Guide Spell Steal Efficiency Analysis

The following is an analysis of spell steal efficiency and related metrics relevant to hybrid playstyles under various conditions. While the focus is on spell steal - defined here as using melee primarily to trigger mana steal, without regard to damage dealt from melee hits - a lot of the data is very important for fast hybrid, and there is some analysis along these lines.

Part 1 - Background

Clicks per second (cps) is a general metric that I'll be using throughout this post. While cps of a particular player, and especially can vary in the case of alternating right and left clicks, I don't have the time or resources to rigorously test this so there is not much I can do about the variation (though the variability tends to be rather small anyway).

A quick survey of meta spell builds will make it clear that most builds assume a cps around 4 to 6 - though spellsteal generally targets slightly higher cps, around 5 to 7. Especially fast players (e.g. @highbread ) may have cps approaching 10 or 11 - it is very uncommon to go faster than this, and Wynncraft's own detection throttles the player somewhere in the range of 12-15 cps.

Part 2 - Stealing Patterns

The general pattern for spell steal, at least at slower attack speeds, is to cast spells with intermittent melee, which I will refer to as "interpolated hybrid" (a discussion of other methods along the continuum with what is generally called "alternating hybrid" will come later). For a given player's clicks per seconds/clickrate (cps[1]) we can see the following pattern:

Note, however, that in order to get maximum efficiency out of this basic pattern, there is an assumption that an integer number of spells will perfectly fit between two consecutive melees. For example, if the weapon in question has a Fast attack speed, the gap between two melees is 0.4 seconds. This means that for maximum efficiency (not necessarily maximum power, as shown in the graphs later on) the player would need to have a clickrate such that an integer number of spells would perfectly fit in that gap. For example, 10 cps would allow for this. Remember that a player can't just start casting a spell immediately after a melee - the melee is a click too, so there is some delay depending on the player's cps.

Of course, this is the exception rather than the rule. For the vast majority of combinations of cps and attack speed, there will not be such a neat fit. In this situation, there are two possible ways for a player at their peak cps to deal with this, which I will refer to as "spell throttling" and "melee throttling".

Spell throttling is where the in-between spell(s) are stretched - if the player can only fit, say, 3.7 clicks in between two consecutive melees, the player would just cast a single spell and wait until they can melee (or alternatively cast that spell slower - the exact method is irrelevant, and depends primarily on what is easier for the player). This incurs a penalty relative to being able to actually cast fractional spells in between melee hits.

Melee throttling is the opposite - if the player can click, say, 5.1 times between two consecutive melees, they instead cast two spells (6 clicks) and delay each melee hit a little. Similarly to spell throttling, this incurs an indirect penalty - slower than ideal melee means that mana steal becomes less effective. A later part of this post gives a more complete treatment of this consequence. Melee throttling also decreases melee damage and lifesteal efficiency - the former will be touched on later in the post, but a treatment of the latter is outside the scope of this analysis because the offensive/defensive tradeoff is inherently subjective.

In addition to these penalties, all hybrid builds incur a penalty to spell efficiency (relative to pure spell builds) as a result of the clicks that must be spent meleeing.

Note that, for the mathematical calculation of spell efficiency, spell throttling is effective floor() and melee throttling is effectively ceiling().

Part 3 - Alternative Cycles

Sometimes a different method of hybrid cycling (for faster attack speeds), generally called alternating hybrid, is put forth. Essentially, this is a few seconds of spellcasting followed by a few seconds of melee, alternating. Generally speaking though, this should be less effective than interpolated hybrid.

Consider the case of a player with 8cps and a Fast weapon. Notice that between two melee hits, this player can fit 2.2 clicks. If the player interpolates with melee throttling, a relatively small throttling penalty is incurred, whereas if the player alternates, the spell portion incurs no throttling penalty but there is a lot of wasted time in between the melee hits during the melee portion of the alternating cycle.

I haven't been able to prove that this applies for the entire problem space of cps x attack speed - if someone else would like to do this analysis, that would be very helpful.

Note that the exact results can vary based on a player's corresponding melee and spell damages - for builds with an especially large amount of melee focus, it may be that the mana sustain is not there and as such there is space for more melee. Also this gets more complicated very quickly once melee dps needs to be taken into account (which it would want to be, since the comparison is mainly about faster attack speeds).

Part 4 - Data

Considering the calculations above, spell efficiency (the ratio between a spell steal build's spell output and a comparable pure spell build's spell output) can be plotted as follows:

Notice that the melee throttling penalty only applies to mana steal - depending on a build's ratio of mana regen to mana steal, the efficiency of melee-throttled data points may change. The following charts, and corresponding graphs, show these efficiencies.


The red regions indicate the area where melee throttling is obligatory (i.e. where less than 1 spell fits between two consecutive melee hits). Each step on the mana regen graph corresponds to the point at which another spell can fit between two consecutive melees. The peaks on the mana steal graph are a little to the left of the steps - this is because the point at which peak efficiency is reached will be below the corresponding number on the mana regen graph, because of spell throttling.

Note that 100% mana regen actually means no natural mana regen as well. In practice, most hybrid spell builds will tend to have between 1/3 and 2/3 of their net mana coming from mana steal, so the true spell efficiency will be somewhere between the corresponding curves on these two graphs.

You may be wondering: does this mean pushing a spell steal build more towards mana regen is more effective? The answer is, in some sense yes - if you could exchange 1ms for 1mr it would be a good idea. But of course, you can't generally do this - a quick look at existing items makes it clear that items tend to have more mana steal than mana regen, so practically speaking the quantity of each you take is very situational. And of course, if you exchange all of your mana steal for mana regen and don't have lifesteal, you just end up with a pure spell build anyway.

Note that spell steal efficiency does not correspond directly to actual spell output. The following graphs show the actual spells per standard cycle (i.e. 4 seconds) in place of efficiency.



This last chart shows the melee efficiency component assuming you avoid melee throttling as much as possible.


If you are planning on actually using fast hybrid, this may be a useful chart. Ideally you would want a similar chart where melee throttling is assumed for the applicable parts of the upper-left region. Using these charts you could then compute effective dps numbers based on a build's nominal damage values. Such a treatment of fast hybrid damages would require a lot more work that I'm not willing to put in right now, so I'll end the post here.

 

Jesus christ

 

motoki2 but it's druser

 

I don't understand anything but cool

 

It would be really helpful for the people who don't understand these fancy charts if you could just tell us the most optimal cps or something like that at the beginning of the post

 

Higher cps is more optimal. But that is pretty obvious. You can't really change your cps just like that.

These charts are interesting for certain slower speed comparisons, but it's largely groundwork for a fast hybrid analysis that I intend to do at some point.

 

more evidence that slower attack speed is better than faster
rework steal chances when

 

*cries in mouse that double-clicks constantly*

 

Doesn't need a rework. This makes playstyles much more interesting.

 

Me over here with me 2 clicks per second and equal amount of braincells trying to figure out what the fuck just appeared before me

 

Not rework to be equivalent, rework so that the disparity isn't as big for people who have <7 CPS

 

Quarantine is really starting to get to some people

 

Nice work. I’d label the axis of your graphs though :(

then tell them to git gud

 

I don't want to be more toxic to kio than I already am ;-;
joke but i'm pretty sure kio has good cps even though claim is 2 cps

 

You can account for mage meteor delay or warrior cursed knockback
Will the efficiency go up?

 

You put way too much work into this. Still, useful info for building.

 

Just everyday Druser :P

 

I have a mouse which double-clicks alot but high ping fixes the problem

 

classic case of double negatives

 

I...It's not like I d...don't like you or anything!!