Improving on DPM — Introducing Average Damage per Minute Difference

Damage statistics in League of Legends are a tricky thing. Dealing damage is a big part of the game, but how much is inflicted depends on many factors. Some of those within the control of the players, some not. Let’s take the NA LCS team Immortals for example. If you look at their damage per minute (DPM) statistics, they ranked fairly high. They ranked first in DPM during the 2016 Summer Regular Season for top, mid and ADC and second for jungle. If you watch their games, you know that they like to fight. A lot. They also ranked number one in the number of Gold Shift Events (GSEs) as well as Combined Kills per Minute (CKPM) — by far — during the regular season. What does this mean? They simply put themselves in more situations than other teams to deal damage to champions. Team SoloMid on the other hand, while not being afraid to brawl themselves, play a more organized and macro-heavy style. As a result, IMT’s members have an edge in DPM, despite being behind TSM in the standings. Huni’s damage heavy champion picks further exacerbate the discrepancy.

Overall, I would say there are three main aspects which can make it difficult to read too much in to the DPM metric.

  1. Champion Picks: If mid laner A plays a lot of Varus — a champion that deals an insane amount of damage over the course of a game, because he can poke from long range while also providing sustained damage through auto attacks in team fights — and mid laner B a lot of Lulu, A’s DPM will be a lot higher if put in similar situations. That does not mean that A is performing better, because B is adding a lot more utility to his team (and probably dies less often).
  2. Play Styles: As mentioned above, some teams fight more, some less. One is not necessarily better than the other, but the former will lead to a higher DPM for the players involved.
  3. Game Length: Longer game times means more gold, more items, often times more fights and as a result more damage. While the late game is missing out on some damage that is inflicted through continuous trading in the laning phase, that fact does not make up for the increases that result from the aspects mentioned above.

I have previously talked about the issues with damage statistics here, but I recently came up with an idea to improve upon DPM in particular: Average Damage per Minute Difference to Lane Opponent. Short: DPM Difference or DPM-D.

What is DPM-D? It is fairly simple. It measures the difference in DPM to the player from the opposing team playing the same position. Then the average over DPM-D for all games is taken similar to something like creep score difference at 10 minutes (CSD@10), only for damage per minute calculated at the end of each game. An example? Let us say TSM plays vs. CLG in game 1 and vs. C9 in game 2. In game 1, Doublelift deals 700 DPM and Stixxay 600, in game 2, Doublelift deals 650 DPM and Sneaky 680 DPM. Doublelift’s Damage per Minute Difference vs. Stixxay is +100, vs. Sneaky it is -30. His DPM-D over the two games is therefore (+100+(-30))/2 = (100-30)/2 = 35.

What are the advantages compared to DPM? First of all, it matters how you compare to your opponent directly. More importantly, DPM-D mostly gets rid of two of the problems mentioned above. Firstly, since you, by definition, play the same amount of minutes as your opponent in every single game, there are no differences in average game length to the players you are compared to. Yes, game length can still have an influence, because there is more damage to go around in the late game, thus increasing the opportunities to build damage leads over opponents, but the effects are a lot smaller than what we would expect from DPM and can be positive or negative (DPM-D is a zero sum statistic!).

Secondly, while play styles differ between teams on average over a season, within one single game there cannot be a difference in the number of fights. Again, by definition fights involve both teams. Maybe one team wants to brawl and the other does not, but only one will get its way in each individual game. Furthermore, roles usually participate in fights in a similar volume as their counterpart. If one ADC is involved in a lot of fights, usually the opposing one is too. The biggest discrepancy will probably be found in the top lane, where TP timings differ and split-pushing instead of helping out the team is sometimes still a possibility. But, again, the biggest problem mentioned in point 2. — different play styles of teams — is taken care of with DPM-D. Overall, I think DPM-D is most suited to evaluate the most damage heavy roles, mid and ADC. Unfortunately, while DPM-D doesn’t directly punish you for being on a low-fight team, it does not deal with the issues of damage opportunities. Yes, if you don’t interact with champions, your opposition doesn’t either, but you both get less chances to improve upon your DPM-D. Again I would argue that DPM-D reduces the influence of play styles drastically when compared to DPM and we will find evidence in the stats that support this (see Sneaky/Jensen and C9).

 

The Stats

 

Now that I have introduced the metric and elaborated on it a bit more, it is time to show you the stats. Who does well? Who doesn’t? How does it compare to DPM? What are the differences between roles? To do this I will use the regular season stats from this summer split for mostly the EU and NA LCS (with some info on LCK players), because it provides a lot more data than the playoffs. Lane swaps probably affect the absolute size of the differences a bit, so it will be interesting to take a look at it again once we have more data for post 6.15 games. For now, lane swaps should not pose a big problem for the overall interpretation.

Below you can find a Tableau table where you can filter by region and position. It is the easiest way to show you the stats for all players (only those with at least 10 games). I included DPM and it also shows the ranking for DPM-D and DPM for comparison (the rank adjusts with filter selection, so it is most useful when only selecting one position and possibly only one region).

As we can see, Huni ranks on top of all players within the three regions with a DPM-D of 195.1. That means that on average, he deals 195.1 damage more to champions than his opposing top laner. Unfortunately, DPM-D does not correct for champions picks, and it is pretty obvious that Huni likes to play above average damage champions for top laners. Furthermore, he plays on IMT and gets a lot of jungle attention. His numbers should be read with this in mind. If we go further down the list, we see a lot of top players from their region, including Bang, Zven, Faker, Smeb or Doublelift, in the top 12.

Filtering by region and position reveals some interesting differences between DPM and DPM-D. In NA, Sneaky ranks first in DPM-D, despite only having the fourth highest DPM. While there are others who deal more damage on average, he tops the list when compared to his peers directly on a per-game basis. Similarly, Jensen climbs the ranks for mid laners from 7th (DPM) to 2nd (DPM-D). It is not surprising that Cloud9 members are rated higher by the new metric. If we look at their Combined Kills per Minute (link oracles elixir) or Gold Shift Events, both measures that give clues about the amount of fighting a team participates in, C9’s games involve less player-on-player interaction it seems. As a result, their DPM values are fairly low. DPM-D on the other hand is not too concerned with that and manages to give information that seems to align more closely with C9’s success. It would be weird if the 3rd-placed team in the league was overall bad at dealing damage compared to others.

On the EU side of things, DPM-D might give hope to fans of H2k’s Freeze, while putting ROC Steeelback’s numbers more into perspective. Yes, Freeze does not deal a lot of damage, but the ADC’s he is matched up with do not either (in their games vs H2k), so his DPM-D is only  -12.2. Steeelback on the other hand seems to be involved in damage heavy games and despite putting up 544.4 damage per minute, his opposition is, on average, putting out almost 120 damage more per game, leaving him in last place in terms of DPM-D.

 

DPM-D and win percentage

 

I also took a look at how average damage per minute difference is correlated with win percentage for different roles. As you can see in Graph 1 below, there is — as expected — a clear trend overall and for each position individually. Everyone to the left of 0 DPM-D is, on average, dealing less damage than his lane opponent, everyone to the right more. The biggest outliers come from the mid lane, most notably Cry, who played 10 games for the ROX Tigers this split, Froggen, and PowerOfEvil. From the data, it looks like Cry was to some extend carried by the other members of Korea’s powerhouse, but the team still only managed to win 58.3% of their games with him vs. 82.1% with Kuro, who posted a DPM-D of 113.9. Froggen on the other hand was by far the best player on his team and his slightly above average DPM-D was not enough to get more wins. PoE is the biggest surprise. Investigating him would mean taking a deeper look at his champion pool to see if his high DPM-D (and DPM) numbers come from that, or if he simply did a better job of dealing damage than perceived. This is beyond the scope of this article though, since it would involve an analysis of champion damage statistics in general.

damage per minute differece vs. win percentage

Comparing DPM-D to gold income

 

When looking at damage, it usually makes sense to look at gold income also. While some gold comes from kills and assists — which themselves rely on damage — towers and especially farm contribute heavily. Since we are observing damage in relation to the opponent, it only makes sense to do the same for gold. So Graph 2 plots the aggregate DPM-D versus GPM-D — average gold per minute difference to lane opponent. If we look at the observations from graph 1, it makes sense that Froggen and PoE — players who had a high DPM-D for a losing team — are among those making the most of their negative gold per minute differential. Cry on the other hand is doing the opposite, giving further confirmation that he did not have the best showings in his 12 games.

gold per minute vs damage per minute difference

Throughout this analysis, a player that is really sticking out is SKT’s Bang. He has high numbers across the board and is one of the top performers in graph 2. He has the best DPM-D to GPM-D ratio. Bang, on average, “out-earns” his opposing ADC by almost 40 gold per minute less than Doublelift (42.0 to 80.4), but manages to “out-damage” his opposition by 90 damage per minute more than Doublelift (188.7 to 99.9). Overall, both Doublelift and Bjergsen are on the lower end of the DPM-D to GPM-D ratio, which might indicate decreasing damage return on gold. TSM has been so dominant, maybe it is just not possible to transfer all that advantage into damage at the same rate as it is possible for closer games. That hypothesis is a topic for another DPM-D article.

For now, I hope I have given you a good introduction into this metric and provided some interesting player stats. There is a lot more analysis that needs to go into this topic and I welcome any feedback or discussion to improve the insights that can be gained from this. The statistic still has its flaws and should, as all stats (in particular damage stats), not be taken at face value alone. I do think that it improves upon DPM though. Go ahead and play around with the Tableau table above. We will add the DPM-D (and possibly GPM-D) to our stats pages for worlds. If you want to know when we publish new work or update our stats, you can follow us on twitter.

 

Edit: Got some good feedback from Tim Sevenhuysen from Oracle’s Elixir.

His input regarding the downsides compared to DPM definately helps to put the metric a bit more into context:

  • You now have to take into account both their own champions *and* the opponent’s champion, which is harder to investigate.
  • The player’s statistical performance now relies on the performance of their teammates, in ways that may be hard to measure.

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