Boards›Esports

Introducing Damage Rating: A better metric to track damage

Riot·8/4/2017, 5:50:55 PM·2 votes·38,611 views

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 Shen, 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 winning to be dealing the same damage as someone who’s losing.

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

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Jungle

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Middle

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ADC

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Support

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

32 Comments

lucello8888/4/2017, 6:21:50 PM6 votes

In terms of taking game time into account, you could look at Damage Rating for certain time periods of the game. For example, finding the average Adjusted Damage per Minute between minutes 20 and 30 and then calculating Damage Rating only for that period of time. You could then use this stat for multiple situations. Who's best at dealing damage in lane? Look at the stats between 0-10 minutes. Late game teamfights? Look at the stats between 30-40 minutes. You could also use it to break down a player's Damage Rating and focus in on what they are best at. Maybe Doublelift has a crazy high damage rating in lane, but is only average when it comes to later game teamfights, resulting in the high number we get for his overall Damage Rating. Unfortunately this doesn't solve the issue of including game time into an overall Damage Rating, but used properly I think it could provide a lot of information and context.

Tehemai8/5/2017, 2:42:29 AM4 votes

This is how you fabricate stats. Selective manipulations and a grand all encompassing labels such as Damage Rating.

Takin' a page out of good ol' Riot Lyte's notebook I see. Gotta control that narrative!

[slayer-jinx-wink]

KingThomasthe1st8/4/2017, 6:14:35 PM3 votes

You do realize that anybody who spams abilities/auto attacks instead of focusing on well timed abilities and proper positioning can have high damage rating. stats are useless and mean nothing out of context, no matter how much work is put into the stat, it will never be specific enough to be taken at face value.

Xonra8/5/2017, 9:50:00 AM3 votes

What I took from this "Woah, how does Cho have 3rd most damage?!"

HarambeDiedA Fga8/9/2017, 4:37:42 AM2 votes

FInally finding solace from C9 fans shoving "C9 IS THE BEST IN EVERY LANE AND BEST COACH" down our throats all the time, on any statistic argument or video online

Beddlam8/10/2017, 1:27:52 AM2 votes

It seems to me that any stat like this is going to be severely limited as long as you are basing it on metrics that can be automatically pulled out with no subjective analysis. The 2000 unit metric seems very arbitrary. "Could this player be doing damage?" is not nearly as useful a question as "Should this player be doing damage?" The latter can only be answered using subjective analysis, but that would be time and money-intensive. For example, if a player's lane opponent has backed, but the enemy jungler is hovering in FoW looking for an over-extension, the player will be penalized for not dealing damage, or if a player is sieging a a turret an opponent is hanging around to thin out the minion wave, the player will be penalized for damaging the turret instead of the opponent. These are just a few examples, but there are many more times when being in range of a champion doesn't mean you should be damaging them. It also doesn't consider opposing champion. A player should be doing very different damage depending on weather they out range their opponent, what their opponent's resistances are, and the current health of both champions. Damage/M is very flawed, but at least it is flawed in very obvious ways. The danger of this stat in my mind is that it is still very flawed, but because of its complexity, and because it's calculations aren't obvious, people won't be as smart about how they interpret this stat.

King of TroIIs8/6/2017, 4:52:15 AM2 votes

Could you please calculate this rating for each player for each division then attach that rating to a player's champion hover in champion select for Draft Queues so that we can better assist with everyone champion selection?

Thanks!

TimWNG8/5/2017, 11:17:18 PM2 votes

What if the adjusted DMG/M was calculated using a weighted time measurement? Generate a flat line (average) DMG/M over a set period (e.g. 30 mins in the graph) and assign weightage to each minute that pulls the DMG/M at that time stamp up to the average.

So if the straight line was @ 150 DMG/M for example, and assuming the graph represents average DMG/M vs. Time over a large set of samples. And say we wanted to calculate what was the equivalent "normalized" DMG/M @ 18 minutes (looks like ~200), then we would use a weight of 0.75 (2000.75 = 150DMG/M). Another example, say we wanted to calculate weight @ minute 30 (looks like ~275), we would use a weight of 0.54 (2750.54 = 150 DMG/M). Now lets say we want to compare Doublelift's single game where he had an adjusted DMG/M of 1000DMG/M @ 30 minutes around opponents, his actual score is 540DMG/M. This way, everyone is compared against the same standard. Longer games receive less weight, shorter games receive more weight, and everyone is equal. Finding a good way to generate that flat line is key.

huyvW5Zd6w8/6/2017, 1:44:22 AM1 votes

Why (Adj.) DMG/M and not (A)DPM?

DPM increasing with game length makes sense, because more items = more damage. Thus, compensate for items. Count not just total damage dealt, but also gold-adjusted damage, e.g. damage dealt divided by gold value of items. Obviously this stat can only be calculated retrospectively if there's an accurate log of when damage was dealt.

Experience is likely another factor impacting DPM and could be compensated for similarly (though probably not straight-up dividing).

IZ4K8/6/2017, 6:02:13 PM1 votes

With no offense intended Riot, please edit / proofread before posting. Just a few examples:

"TL DR; these are the people who make the best use of their champions damage potential" The semicolon is in the wrong place, there's no apostrophe on "champions" and no period.

"We landed on 10 weeks (plus the current week) of regular season data - which is roughly about 700 games of data." The "about" is redundant.

"We also factor in any major champion reworks are taken into account." Redundant "are taken into account."

I really love reading the articles on here to learn more about the game, but this article reads like a Reddit post rather than something published by a professional video game company. End rant.

ZmanElete8/7/2017, 6:54:57 AM1 votes

At 5 minutes 500 damage is much more prized than at 45 minutes. My proposal is to diminish(or the oposite) the value of the damage based on the minute. Rather than only measure the amount of time a person is near a champion, also take into account during what time in the game this is measure in. Obviously do math to make it more realistic though and example might be. A player bullies early in lane hey does 500 damage or so. the value of 500 damage at 5 minutes is valued at 20% more than when he does 500 damage later in a team fight that this player was unable to do damage in. A damage value score if you will. Side note damage per minute per minute seems to normalize around 5 to 7 minutes where you can make a line of best fit to more easily make the percentages to value damage.(might have to just drop 5-7 minutes for late game and keep up to 10 minutes to show lane dominance or something). Not to mathy of a person just thought I'd shoot my idea regardless.

Wewu Owo8/8/2017, 6:42:46 AM1 votes

I am quite confused about this and probably have no right in asking this, but does this calculation include the maximum health of the opponents or dmg dealt by neutral sources? Could that affect the damage rating? I'm pretty sure that if by some instance a team always faces against many tanks, by chance, it might affect this rating. Or if the enemy team is always around a neutral objective (towers, baron, dragons), taking damage, it would reduce their health and make the damage dealt lower for the ally team. And again, I am quite ignorant of all these calculations but I am very puzzled and would like a list of all the factors that are not taken into consideration, that matters.

Nimmer8/8/2017, 7:14:43 PM1 votes

If it doesn't take game time into account it's completely useless... the best teams stomp hard and fast... C9 has absolutely obliterated opponents for the past three weeks, the game times were really short, and Sneaky is clearly doing more damage than Turtle, Altec, Stixx, etc. yet falls to sixth. Jensen is the best laner in the NALCS and always does crazy damage, yet is fourth? This list is literally useless when talking about players on dominant teams.

Brucus Mays8/12/2017, 6:10:11 PM1 votes

@lucello888 not a bad idea especially for tracking throughout periods of a game and seeing the difference between champion weak/strong points in either wins or losses; but that may make the stat a much larger mouthful to swallow than what analysts on any given LCS weekend may be willing to dig through on air. In order to better linearize the data, use a logarithm based scale. It's a method used in many scientific studies for extrapolating data in the long run and determining certain constants that describe physical phenomena. Take the natural log of your data to give you a new data set and use this number for your adjusted DMG/M and DMG rating metric. Your percentage margin between players will decrease and thus better reflect the true DMG rating disparities between players mitigating the time factor in those percentage differences. It may also be worth removing minutes 1-3 from your calculations as this is the lowest DMG output in the game and can be statistically classified as outliers in data sets for most champions.

Even as is, I really like this metric as a way to truly measure the value of a players influence on a game win or lose. Much more telling than the current DMG/M statistic.

baconapplepie9/4/2017, 9:15:11 PM1 votes

If it's of interest I wrote up my thoughts on this stat and how it can be improved with lots of graphs and modeling (using gold, not game length!). Plus possible extensions to get real-time expected damage throughout a game, lots of exciting applications there (look into functional data analysis).

This was mostly just done for fun (I had a really boring summer), so any critique is welcome.

WhatTheDeef8/4/2017, 6:18:07 PM1 votes

I like the metric, seems much better overall than pure DMG/M. One thing I'm concerned about is the sample size you've chosen though. Doing a minimum of 5 games still seems small and prone to effects of outliers (1 very strong or very weak performance). I'm not an expert in statistics, but it seems like you could bootstrap the distributions of games to create a more normal distribution and reduce the effect of outliers. This is assuming there were problems of that sort to begin with though.

Also, to account for game length, you can already get DMG/M at each minute of gameplay as seen in your graph. You could compute DMG rating at each individual minute for a player instead of for a game as a whole. Each of these individual DMG ratings could then be averaged or combined in another fashion for an overall damage rating for that game. There would obviously be minute marks where the player dealt 0 damage and could be excluded or dealt with in some other manner I can't think of right now. It could be a sort of starting point though. I could be completely off base on everything though

III BAKURYU III 8/4/2017, 7:50:54 PM1 votes

mmmmmmm, stats ! Also, can you please do a list of all time stats ( games/Kills/deaths/assists/cs) from regular season splits PLEASE !

Smax8/4/2017, 10:43:47 PM1 votes

I think I see what UoL's problem might be ;)

CanadaHonour8/4/2017, 11:41:25 PM1 votes

What about champions that are played differently based on player preference? For example, Rek'sai has been played both as a tank and as a fighter recently. Granted, patch changes have favoured that tank more recently. Nevertheless, if one player chooses to play the same champion differently than the majority of others, the player's damage output would be skewed upwards or downwards from the mean not because the champion is different but simply because the role on the team (e.g., tank vs. fight) is different.

QED icanhaz8/5/2017, 12:05:52 AM1 votes

What about additionally normalizing by gold differential vs position opponent? For example, if Player A has 10% more gold than Player B, you would expect them to do ~10% more DMG/M. If they are have equal DMG/M, Player B is being more efficient with their gold and should be rated higher than Player A. This method may let you combine wins and losses together (since losing usually means negative gold differential which usually means less DMG/M) while still better accounting for cases where a player smashes their lane but still loses because someone cough bot feeds. It may also help smooth out the DMG/M vs time plot.

TrollFan018/5/2017, 10:52:12 PM1 votes

NO ONE SAID THERE WOULD BE MATH![zombie-brand-mindblown]

xJLx MCHammer8/5/2017, 11:34:30 PM1 votes

This stat still doesn't tell the truth.

It's all about match ups and champions. You are comparing which who did more damage but are completely disregarding what weapon they used. If I'm throwing a orange and you're throwing a apple, it's different outcomes.