Direct Hit; how much is "enough"?

[nand]

Hey,

I'm new to FFXIV and found this thread while searching for resources on how damage formulas work in this game. I thought it was an interesing enough question to try and answer conclusively via the power of mathematics. I used the formulas from the following website to calculate the effective DPS gain from crit / direct hit rating, respectively:

https://docs.google.com/spreadsheets...F38/edit#gid=0

The way I decided to approach the problem was by making the assumption that we have a "fixed" pool of stats to allocate from (say, 3000 rating in total) and it's up to us to decide whether we want to lean that pool more towards crit rating or more towards direct hit rating. That is, I assume that we're presented with a series of choices such as "would I rather have 40 crit rating or 40 direct hit rating?". In the context of this framework, the question is: how much should I lean towards one or the other?

One thing that we can see quite clearly is that for the upper end of what we can realistically achieve with current gear, critical hit rating alone completely dominates direct hit rating. But this is not always the case - there's a phase reversal somewhere at around 3000 shared total stat between the two. More fascinatingly, in a result that I didn't expect at all, in this "transition" region, it's worse to have a mixture (say 50% crit and 50% direct hit) than it is to stack 100% of either, even though they multiply each other! (This is a direct consequence of the fact that crit rating is essentially useless if you don't stack enough of it)

To best visualize these results, I decided that we should use "50% of each" as the baseline - under the assumption that on average, we'll always be able to balance the two stats as a baseline, and the question is how much we want to "lean" towards one or the other as a function of how much stat we have available. That formula looks like this:

https://www.wolframalpha.com/input/?...000,+0%3Cy%3C1



The short summary is that for <3000 total stat, you want to stack direct hit rating as much as possible. For >3000 total stat, you want to stack critical hit rating as much as possible. For ~3000 total stat, it doesn't really matter which one you go for - but always try to get as much as possible of the same stat, never mix the two.

The formula was generated using this haskell program: https://0x0.st/zz6d.hs