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Damage Rating: Who packs the hardest punch?

Rekkles is a pretty average ADC, at least that’s what his damage per minute (DMG/M) would suggest. But with the new stat called Damage Rating, we can see which pros make the best use of their champion's damage potential.

Rekkles is a pretty average ADC, at least that’s what his damage per minute (DMG/M) would suggest. As of week 8 of the EU LCS he sits firmly in the middle of the pack at 5th place in DMG/M. And as we know damage is a pretty important element of the game -  lots of damage means lots of kills and lots of kills means winning. And winning is good. But without actually looking further and seeing what champions Rekkles is playing, how much he’s winning or losing, how long his games went and a bunch of other things can we be sure he’s really as mediocre as his DMG/M suggests?

For such a fundamental aspect of the game it would be nice to have a way to quickly discern whether or not a player is dishing out buckets of damage. That’s why we created damage rating. Damage rating takes in a whole bunch of different factors and shows you how much more or less damage a player is dealing than is to be expected. TL DR; these are the people who make the best use of their champions' damage potential.

Curious to see who’s putting up crazy damage numbers? Here’s the top 3 ADCs across a few regions:

 
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And would you look at that, Rekkles jumps from 5th in DMG/M to 1st in DMG rating! - So what is damage rating?

On a high level damage rating is the percentage difference between a player’s DMG/M and their expected DMG/M of an “average player”, taking into account the champions they play and how much they’re winning.

We calculate this “Average Player” using data from EU LCS, NA LCS, LMS and LCK.  We want a big enough sample to compare to, however we also want our data to be relevant enough that the comparison is meaningful. We landed on 10 weeks (plus the current week) of regular season data - which is roughly about 700 games of data.  Right now at the end of week 8 of Summer Split, that’s 8 weeks of Summer data, and the last three weeks of Spring Split. We also factor in any major champion reworks are taken into account.
 

But who are we kidding? You’re really here to read the math behind damage rating, so let’s get into it.

THE MATH

So to start off, let’s run through an example for how damage rating is calculated for a single game. We’re going to look at how Faker performed on Kassadin vs Samsung Galaxy, back in Week 6.

These were his stats for that game:

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First we get Faker’s adjusted DMG/M for that game, which only accounts for the amount of time he spends within 2000 range of an enemy opponent. We do this as we want to exclude the time that Faker couldn’t possibly do damage. For this game it works out at 1584 adj. DMG/M. SKT ended up losing this game - so we take all mid lane Kassadin performances from other players in losses over the past 10 weeks of regular season data. There are 23 games which meet this criteria.

The number of data points used to calculate the expected DMG/M is important - we want a big enough sample size that individual games don’t skew the average. We decided that there need to be 5 data points, excluding all games played by that player. By having this cut off of 5 data points, it means that for some games a damage rating can’t be generated for a player. That being said we don’t want to make it unfair for the trendsetters - so those games will retroactively be calculated when there are enough points in the data set.

Back to our example! So with 23 other losses on Kassadin our sample size is more than big enough. We grab the average adj. DMG/M of these games to get our expected DMG/M and then it’s all plane sailing from there.

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It’s this percentage difference which makes up the damage rating. So we know that for this game - Faker did an astounding 62.2% more damage than would be expected!

 

How did we get here?

The process of getting the adjusted DMG/M and calculating the expected DMG/M isn’t trivial - so why are we bothering, couldn’t we just use DMG/M and call it a day? If you just wanted to say that one player is dealing more damage than another player than sure. But if you actually want to say that one player is a better damage dealer, then you first have to look into a slew of different factors.

So what are all these different factors?

 

Champion pool

Champion pool is probably the biggest bias for both DMG/M and DMG%. If we look at top lane  champions with more than 10 games played you can see a huge difference between Rumble, the champion with the highest DMG/M and Maokai, the champion with lowest DMG/M.

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Wunder (as of week 8 of the EU LCS) has the second highest DMG/M - and that makes a lot of sense when you look at his champion pool, where his top three champions played are Rumble, Kled and Fiora. Just from his champion pool we should expect him to be putting up really good damage numbers. Is he actually the best at dealing damage? Well if we look at damage rating the answer is no. With a +4.6% damage rating he ranks 5th - still pretty good but not as amazing as his DMG/M would initially suggest.
 

Win bias

Like a lot of stats, DMG/M is highly win biased. Usually if you’re winning you have more gold to buy items which in turn means that you can deal more damage (if that’s how you’re itemizing).

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These are all the ADCs who have been played more than 10 times in our sample set and their DMG/M in wins and losses. At a minimum for ADCs, a losing champion will deal 17% less damage than the same champion in a win. You can also see that the disparity between wins and losses is also champion dependent. A winning Kog’Maw will do 31% more damage than a losing one. This is why when we are calculating the expected DMG/M we take wins and losses into account - we can’t really expect someone who is losing to be dealing the same damage as someone who’s winning.
 

Playstyle

Decoupling stylistic choices from performance metrics is difficult. Some teams like to fight more than others, some players like to split push - there are lots of choices like these which will impact DMG/M.

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If we look in the NA LCS the team with the highest combined kills per minute CK/M is Immortals (IMT) and the team with the lowest is NV. NV ranks 6th in team DMG/M whereas IMT rank 2nd. This doesn’t necessarily mean that IMT are better at dealing damage than NV - they may just play more conservatively, or maybe give themselves less opportunity to deal damage.

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The above graph shows the amount of time a team spends within 2000 range of at least one opponent and their average DMG/M for that game. As you can see the more time you spend around at least one opponent the more damage you deal.

The more time you spend in proximity of at least one opponent the more opportunity you have to deal damage. When we look at how well someone is at outputting damage we only want to look at times when they have the opportunity to deal damage. This is why we calculate an adjusted DMG/M. Instead of dividing the total damage dealt to champions by game time, we instead divide by the time that they spend within 2000 range of at least one opponent.

We chose 2000 range as it encompasses most champion abilities in the game. There are obvious problems with champions with longer ranged abilities, however we’ll touch on that later.

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Let’s take a look at EU top laners and how they measure up in both DMG/M and adjusted DMG/M. The rankings between DMG/M and adjusted DMG/M don’t vary too much, however it should be noted that the rankings for almost every player does change. However if we look at someone like Profit, probably the split pushing champion of EU LCS right now - we can see that his adjusted DMG/M is five ranks higher than his plain old DMG/M. So when Profit has the possibility to do damage he’s actually outputting a lot!
 

Shortcomings

As excited as we are by our shiny new damage metric this stat is by no means perfect - we could analyse damage until the cows come home and try and account for endless biases.  So let’s look at where damage rating falls short:

 

Game time

With a game with countless variables every metric is going to have it’s potholes. However let’s talk about one of the most glaring ones with damage rating. It still doesn’t take into account game time.

It might seem like DMG/M already accounts for time, as you’re somewhat normalizing the stat by dividing the total damage dealt to champions by the game length. However that only really works if the amount of damage you do increases linearly over a game which it doesn’t.

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The graph above shows that as the game progresses a player’s DMG/M also increases. If dividing damage by minutes actually normalized for game time the above graph wouldn’t increase over time.

We looked at a few different ways of tackling this, however nothing felt very intuitive or significant. If you have any suggestions on how to account for game time we would love to hear them!

 

Adjusted damage rating

Adjusted damage rating is a bit of an issue. 2000 range is the max range of Caitlyn’s ultimate so whilst it encompasses a lot of the abilities in the game what about champions that have abilities that are longer than this range? Whilst this is an issue, as damage rating is about comparing a champion to other performances of the same champions, it doesn’t raise huge problems. The amount of time that someone deals damage outside of this 2000 range doesn’t vary hugely between performances on the same champion.

 

Major reworks

There’s also an issue with what happens when we have major shifts in the game - is the data still going to be relevant after pre-season or mid-season changes? This is something that we’re going to evaluate after these changes happen. We already account for major champion reworks however rune and item changes can also have a big impact on damage. Perhaps after pre-season changes we’ll have to decide that the previous 10 weeks of professional data are irrelevant. If this is the case that means that we won’t be able to generate damage ratings until we have a big enough sample size. Overall this is simply a reflection of the fluidity of the game - things change, and whilst we would like for numbers and stats to be safe constants sometimes they simply have to encompass the flux.

 

Damage rating across regions

And if you’re curious, here are the damage ratings for each role across NA LCS, EU LCS, LCK and LMS. Only players who have played 30% or more of the average number of games in their league are included.

 

Top lane

10

Jungle

11

Mid lane

12

ADCs

13

Support

14

All stats are up to date as of week 8 of EU LCS, LCK, LMS and NA LCS.