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### DPS and Crit Chance: Thresholds for Success

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AutoSponge

Senior Member

Given your attack speed, the difference between stacking AD or CS has clear thresholds for your return on investment.

At 90 AD and below, with an Infinity Edge, you should stack AD. Over 90, you should stack CS (until it caps).

Without Infinity Edge, the threshold is 135 AD. At or below 135, stack AD. Over 135, stack CS.

In all cases, once you pass the threshold, the more CS you stack, the faster the value gets returned.

Quote:
without I.E. (2x crit dmg)
 base < 36.5% => stack more crit chance runes
 base > 36.5% => stack more crit damage runes

with I.E. (2.5x crit dmg)
 base < 56.5% => stack more crit chance runes
 base > 56.5% => stack more crit damage runes
EDIT: On the surface, if the Crit damage vs. Crit chance analysis holds up, you should be able to apply those numbers over these so the decision tree looks like this:

1. Start shopping.
2. Have IE?
3. Check Damage.
4. Check Crit chance.
5. Make purchase.

My most recent numbers take into account AS. For now, the above post reflects a baseline 1 AS. Suffice to say, the lower your AS, the higher your threshold at about a 25:.1 ratio down and 25:.4 up.

So, at .9 AS, the threshold is ~150. At .8 AS, the threshold is ~175. At .7, it's 200. In the other direction, you need 1.4 AS to drop the threshold to 100. With AS 2, the threshold is 75.

Example:
If your champion has ~1 AS @ 18 (like Ashe) and you don't buy an AS item, her threshold is 90 with an IE which is already under the IE's bonus plus her base damage. So, don't buy another AD item on Ashe until you max CS. CS has a larger impact for less gold when you already have an IE.

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Riot aBhorsen

Recruiter

Are you trying to show when it is beneficial to stack Crit Chance as opposed to Attack Damage?

Heat n' Serve has already done similar but more in-depth...

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AutoSponge

Senior Member

Heat n' Serve looked at Crit Chance vs. Crit Damage. I'm looking at AD (attack damage) vs. Crit Chance. The analysis was in depth, but I didn't think it necessary to put it all here. I just summarized my conclusions.

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Riot aBhorsen

Recruiter

Would you mind posting it? I'd find it interesting to look at your numbers to understand it better.

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AutoSponge

Senior Member

Explanations of calculation:

I focus on max X for value. It answers the question, "how can I maximize X given the limited resource of Y?" Y, in this case is gold. As I understand it, the higher up the ELO you go, the more scarce gold is.

Attacks/Second. This stat varies by champion but when comparing damage and crit for the purposes of maximizing DPS, it is a constant, not a variable. All we need to decide is, if the damage output per strike will be greater for the gold spent.

The base cost (somewhere between optimal and average) of a point of damage (items only) is 37gold (based on 1850/50 BF Sword). The base cost of a point of crit % is 50 (based on Brawler's gloves 400/8 = 50 or Agility Cloak 880/18 = 48.9).

For any given AS and a variable crit % and AD, calculate the DPS. Do the same calculation again but using 250% damage using an IE. Calculate the costs of the variables used in gold (i.e., multiply your CS% by base cost). Add those costs together and compare them to the value of the DPS.

As soon as the value exceeds the cost, you have a threshold (of incrementing returns). As you progress toward the CS cap, your value-added gains increase as well.

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EasymodeX

Senior Member

Quote:
For any given AS and a variable crit % and AD,
[...]
As soon as the value exceeds the cost, you have a threshold (of incrementing returns). As you progress toward the CS cap, your value-added gains increase as well.

You're missing the baseline crit% chance that all champs have. This would increase the "breakpoint" where you switch from AD to crit%. Also, only stacking crit after the breakpoint would have reduced returns after a certain point (where it would be beneficial to go back and stack more AD, in a pure AD vs. crit comparison).

Furthermore, it may be a good idea to remind the noob audience that ArPen and ASPD also scale champion damage, and that neglecting those will result in relatively gimp DPS.

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AutoSponge

Senior Member

Quote:
EasymodeX:
You're missing the baseline crit% chance that all champs have. This would increase the "breakpoint" where you switch from AD to crit%. Also, only stacking crit after the breakpoint would have reduced returns after a certain point (where it would be beneficial to go back and stack more AD, in a pure AD vs. crit comparison).

Furthermore, it may be a good idea to remind the noob audience that ArPen and ASPD also scale champion damage, and that neglecting those will result in relatively gimp DPS.

As a shortcut to doing the analysis all over again for each character at each level with varying rune setups, you can subtract your natural CS % from the AD totals I provided to set your "current" threshold. It's not perfect, but falls within a small margin of error for most every character.

For instance, Ashe (13.53 CS @ 18) has a few spots where CS is better than AD because she spent less on her CS total. With an IE, she starts showing the threshold around 75 AD, not 90. So, if you subtract her natural 13 from 90, you get ~77. Over 78 AD, stack CS to the cap, otherwise stack AD.

I think the point you missed (given your breakpoint comment) is that for a constant AS, you should at some point return to stacking AD--that's not the case. After the threshold, stack CS like it's your job until you cap it. Then apply your AD/AS. This will max your DPS for a given AS.

Because AS varies so widely among champions and greatly influences DPS calculations, I'm leaving it out right now. Either you bought a +40% item or you didn't. However, since a lot of people are concerned with burst damage over DPS anyway, AS holds less significance.

re: armor pen. Armor pen comes in two forms, % or points. When we're talking about crit damage (2-2.5 times base damage) at AD over 90-135, I think your points of ArPen are basically useless. There are very few sources of it, and it's not cheap. For example, let's say you have brutalizer and some runes for a total 30 armor pen. On the other hand, I have 28% crit (from a cloak and runes ~ same cost). You do +30 damage (assuming your target has that much armor) on every strike 135+|0-30| = 135-165 depending on the target's armor. I'm doing avg 135+(.28*135) = 172.8.

So you could argue that at lower levels armor pen points are better than damage, but at lower levels, people also have less armor--again, I think it's a wash. Last Whisper's % armor penetration is different and could allow high armor targets (tanks and turrets) to melt before your awesome damage or rebuff your attacks entirely.

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EasymodeX

Senior Member

Quote:
After the threshold, stack CS like it's your job until you cap it. Then apply your AD/AS. This will max your DPS for a given AS.

I doubt that. Quick analysis, assuming your original numbers are correct:

At 135 AD, 100 gold spent on AD will net the same return as crit. Quick test:
135 AD + 100/37 = 137.7.
135 AD * 1 + (100/50)/100 = 137.7.

Check.

Assuming you've spent 2500 gold on crit for a 50% crit rate, the new baseline is:

135 AD * 1.5 = 202.5 dps.

So let's spend another 100 gold.

(135 + 100/37) * 1.5 = 206.55
(135) * (1.5 + 100/50/100) = 205.2

As demonstrated: sometime before you have 50% crit chance, and after you have 135 base damage, it's better to spend 100 gold on raw damage, rather than crit.

Quote:
let's say you have brutalizer and some runes for a total 30 armor pen. On the other hand, I have 28% crit (from a cloak and runes ~ same cost). You do +30 damage (assuming your target has that much armor)

You seem to think damage is calculated as "base damage minus armor = damage".

That's very rarely the case in games. Particularly if you mouse over the armor rating on your UI and it says "reduces damage by X%".

30 flat armor pen against a target with 30 armor is, I think, a 43% damage boost. A 43% damage boost is rather significant.

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poopookaka

Junior Member

YOU GUYS ARE GENIUSES! Can any of you help me determine what is best for a DPS Janna then to maximize DPS? Attack damage -Crit chance - Crit Damage or some other order?

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EasymodeX

Senior Member

Janna has a big base damage pump, so get attack speed and crit, with a side of base damage later on.

Personally I wouldn't use a pure attack damage build on Janna, ever, but I would probably go Zeal -> Last Whisper -> 2x crit cloaks (one for PD, one for IE), then finish the IE and PD.

If you want to maximize Janna's attack damage capabilities, do not use proc-based items like Malady or Wit's End. SotD only against Jax, and Mandred's as a counter when your opponent has 9000 hp.

Also, in a "pure" AD build on Janna, I would get an Aegis as like the second item.