After a heated debate at today’s Gloomhaven game about the effect of rolling modifiers, I decided to get to the bottom of the matter. The debate centers on whether rolling modifiers added to your attack modifier deck help or hinder you. One side felt that the modifiers help your attacks while the other felt it increases the odds of getting null card (and making the entire attack do no damage) to the point that it hurt you more than it helped you.
It’s certainly NOT up for debate that advantage and rolling modifiers opens the possibility to missing attacks that you wouldn’t have missed without the rolling modifiers. This is true. The question is whether or not the extra damage from the rolling modifier bonus offsets this or not.
Since this is just math, it’s screaming out to be settled mathematically. I followed a Monte Carlo method, which is just running a ton of trials and looking at the results to answer your question. My Python code (released to the public domain) is here.
I ran 1,000,000 trials for each condition – it’s still fast, if someone wanted a more accurate result they could easily increase this. Each trial was a pull from an attack modifier deck. After I pulled a 2x card or a miss I shuffled the attack modifier deck. For each trial I calculated the damage that would be done, then averaged this. Except where otherwise noted I defaulted to a base attack of 3. I didn’t use any status effects, since there aren’t any in the starting attack modifier deck and it would be debatable what the damage value of these would be.
After I finished this, I found a comment on Reddit that hinted at someone doing something similar and coming up with the same results as mine (consider this a replication of his results).
Trial 1 – Standard Attack Modifier Deck
Average attack: 2.999727
Miss frequency: 0.071693
Average attack with advantage: 3.845876
Miss frequency: 0.0
Comments: This was a sanity check more than anything. Because the vanilla attack deck is symmetrical (a +1 for every -1) we’d expect it to average the base attack, which is what it does. It’s interesting to see the impact of advantage – in this case it increases the damage 28%. As expected, another sanity check, when there aren’t any rolling modifiers attacks with advantage never miss.
Trial 2 – Standard Attack Modifier Deck With A Single Rolling +1 Modifier Added
Average attack: 3.047854
Miss frequency: 0.07132
Average attack with advantage: 3.860122
Miss frequency: 0.006416
Comments: The miss frequency stayed the same when rolling modifiers were added, so we can confidently say that adding rolling modifiers does NOT increase the frequency of misses, except for the case when rolling modifiers and advantage interact. Even with these misses (which were previously avoided), the attack advantage is a tiny bit higher with the rolling modifier compared to without.
Trial 3 – Standard Attack Modifier Deck With A Single Rolling +1 Modifier Added And A Higher Base Attack
Average attack: 8.04366
Average attack with advantage: 9.500383
Comments: I re-ran the analysis with a higher base attack, just to see the verify that it isn’t the difference between small and big attacks.
Trial 4 – Standard Attack Modifier Deck With An Additional +1 Card
Average attack: 3.047966
Average attack with advantage: 3.876581
Comments: At this point I was wondering how much impact any 1 card really had – maybe the +1 rolling modifier was helping more than I thought it was. I tried running the analysis with an additional +1 card in place of the rolling modifier. These results were very comparable (a little bit better) than the rolling modifier, so it’s worth less than a +1 card.
Trial 5 – My Level 6 Spellweaver’s Attack Modifier Deck
Average attack: 3.475639
Average attack with advantage: 4.414492
Comments: I thought that maybe the effect was unpronounced with a vanilla attack deck, but may be stronger with a more streamlined / enhanced deck. I used the deck I currently have for my character to get a baseline. It doesn’t have any rolling modifiers.
Trial 6 – My Level 6 Spellweaver’s Attack Modifier Deck With An Additional +1 Rolling Modifier Added
Average attack: 3.522117
Average attack with advantage: 4.419303
Comments: The rolling modifier increased the average attack a little bit and with advantage it was pretty much the same.
Trial 7 – 10 Million Trials to Examine Misses
Just to double check the misses result (which was the real debate), I re-ran all the trials 10 million times and found the misses to be consistent between decks with and without rolling modifiers (at just over 7%). Unsurprisingly adding more non-rolling cards (having a bigger deck) makes misses less likely.
It seems that rolling modifiers don’t hurt the damage output of characters, but neither do they help very much. If consistency is the most important consideration and dealing smaller amounts of damage but avoiding misses is your preference, then avoiding rolling modifiers and advantage may be worthwhile. Rolling modifiers will certainly increase overall damage, will not increase likelihood of misses (except in the above noted situation) and in all situations tested increased the average damage.
The value of status effects is a personal decision and should be incorporated with these results before making any final perk choices.
I would welcome any proof-reading , double checking of my results and code, comments or criticism.