PPM and haste, how does it really work?

[Darksend]

Saw this this morning (obviously from a druid but the theory of it applies to everyone) and was wondering about it, for some reason this seems completely off to me but I know nothing about the topic:


Ok.. I can't seem to post on the druid forums this morning, but after the third post I've seen there recently about weapon procs and haste being good for that, I'd really love it if someone were willing to collect a lot of data on weapon proc chance at different levels of haste. Here's the problem.. if we go by the accepted Burning Crusade mechanics for weapon procs, they don't scale with haste, period. In fact, they anti-scale with haste. Yes, we have confirmation that Omen of Clarity was changed to a flat percentage (5.833333%) chance on hit to proc to allow it to scale with haste, but I've never seen any documented evidence that weapon procs were adjusted similarly. Here's the current understanding of how the PPM system works:

The enchant has a base 'proc-per-minute' value. For nearly all weapon enchants, this value is 1.00, or one proc-per-minute.

We then determine our chance on hit proc percentage, based on our *current* white attack speed (i.e. base speed + haste). So if we have a 1.00 attack speed, it should take us 60 white attacks to get a proc, or a 1.666666% chance on hit to proc. We of course will see more than one proc-per-minute on average because yellow attacks have this same 1.666666% chance on hit to proc, although missed attacks will reduce our proc rate slightly too.

Now we add say 10% haste..

1 / (1 + 0.1) = 0.90909091 attack speed. To get one white attack proc-per-minute with a 0.90909091 attack speed, it would now require a chance on hit of:

60 / 0.90909091 = 66 attacks required, or:
0.90909091 / 66 = 1.37741% chance on hit to proc. By adding 10% haste, we still have the same white attack procs per minute, but we've effectively reduced our yellow attack procs per minute (because the frequency of those is nearly (haste increases Omen of Clarity procs, which increase energy regen rate, meaning more yellow attacks too) unchanged by the 10% haste).

Thus the Berserking enchant actually averages as its highest uptime without any haste at all, and typically drops below Massacre in relative value the moment you add in Windfury.

But is this correct? I'd really like to find out if there's been a change to the PPM mechanics as of patch 3.0.

posting this here instead of the DPS forum because I am assuming that blade warding and mongoose are PPM as well

[Molohk]

Based on the data from the EJ thread posted by Darksend two posts bellow this post, since proc chance per swing is not affected by haste, the number of expected procs should increase as you gain haste.

Win no haste:

Your base weapon speed = 1.5
Your swings per minute = (60/1.5) = 40
Proc chance per hit = (1/40) = 0.025 (based on a 1 ppm enchant)
Number of yellow hits per minute = (60/1.5) = 40 (assuming a melee hit on each GCD)
Total hits per minute = 80 (40 white, 40 yellow)
Expected procs during a minute without any haste = 0.025 * 80 = 2

Now add 10% haste:

Your base weapon speed = 1.5
Your hasted weapon speed = 1.5/(1+0.10) = 1.363636
Your swings per minute = (60/1.363636) = 44
Proc chance per hit = (1/40) = 0.025
Number of yellow hits per minute = (60/1.5) = 40 (your GCD isn't affected by haste)
Total hits per minute = 84 (44 white, 40 yellow)
Expected procs during a minute with 10% haste = 0.025 * 84 = 2.1

As you can see, the number of expected procs increases with haste. This is just a sample calculation, based on the findings of Rezarel's research over at EJ (link 2 posts bellow).

Edit: I originally was incorrect in thinking the chance-per-swing was affected by haste rating, I edited my post to incude correct math based on the link posted by Darksend 2 posts bellow.

[jere]

Do we have a source on how PPM worked in BC that has data to support it? I was under the assumption (probably wrongly) that PPM chance on hit was based purely on the base weapon speed regardless of your haste (thus increasing the number of procs as haste increases while not affecting the proc chance at all).

I don't have any data either, so it would be nice to see some actual data showing which way it worked.

[Darksend]

I am not a math guy so I have no idea what any of this means or how it relates but someone posted this link to ej on the other thread

3.1 PTR PPM Test Results - Elitist Jerks (http://elitistjerks.com/blogs/rezarel/288-3_1_ptr_ppm_test_results.html)

[Molohk]

Do we have a source on how PPM worked in BC that has data to support it? I was under the assumption (probably wrongly) that PPM chance on hit was based purely on the base weapon speed regardless of your haste (thus increasing the number of procs as haste increases while not affecting the proc chance at all).

I don't have any data either, so it would be nice to see some actual data showing which way it worked.

The link posted by Darksend shows Rezarel did the testing for 3.1. The conclussion is that proc chance per swing does not change with haste rating. As you pointed out, this means haste does increase your expected procs.

I've edited my original post to include the correct math, based on Darksends link, just to keep the math on this site accurate and eliminate missinformation.