Avoidance Diminishing Returns in MoP – Part 3

In parts 1 and 2, I presented the data and calculations that led us to the analytic forms of the new diminishing returns (DR) formulas. However, while having the formulas is a great thing, most tanks are probably more curious about what it means for them. In other words, “how does this change how I approach gearing?” That’s what I’ll try to address in this blog post.

Recap – The Formulas

Before we get there though, let me quickly re-post the formulas once again. Between taking and analyzing the data and writing these blog posts, a new build went live that added 2% dodge to Sanctuary. While I haven’t tested it yet, it’s almost certain that this 2% dodge will not be affected by diminishing returns. As such, it’s just an addition to base dodge (check for yourself – your level 90 paladin should have 5.01% dodge while naked if I’m right). So to summarize the last two posts, the new dodge and parry DR equations are:

$Large {rm totalDodge} = {rm baseDodge} + left (frac{1}{C_d}+frac{k}{rm preDodge} right )^{-1}$

$large {rm totalParry} = {rm baseParry} + frac{rm baseStr}{Q} + left (frac{1}{C_p}+frac{k}{frac{{rm totalStr}-{rm baseStr}}{Q} + {rm preParry}} right )^{-1}$

with ${rm preParry}$ and ${rm preDodge}$ being the pre-DR avoidance values as read off of the respective tooltips, and the following constant values:

${rm baseParry}=3.00$
${rm baseDodge}=5.01$
${rm baseStr}=176$ (for a BE, varies per race)
$Q=952$
$C_p=235.5$
$C_d = 65.631440$
$k=0.885$

I chose Q to represent the Strength-to-Parry conversion factor because it takes us from “S” to “P” in “PQRS”, and Q is more fun than R.

What Does It All Mean?

Now that we have the formulas, let’s look at what they mean. First of all, here are the DR curves plotted for you:

It’s clear that by 10% worth of dodge rating, we’re already seeing the effects of diminishing returns (which is why the L90 dodge data was easy to fit, the curvature starts to happen much earlier). But it takes 2-3 times as much parry to start seeing distinct curvature. This means our gearing is going to be very lopsided – we’re going to want a lot more parry than we have dodge.

To illustrate that more clearly, let’s look at the differential gain in avoidance. The following plot shows how much avoidance you gain by adding 1% pre-DR avoidance, plotted as a function of your post-DR avoidance level. To put that in less technical terms: if you already have X% post-DR dodge (i.e., as read off of your character sheet), then adding another 1% pre-DR dodge will give you Y% post-DR dodge, where X and Y are the values on the plot.

The dotted lines are guides to help us see how to “balance” dodge and parry. You’re probably familiar with the Cataclysm rule of thumb, which is “keep dodge and parry rating approximately equal.” But with different diminishing returns curves, keeping them equal isn’t optimal anymore, because dodge will be much more severely diminished. As a result, adding 10 parry rating would give us more net avoidance than 10 dodge rating.

That’s what the dotted lines tell us: “how much parry do we want to have at 10%, 15%, and 20% dodge to keep dodge and parry balanced?” Again, “balanced” means that adding 10 parry rating gives us the same amount of post-DR avoidance as adding 10 dodge rating. Note that I’ve already included base dodge and parry in this plot, so that’s accounted for.

This plot tells us exactly how bad the discrepancy between dodge and parry is. If we have 10% total dodge on our character sheet, we’d want to stack up to 21% parry to make sure that we’re not being inefficient with our diminishing returns. And it gets worse as we go higher – at 15% total dodge, we’d want 39% parry, and at 20% dodge we’d want 57% parry. The ideal ratio of parry:dodge gets larger as we stack more dodge (though to be fair, this is only because of base dodge and parry – the ideal ratio of pre-DR parry and dodge is a constant).

We can express this mathematically as follows. The differential gain in post-DR dodge and parry $dA_d$ and $dA_p$ due to a small amount of pre-DR dodge and parry $da_d$ and $da_p$ are:

$dA_d = frac{1}{k} left (1-frac{rm postDodge}{C_d} right)^2 da_dlarge$
$dA_p = frac{1}{k} left (1-frac{rm postParry}{C_p} right)^2 da_plarge$

where ${rm postDodge}$ and ${rm postParry}$ are the post-DR dodge and parry values gained purely from sources subject to diminishing returns (i.e., subtracting out base dodge and base parry). I have also called these “${rm netParry}$” in the previous posts, and I’m being sloppy here for the moment and rolling the parry granted by ${rm baseStr}$ into ${rm baseParry}$. If we set $dA_d = dA_p$ and $da_d = da_p$, we can solve for ${rm postParry}$ in terms of ${rm postDodge}$:

${rm postParry} = left ( frac{C_p}{C_d}right ) {rm postDodge}large$

If we want to compare total parry $( {rm totalParry = baseParry+postParry})$ to total dodge $( {rm totalDodge = baseDodge + postDodge})$, we get:

${rm totalParry} = {rm baseParry} + frac{C_p}{C_d} left ( {rm totalDodge}-{rm baseDodge} right )large$

which we could plot if we wanted to know exactly how much parry we should aim for at a given dodge level. If you’re interested, here is that plot.

We can also consider the ideal parry-to-dodge ratio, $R_{rm pd} = {rm totalParry}/{rm totalDodge}$. That’s simply:

$R_{rm pd} = frac{rm totalParry}{rm totalDodge} = frac{C_p}{C_d} – frac{(C_p/C_d){rm baseDodge}-{rm baseParry}}{rm totalDodge}large$

which looks like this when plotted:

As you can see, the ideal parry-to-dodge ratio quickly jumps up to 2:1 and then slowly increases to 3:1 and higher as you stack more dodge. It saturates at $C_p/C_d = 3.588.$ This is going to make balancing slightly annoying, since we’ll have to keep referring to the above equation (or using a spreadsheet or a tool like askMrRobot) when our gear changes.

It’s worth noting that there’s an easy solution to this, if Blizzard wanted to implement it. If strength granted parry rating rather than invisibly giving pre-DR parry percentage we’d have it pretty easy. In that situation, all we’d have to do is make sure that the ratio of our parry rating to dodge rating was 3.588, regardless of what our post-DR values are. That’s all the equation is doing, in fact; it’s complexity is purely due to accounting for the invisible parry granted by strength that isn’t showing up in the tooltip.

In summary, we’re going to value parry a lot more than dodge at level 90. Expect to have 2x-3x as much parry as dodge under normal conditions.

I said this in the last post, but it bears repeating: while I have only tested this with a paladin, it’s a reasonable assumption that these formulas will work for warriors and DKs. Since druids can’t parry, their DR formula is likely to have a different (i.e. much higher) value of $C_d$, otherwise they’ll be severely disadvantaged compared to tanks that can parry. I wouldn’t be surprised if their value of $C_d$ was the same as our value of $C_p$, in fact, but that’s just wild conjecture at this point. If there are any druids in the audience that want to submit some data to me (naked agi/dodge as well as agi/dodge rating/pre-DR dodge/post-DR dodge in various gear sets), I’ll be happy to perform the fitting and figure out what your $k$ and $C_d$ value are.

It’s less clear whether Monks will use the same constants as the plate tanks. My guess is no, simply because while they can parry, they won’t be getting much parry rating if they share gear with druids. A small amount from rings, amulets, cloaks, and trinkets, perhaps, but probably not enough to make a huge impact. Most of their avoidance will probably come from dodge, and as a result I’d expect their value of $C_d$ to be a little higher. In fact, it wouldn’t surprise me at all if they were just swapped for monks, such that their dodge cap was around 235% and their parry cap was around 65%. But again, that’s wild speculation. And again, if any monks want to submit the appropriate data sets, I’ll be happy to do the rest of the work.