Direct Hit; how much is "enough"?

[nand]

Also, sorry for the triple post, but I wanted to dispel some of the claims made in this thread about the existence or nonexistence of "diminishing returns". While it's true that (assuming you haven't hit the 100% hard cap) Direct Hit rating is a "linear" stat, in a system of linear multipliers (which is pretty typical for games like these), it's generally better to balance your stats than it is to stack one. For example, if each stat "weighs" about the same on average, then instead of a 10% increase to one multiplier (=10% more damage), I could instead split them up to get two 5% increases (=10.25% more damage) instead. Mathematically, if stacking every stat into one linear multiplier results in a linear curve, then evenly distributing them across n linear multipliers results in an nth-order polynomial curve. Eventually, this will outscale the linear increase - it's just a question of how big your stat "pool" is. This phenomenon is what people often mean when they use the term "diminishing returns", but I think a better term for it is "opportunity cost". Or really, what's happening under the hood is sort of the "opposite" of diminishing returns - stats grow more powerful the less of a stat you have. So after a certain point, a badly scaling stat B will outvalue the well scaling stat A if the two become too imbalanced.

Incidentally, this can be generalized from linear stat systems to all systems of polynomials, including critical and direct hit rate. Indeed, once we go to absurdly high stat values (>50k and above) in the above graph, it again becomes better to mix your stats - because now you have a cubic scaling curve (quadratic scaling * linear scaling). So even though locally, critical hit rating seems strictly better than direct hit rating, we can still observe "opportunity cost" once going high enough. Of course, at that point, we hit the 100% hard caps anyway so this argument is moot - but it demonstrates a general concept, so I though I'd point it out.

That being said, the real question in practice is more complicated to answer (and depends strongly on the game), because the constant factor on each stat plays an important role in determining the stat weights within a bounded region (say, from 0 to 3000). The previous image illustrates that perfectly - the only reason direct hit rating outscales critical hit rating for low stat amounts is because the constant factor on it is better. So in some games it's still best to ignore all stats except the best one, if that stat is so good that it's better than the rest even after the "opportunity cost"; and it seems like this might be the case for FFXIV.