Disclaimer: this is a guide solely about choosing CritH and CritD. I will not discuss the larger picture relating to other gear mods ([DMG] etc.) nor will I discuss the larger STO meta-game (like things that trigger off of crits). My goal here is only to teach you the maths so that you can decide, for yourself, without a calculator, spreadsheet, some internet friend told you, etc., how to choose between, say, Spire consoles, or CritH and CritD weapons modifiers; assuming you know your current values of CritD and CritH.

On the other hand, these are handy maths that happen to apply to calculating crit damage in ANY game. They're also useful in RL, yo.

**The Guide.**

The purpose here is to compare only CritH to CritD. Hence, we will assume that our hit chance, and non-crit damage remain constant. In this scenario, our expected damage per landing shot is thus:

(Eq. 1): TED = BD * ( 1 + H * D),

where TED is our total expected damage, BD is non-crit damage H is CritH and D is CritD. The equation is dead simple, but we can ellaborate.

First, notice that H is a probability, hence we can only ever talk about the total expected damage. This is not going to be your actual damage per shot. Rather, if you were to shoot your gun from now until infinity, and you took the average damage per shot, then that would equal TED. In more useful terms, during the course of an ISE, your average damage per shot will, with high probability, be very close to TED.

Second, notice the 1. That is there because the base damage is always applied (when we land a shot), regardless of whether we crit or not. When/if we crit we get to do extra damage. The amount of extra damage is dertmined by our CritD, or D in the equation.

TED is what we want to maximise. How do we do that? Well, if you remember your high school calculus, you can see that if you take the partial derivative of TED with respect to H you get D, and vice versa. But if you remember your high school calculus you probably already know the right answer, so let's assume you don't.

Let's simplify the equation then. Since the BD is always applied, and we're assuming that other modifiers remain constant (weapon type, [DMG] modifiers, etc), we can consider BD to be constant. 1 is also, of course a constant. So we have only two variables H, and D, which together dermine the expected extra damage we get to inflict per shot (over our base, that is always applied on a hit). Let's remove the constants, and we're left with:

(Eq. 2): EED = H * D

Where EED is Expected Extra Damage (in units of base damage). This is what we wish to maximise with our choice of CritD and CritH. How do we proceed? suppose you currently have H amount of CritH, and D amount of CritD. You got a new, hypothetical, piece of gear, and can now add one extra CritD, or one extra CritH, which one do you go for?

Well, turns out we don't need high school calculus, we can use grade school arithmetic. Remember that multiplication is distributive. With that in mind, we have two choices. We can increase our D by 1 in which case our new EED is:

(Eq. 3): EED2 = H * (D +1)

= H * D + H

= EED + H

So, increasing our CritD by 1 increases our expected bonus damage by exactly H! Likewise, if we increase our CritH by one, we get a new EED of:

(Eq. 4): EED3 = (H + 1) * D

= H * D + D

= EED + D

So, increasing our CritH by 1 increases our expected bonus damage by exactly D!

Hence, at any point, if we can increase either CritH or CritD by one, we should always choose the one that is currently lower.

The Myth of the Magic Ratio

But, you say! You had heard of a magic ratio of 1:10. Where does that come from? Were you lied to? Or am I lying to you now? Well the math doesn't lie. This ratio comes from the fact that in STO you don't normally get to choose between ONE of CritH, and ONE of the other. There are, let's call them, exchange rates. For example, on weapons you can either get a CritH modifier for 2%, or a CritD modifier of 20%. So the exchange rate on weapons is 1:10. This is the same exchange rate found on universal consoles. In fact, the 1:10 rule came about at a time when the game only allowed you to choose, or exchange between, CritH and CritD at a ratio of 1:10. This is no longer the case, though.

So, what changes now? Well, imagine your company offered to pay you either British pounds, or Euro's. But they decide that if they pay you in Euros they'll give 10 times as many Euros as pounds. Which should you take? You might jump and say "Of course Euros". Well, that might be the case, but for a trully correct answer you need to look at the current exchange rate. Imagine, completely hypothetical I know, that the pound was worth 100 times as much as the Euro. Should you still go for the payment in Euros? Clearly not! If the pound is much more valuable than the Euro, you should choose the pound. But where is the cutoff point? Well, when the pound is worth exactly 10 times as much as the Euro, it doesn't matter how the company pays you. If the pound is any stronger, you should go for pounds, any weaker, and you should opt for Euros.

Same thing in STO. When you get the choice of 10 CritD or 1 CritH, you need to look at how valuable these two are for your current build. Remember the worth of a single point of CritH is exactly your current CritD, and the worth of a single CritD is exactly your current CritH. Hence, you should always go for CritD on a weapon, unless, your CritD is more than 10 times larger than your current CritH.

What about the new Spire Tac consoles? Well, there the exchange rate is different: it's 1:5 rather than 1:10. So, you should take the CritD only if your CritD is currently less than 5 times your CritH.

An important thing to keep in mind, though, is that each new piece of gear you add changes your current CritH :: CritD ratio. Where you start off, may not be where you end! For instance, you may decide, looking at your current numbers that locators are better than exploiters. But after you add one, or two, of these consoles, the ratio may change to favour the other!

If cryptic were to introduce a new item slot that gave you either X CritH, or Y CritD, the same maths would apply, with a new exchange rate of X:Y. The important thing here is that there is no magic ratio, and it is certainly not 1:10. There are merely item stat budgets, and conversion rates between stats. These conversion rates are what we have to pay attention to when picking an item, but remember that they apply only to that item or slot.

There, you no longer need a spreadsheet, or calculator. If you know your current CritH and CritD, then you IMMEDIATELY know which pieace of gear is better for you.