Hanging out in forums/reddit/youtube concerning crusader builds such as LoN Bombard and Invoker, there seems to be a recurring question about whether it would be worth increasing Vitality instead of Strength with gems/augments/paragon, when wearing a Heart of Iron (seem to have seen it 3-4 times in just the last week).
(I am posting here though because it is not a crusader-specific piece and other classes may be interested in it - barbarians perhaps? Please feel free to move this to crusader subforum here if it doesn't belong here).
The consensus is that damage-wise it's always better to increase the main stat. One post that is often cited (and I have often cited myself), is this reddit post on Invoker interactions. The part regarding Heart of Iron states:
Assuming Iron Maiden and 300% Heart of Iron an extra 280 STR gem is better than an extra 280 VIT gem when ((2.8x Current Thorns)/1260)*100 > Current STR The amount of thorns at which STR is better than VIT is:
6000 STR – a STR gem is better with more than 27000 Thorns
7000 STR – a STR gem is better with more than 31500 Thorns
8000 STR – a STR gem is better with more than 36000 Thorns
9000 STR – a STR gem is better with more than 40500 Thorns
10000 STR – a STR gem is better with more than 45000 Thorns
So VIT is never better for any realistic combination of STR and Thorns
However, looking at it, I am now not sure where numbers and reasoning come from.
Where does the 2.8 come from?
Where does the 1260 come from?
How did they derive that inequality?
Any insights as to these questions would be greatly appreciated (it looks like the poster hasn't been active for a year, since the very topic in question).
Instead, I have tried to do my own calculations using the following simplified formula:
damage = (thorns+3*vitality)*(1+strength/100)
where thorns is the amount of thorns from gear, Boyarski's and Iron Maiden but excluding HoI, which is manually added. Then each point of strength increases it by 1%.
This is a function of three variables. But by choosing a fixed value of thorns it is possible to make a 3d or contour plot, for example for thorns=250k:
My interpretation of this is that strength is unconditionally better than vitality: for any given strength and vitality, adding vitality would move up a color band at best, while adding strength will move up 2-3 color bands.
Plotting for different values of thorns seems to produce similar results.
No inequality, no combination of strength/thorns come into play.
Is this reasoning sound? Your insight would be immensely appreciated.