## A Theorycrafting Stumble

EDIT: And the mystery is solved! Huge thanks to Suicidal Zebra for pointing out where I went wrong and how to fix it. I’m going to leave this post here though, as it’s a good lesson for other number newbies like me who’re trying to figure how this mathematical magic happens.

You number people will love this one.

I promised I’d do some research to find the new spell coefficients for holy paladins. Since the tooltips weren’t updated with the paladin hotfix, I was left with the immense pleasure of doing it all by hand. So that’s what I did. I stood in Darnassus, hit a dummy to stay in combat and recorded my overheal as I showered myself with heals.

I tested all of our spells, approximately 50 hits per spell and was feeling rather smug about myself. Then I got the idea to retest the spells with a different spell power.

Surprise, surprise, they didn’t match up.

The equation: Heal output = Base heal + SP*Coefficient

I used the base values from Wowhead, which, for Holy Light are 2871 to 3197, averaging at 3034.

I made a special blank talent tree to avoid the annoying Conviction talent. I left my retribution glyphs in, but I checked several times to make sure none of them affected healing. Finally, I removed my Ashen Band of Endless Wisdom to avoid the spell power proc. None of the rest of my gear had any procs that affected spell power or healing.

My results with 3427 spell power were the following:

I used the crits as a second sample to compare values. Dividing the crit values by 1.5 produces 6014-6343-6742.

Both samples produced the same coefficients: 0.92 for the minimum value, 0.97 for the average value and 1.0 for the maximum value. While the coefficients don’t exactly line up, I took into consideration that the max and min values are extremes and concluded that 0.97 was my Holy Light coefficient.

Just to be safe, though, I retested it a few days later after removing some clothes. At 1968 spell power, I received the following values:

Dividing the crit by 1.5 produced 5533-5797-6040.

I plugged in my coefficient equation and obtained: 1.35 as minimum, 1.4 as the average and 1.44 as the maximum.

Again the crits and hits produced identical coefficients.

Which leaves me with the following theories:

1) I screwed up somewhere (that’s where you guys come in handy!)

2) There’s diminishing returns to our spell power, at least for Holy Light.

3) The spell power coefficient is now exponential.

4) We received a hotfix between my high spell power and low spell power testing.

I checked #4 by testing Holy Light at full spell power again, this time on the same day as my low spell power test. At 3622 spell power, I received the following:

The crit values, divided by 1.5 are 6111-6358-6579.

The coefficients for this sample are: 0.89 minimum, 0.91 average and 0.93 maximum.

Again, the coefficients for the crits and the hits are almost identical.

These results seem to suggest diminishing returns with spell power, at least for Holy Light: the more spell power we stack, the lower the coefficient.

Thoughts?

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### 8 Comments on “A Theorycrafting Stumble”

1. Brangwen Says:

I am going to give this another crack over the weekend if I get time, probably with flash of light. I came across exactly the same issues you did when trying to figure all this out.

In the end I gave up and just followed your lead with regards the calculation.

This is going to hurt, but the only way is to get multiple sample points to determine what is going on per spell. I DID find that conviction (either 0,3,6 or 9%) buffed the cast as expected, so that was fine as long as you marked down what the stack was when you cast the heal.

• Ophelie Says:

Yeah, but with 50+ heals per sample, they’ll all have different stacks of conviction. It’ll completely throw off averages. I just used a blank talent tree to keep it simpler.

I’m sure there’s something we’re not doing right…although if we suddenly discovered that spell power is affected by Diminishing Returns, it would be pretty exciting ;D

2. Suicidal Zebra Says:

Right, there’s actually a 5th point you need to consider: your base values for Holy Light heals were incorrect.

Ideally you should be constructing two simultaneous equations to solve for your two unknowns – base spell heal value and coeff – assuming that the scaling is linear. I.e.

1.) BASE + COEFF*1968 = 5797
2.) BASE + COEFF*3622 = 6358

(Re-calculate the values from the data you gathered on the second day you tested)

When you’ve derived a new BASE and COEFF, generate a third set of data to test this new equation, plugging in new Spell Powers and Average Heal values.

I’ll let you give it another go without me potentially biasing your results by mentioning my own.

• Ophelie Says:

But even if the base values are incorrect, using the same base value for both spells should produce the same coefficient since the base values would cancel out, no?

I’ll play around with these and see what happens…

EDIT: I totally see it now. /facepalm @ self. I apparently forgot everything I knew about basic algebra.

I’ll plug in the actual numbers once I get out of class and have time to pull out the calculator.

Huge thanks!

• Ophelie Says:

And it seems to work!

Because the data is experimental and consists of averages, I’m getting some variations depending on which set I use, but the coefficent I’m getting is around 0.33 with a base value of about 5100.

Thanks again!

• brangwen Says:

so, 5100 for holy light? as a base? Hmmm that doesnt follow if you get nekkid… There’s more here I am missing, and I don’t have time to research it properly 😦

• Ophelie Says:

I don’t know, my computer died on Thursday so I can’t get into the game to check. When you tried naked, did you test your casts on a dummy or checked the tooltips? Our bases were buffed on the 19th, so the tooltips haven’t been accurate since then.

5100 does seem a bit high, but no matter what numbers I try it with, the lowest I get is 4985is. I’ll fool around with Excel and the data I already have once these midterms are out of the way, but the next time I’ll be able to get back in game will probably be right before Cataclysm.

3. Oestrus Says: