Finer Look at Damage Dice Rolls

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Landon
Posts: 226
Joined: Wed Feb 18, 2015 2:27 pm

Finer Look at Damage Dice Rolls

Post by Landon » Fri Apr 10, 2020 5:42 pm

Edit-Disclaimer: This post might wander a bit. I originally started it confident with my conclusion, then after more thought, it became less clear. In the end, hopefully it provides some tools for people to look at damage numbers in more ways than just 4d5 vs 5d4 graphs on anydice.com.

Now that we have access to very detailed weapon stats, I've spent a lot of time weighing ob, pb, bash, and damage variance. In general, we can all agree that more dice for a given maximum damage is better, because it lowers your variance and shifts your mean damage upwards. But how much does that actually matter?

Recently, I've been playing a jagged with 4d10 damage over WSL's 6d6 damage, and it's felt very strong. I should be expecting to see some low damage shots to balance out those big hits though right? Yes, and no. We lose some of the minor differences from damage messages being in a range, but honing and master damage also add variance which levels out the curve. It's not just a shift upwards in damage.

If you go to anydice.com and input the below code, you can see how the curves shift to the right, but also how the 6d6 curve flattens out.

Code: Select all

output 6d6 named "6d6"
output 6d6 + d4 + d4 + d5 +d5 named "6d6M"
output 4d10 named "4d10"
output 4d10 + d4 + d4 + d5 +d5 named "4d10M"
This link may also work, but I'm unsure how long they last, https://anydice.com/program/1ae6e

The next question for me was how do I quantify this? It was too clunky to try and add up each rolls % around the mean on anydice, so I did some very dirty research and tried to apply it correctly. Dice rolls follow a normal distribution curve centered around the mean, so we should be able to calculate the variance, which gives us a standard deviation. Then we can multiply that standard deviation and either subtract or add it to the mean to find our damage range for a given confidence value.

Below is a spreadsheet link for various weapons that I've been considering,
https://docs.google.com/spreadsheets/d/ ... sp=sharing

The X-Sigma drop down box allows me to select the confidence range, as given in the table on the right. What this means is that if I select X-sigma = 1, 68% of my damage with a master honed Jagged will be between 26.7-39.2. Compare that with 27.1-36.9 for the WSL. What does this mean? Honestly, I'm not sure. On average, I'll do slightly more damage with a jagged, but will see more 27s and more 38s. I decided to add one more table at the bottom of 2h longs to look at this differently.

With the damage threshold table, I select my minimum damage and maximum damage, then the table tells me the % chance of going below minimum threshold damage or above maximum threshold damage. My Jagged will go below 24 damage 2.5% more than my WSL. However, it will also go above 40 damage 8% more. We have to be careful here, because it would be easy to say, Jagged goes below 24 damage 50% more than WSL, and goes above 40 damage 150% more often.

How you value and view these numbers will play a large part in your analysis. If I change the threshold to 28 min and 35 max, the Jagged and WSL have almost the same sub 28 chance, but the Jagged will hit above 35 damage 37.5% of the time, compared to 27% of the time with WSL. Is this proof that I should continue playing Jagged? Again, I'm not sure, but I'll probably keep running Jagged for that little extra damage and because they're pretty easy to get with everyone writing them off.

Good luck, have fun, and don't forget to hone your weapons.

Yeri
Posts: 90
Joined: Sat May 23, 2015 4:26 am

Re: Finer Look at Damage Dice Rolls

Post by Yeri » Fri Apr 10, 2020 8:50 pm

Inspired by this, I wrote a script to automatically calculate the average damage, standard deviation, and 95% confidence intervals (aka, most of your damage will be in this range) for all the weapons I had easy access to. If someone has a CSV of all the weapons I can run it on everything else, but honestly getting the tables from the Help! forum into CSV format was a huge chore. More easily-parsable formats please!

For all of these, I simulated 1 million hits and calculated all the stats. The full spreadsheet can be found here: https://docs.google.com/spreadsheets/d/ ... sp=sharing

I think the interpretation is generally a little tricky, but good rules of thumb as Landon's already mentioned: more dice for a given maximum damage (eg 8d5 vs 5d8) is always better, the difference between two weapons with different maxes (eg 7d6 and 8d5) gets smaller as you add more constant stuff (having a honed weapon, being a master), and of course this isn't considering bash or other stuff that may matter to you. And for the love of god, honing adds 5 damage on average to every hit, please do it.

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