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Here's a comprehensive post on AP Elise's damage output. It does not, however, use stat values for AD Elise based on a specific build. That's where I come in!

Here's the damage output of a 6-item Bruiser Elise:

Let's assume an endgame build of - Merc Treads, Wits End, Frozen Mallet, Guardian Angel, Maw of Malmortius (at 50% health for passive), and a Bloodthirster (fully stacked).

This gives us offensive stat totals of:

AS = 40%

AD = 195

Damage/Hit = 42

With Elise's base level 18 stats we have:

297 AD, 1.15 attacks per second, and 42 damage per hit.

That gives us approximately 389.85 dps from Elise alone, just autoattacking. Now, let's add in her spiderlings, and her spider-form W.

Spider form gives us 40 more damage per hit, bringing Elise's spider-form autoattacks to 435.85 damage per second. Since we're also assuming level 18, and max-rank R, Elise has 5 spiderlings. Each of them attacks at .831 attacks per second, for 40 damage. This adds an additional 166.25 dps, bringing us to a total of 602.1 dps.

Then we activate W, increasing both Elise and her spiderlings' attack speed by 140%.

297 AD + 82 on hit damage = 379 damage at 2.76 attacks per second for 1046.04 dps.

200 damage at 1.99 attacks per second for spiderlings = 399 dps.

Total dps for 3 seconds of spider-form W: 1444.92 dps.

Now, let's compare the damage using my preferred build of - Boots, Rylai's, Abyssal, Rabadon's Deathcap, Zhonya's, and Frozen Heart.

With these items we get 507 AP.

In spider form, we get 40 + (.2 AP) or 141.4 bonus magic damage per AA. With a base AA of 102, and base AS of .874 attacks per second we get 212.73 dps.

Now, we have 5 spiderlings. Each attacks for 40 + (.1 AP) or 90.7 magic damage. With an AS of .831 attacks per second we get 372.32 dps, for a total of 585.05 dps.

Now, let's add in the 140% AS increase from spider-form W:

243.4 damage per hit at 2.1 attacks per second = 510.56 dps from Elise alone

453.5 damage from 5 spiderlings at 1.99 attacks per second = 904.46 dps.

Total dps for 3 seconds during spider-form W: 1415.02 dps.

"But Loluthuck", some of you might say, "1415.02 dps is less than 1444.92 dps!"

It sure is less, but only VERY slightly (2%). The kicker here is the rest of the kit. Elise's suicide-spiderling has a .8 AP ratio and 275 damage base. With 507 ap, that's doing a whopping 681 damage. Her Q is also doing 230+18% of her target's health (about 590 damage on a full-health target with 2000 hp) in human form, and 230+18% missing health (about 320 damage on a target at 25% hp and 2000 total hp).

So, let's take all this into consideration as well. Let's assume a 5 second window to cast human form Q/W, then switch to spider and W/AA for full duration/Q.

AP Elise:

590 + 681 or 1271 damage instant burst, followed by 3 seconds of 1415.02 dps or 4245.06 damage, which is then followed by another 320 damage for a total of - 5836.06 damage.

AD Elise:

390 + 275 or 665 instant burst, followed by 3 seconds of 1444.92 dps or 4334.76 damage, which is then followed by another 270 damage for a total of - 5269.76 damage.

Now, all of these calculations have been done assuming zero magic resist and armor. AD Elise is a lot easier to shut down because the vast majority of the damage she will be doing is physical. AP Elise, on the other hand, has the distinct advantage of having large amounts of both physical and magic damage making it that much harder to build defensively against her.

If any of my calculations are wrong, please let me know.

Afterthought: After doing these calculations, I can see Elise built somewhat as an AD carry doing more damage than tanky AP, but (as with going glass-cannon AP) you'd have to sacrifice a lot of tankiness - something she really needs.

**Edit 1: An AP build makes fitting CDR into your build a lot easier too, giving you another boost in terms of sustained damage through having CDs up faster.**
**Edit 2: "Real-world" calculations - Approximate 3-item build AP and AD Elise vs. Approximate 3-item build tank and squishy:**
AP Build - Sorc Boots, Rylai's, Abyssal Scepter, Needlessly Large Rod = 8,455 gold to build

AD Build - Trinity Force, Merc Treads, Frozen Mallet = 8,520 gold to build

Tank Build - Merc Treads, Guardian Angel, Aegis of the Legion, Philo Stone, Heart of Gold = 7,350 gold to build

Squishy Build - Berserker's Greaves, Infinity Edge, Bloodthirster = 7,595 gold to build

Can we agree that two builds, approximately equivalent in costs, and attainable in a normal game, are a good comparison?

For now we will be looking at just damage during the duration of spider-form W. I'll go into damage across the full kit another time.

We'll start with the AP build. Sorc Boots, Rylai's, Abyssal, and NLR give us offensive stat totals of:

AP - 230

MPen - 20

MReduc - 20

These stats will give us an unmitigated damage output of 1021.65 dps for 3 seconds while W is active in spider form for a total of 3064.95 damage done.

Now for our AD build. Merc Treads, Trinity Force, and Frozen Mallet give us offensive stat totals of:

AD - 50

AP - 30

AS - 30%

Crit Chance - 15%

150% of base damage bonus every two seconds with spell cast.

These calculations take a lot into account, so they're more complex. We'll have to break them down into sections, and then add them all together at the end to get our total dps and damage output.

Starting off, we'll get her damage from AA's alone, without the extra damage from her spider form, since that does not benefit from crit. 102 base AD plus 50 from items gives us 152 AD. We get 170% AS increase from W and Triforce, and a base AS of .874, for a final AS of 2.36 after rounding. Therefore we have 358.67 dps. Add in an average 15% damage increase over a period of time from the crit chance and we have 412.493 dps from Elise's AA's alone.

Next we have the dps from her bonus magic damage. 46 damage per hit at 2.36 AS gives an extra 108.56 dps for a total so far of 521.053 dps.

Now we add in the spiderlings. 5 spiders doing 43 damage per hit at 1.99 attacks per second adds on 427.85 dps for a combined total of 948.903 dps over 3 seconds equaling 2846.709 raw damage. Add in a single Triforce proc for pressing W and we get a total of 2999.709 damage.

AP raw dps - 1021.65 | AP raw damage - 3064.95

AD raw dps - 948.90 | AD raw damage - 2999.709

Okay, so we have our raw damage and dps totals, and to be honest, they're a lot closer than I anticipated. Personally, I think this is awesome, but we aren't done yet. We still have to look at damage output on actual targets. Let's pick a random tanky champion, say Cho'Gath, and a random squishy champion, say Caitlyn.

Let's start with damage output for both builds on a tank -

At level 18 Cho has the following base defensive stats:

Armor - 82

Magic Resist - 53, rounded

Merc Treads, Guardian Angel, Aegis of the Legion, Philo Stone, Heart of Gold gives us bonus defensive stats of:

Armor - 98

Magic Resist - 77

So at level 18, with these items Cho has 130 MR and 180 Armor.

The damage multiplier for Armor in League is calculated using the following: 100 / (100 + Armor). With 180 Armor we get a damage multiplier of 0.36 or a damage reduction of 64%.

MR uses the same calculation, so with 130 MR we have a damage multiplier of 0.43 or a damage reduction of 57%.

This is where things actually start to get kind of tricky, and I'll admit that I didn't think about it until this point. Elise's damage isn't all one type, it's mixed. Her spiderlings to physical damage, as do her AA's, but the bonus damage on her AA's is magic.

Starting with AP Elise again -

230 AP

20 Mpen

20 Mreduc

Spiderlings and AA's can be calculated together and give us a raw dps of 841.05 for 3 seconds, or 2523.15 raw damage output.

Bonus magic damage calculates to 180.6 raw dps for 3 seconds, or 541.8 raw damage output.

Our AP Elise build also has 20 Magic Pen, and 20 Magic Resistance Reduction, reducing Cho's MR by a total of 40. This changes our MR damage modifier to 0.53 or a 47% reduction.

64% physical damage reduction puts spiderling and AA damage at 302.778 dps for 3 seconds, or 908.334 damage.

47% magic damage reduction puts bonus magic damage at 95.718 dps for 3 seconds, or 287.154 damage.

This gives us a total dps of 398.496 for 3 seconds, or 1195.488 damage.

Next we'll do AD Elise -

AD - 50

AP - 30

AS - 30%

Crit Chance - 15%

150% of base damage bonus every two seconds with spell cast.

With these stats we have bonus magic damage of 108.56 dps and spiderling/AA damage of 840.343 dps.

64% physical damage reduction puts spiderling and AA damage at 302.523 dps for 3 seconds or 907.57 damage. Extra Triforce damage is equal to 55.08.

57% magic damage reduction puts bonus magic damage at 46.681 dps for 3 seconds or 140.042 damage.

This brings us to a total dps of 349.204 and a total damage of 1102.692.

For now I'm just going to skip the squishy calculations. It's pretty clear that the damage output between the two builds is basically the same

*during the duration of W in spider form.* AD Elise is gimped by being limited to AA's and spider-form W for her damage. Yes, you get two decent % health nukes still as AD, but they're doing less damage than they would if you were AP, and your human-form W is easily ignored.

My synopsis? Both builds work damage-wise, and you should build conditionally for what lane or team comp you're playing in. Playing top vs. a nasty bruiser? Build bruiser too. Trying to fit her into a poke comp? Just build AP, you'll blend right in. Personal preference people.

**Edit 3: Bolded edits to make sections slightly easier to distinguish.**
**Edit 4: I'm playing around with some Mpen/CDR builds and it feels pretty good so far. I'll have to run numbers to see how things match up on paper, but hitting squishies for > true damage is fun **