20's capping.
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3. Results. Now, let's see how Study Subject affects probability of hitting. I'll add in all values for a Goblin's Warrior and the PC. I'm also adding+1 from Study Subject because I'm looking at the probability of Study Subject working and getting a hit. If someone thinks that's incorrect, please educate me as to why.

Goblin Warrior and 1st level Investigator
So:
NPC Will =+3
NPC AC=16
PC Weapon prof=+3
PC Perception prof = +5
Study Subject mod = +1

A 10/10 DEX/WIS Investigator has a 29% chance of hitting with the aid of Study Subject. Across the WIS row, it raises to a mere 36% with a 16 WIS (38% with 18). Down the DEX column, it rises to 39% at 16 (43% at 18). Let's double check this by assuming Study Subject works every time but gives no bonus. So raise PC Perception Prof to 12 and Subject Mod to 0 and we get 45%-65% in 5% steps along the DEX column. Which checks out. An AC 16 with a +3 hit mod means you need a 13 or better, which is 8 chances * 5% = 40%.

I took a look at a level 5 PF2 scenario. The highest Will save of any NPC is +9. The AC 22. Let's look at what that means for a level 5 Inv.

Investigator vs lvl 5 PFS scenario human with Alchemist levels.

NPC Will =+9
NPC AC = 22
PC Weapon prof= 7
PC Perception mod=9
Study Subject bonus= 1

At 10/10 DEX/WiS we get 19%-26% along the WIS row and up to a max of 30% down the DEX column. At 18/18 we get a max of 41%. So if you max DEX and WIS by lvl 5, you are getting bonus damage from Studied Strike about 40% of the time against this particular foe. If you don't boost either, you're only getting extra damage about 20% of the time.

4. To hit modifier. The next thing I looked at was the average To Hit Modifier for the Inv based on DEX/WIS. It should come as no surprise that DEX dominates the to modifier for the Investigator. The +1 from Study subject doesn't even add an expected +1, this is true against all levels of WIS.

As I stated, I spent more time on this write up than the model, so maybe it's got some critical flaw. I'd be interested in getting actual NPC stats from things people have fought to plug it in and see what the numbers say. I'll need

NPC Will
NPC AC
PC level
PC DEX/WIS (If STR is the main combat stat, it works out the same)