Arcazua

MT vs Imp AotH:


For purposes of this discussion, R = average shot rate. (So 1.25 if you tend to shoot twice every 2.5 seconds. OK, so technically this is average time per shot rather than shots per time. Sue me. It'll work.)



MASTER TACTICIAN

This is the easier of the two. In a given period of 8 seconds prior to the shot you are taking, there is a 1 - (.94)^(8/R) chance of MT being up. Other than the "1-" part, that is the chance to not activate in any of those shots. So if you can pull off one shot every second, Master Tactician will be up about 39% of the time, for an average contribution of 3.9%.

Of course, that's best case scenario. In intermittent or short fights, the advantage is much less, but since we're comparing it to Improved Hawk, we'll disregard this.

A 3.9% increase is +3.9% of your non-crit DPS added overall, or 5.1% with Mortal Shots. If you've got 30% crit and Mortal Shots, you're already doing ~139% of non-crit, so jumping to 144% is an actual increase of about 3.6% total damage.

By contrast, if you're shooting every 1.25 seconds, you'll get an uptime of about 32.6%, an effective crit rate of 3.3%. If you're somehow shooting every 0.75 seconds, you'd get an uptime around 48%, or a boon of 4.8%. As you can infer from the previous example, whatever percentage you DO have, is probably slightly less of a percent of your total damage with Mortal Shots.



IMPROVED ASPECT OF THE HAWK

Because the probability is dependent on if we are hasted or not, we have to break this in half.

If hawk is not active, it will take 10 shots to retrigger on average. This takes 10R seconds.

Once it is active, it will last 12 seconds if it is not retriggered. You will fire 12/R shots in that time, each with a 10% chance of reinitiating Hawk. The chance of none of those succeeding is 0.9^(12 / R/1.15) = 0.9^(13.8/R)...so one minus that is the chance of retriggering.

However, we could retrigger off the retrigger, and retrigger off of that...we end up with the sum of a geometric series. So the average number of retriggers is going to be 0.9^(-13.8/R). (Sum of a geometric series is 1 / 1-P.) This number includes the original trigger.

Time to make a few assumptions so the math is relatively simple:
1) Assume that on average a reproc will add 6 seconds (half the duration) to the active period. This is slightly faulty, since the shot it activates on will be front-heavy, but it can't activate for at least R/1.15 time, so we'll pretend that balances out.
2) Assume that a 15% haste will increase your damage by 15%. Theoretically, it should. Work = Rate * Time, so +15% rate in the same time should be +15% work. In practice, it might not.

Then we have an uptime of...6+6*[0.9^(-13.8/R)]...31.7 seconds if you were attacking once per second without Quick Shots. The downtime was 10R, or 10 seconds. So the effect will be active 31.7 out of 41.7 seconds, or 76% of the time. That's an effective 11.4% haste increase, for 11.4% damage!

If we assume a slower attack rate, say 1.25, then the result is 25.2 up, 12.5 down, active on average 67%, for a 10% increase.



There's really no question which one is better, until the haste starts screwing with your shot cycles. If maintaining a 1 second shot speed as a non-BM hunter requires a slow weapon with a tight specials cycle, 15% haste very well might F you up. However, even for straight auto-steady, it's still a very good increase. We're talking a magnitude of about 3:1 in value, unless you start putting in contingencies like "but I like to use Aspect of the Viper," "I mostly PvP and so I never use autoshot," or "but the extra crit adds more than just raw damage for a survival hunter."

In fact, if I did the math right...and I've done it before and don't remember it being THIS good, so maybe I haven't...this is better damage than all other talents except SS or maybe MS.