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Stats Science 101: Top Laner Performance

Welcome to Top Lane Week, Summoners! To kick things off, we wanted to take a deeper dive into how things are shaking up in the loftier area of the Rift, by looking at the numbers and equations behind how we rank the pros.

Check out the video to get a breakneck breakdown of Top Laner Performance! Although Professor Pira does a great job enlightening us with those stats knowledge nuggets, we wanted to take a closer look at Damage Rating and the methodology behind our final leaderboard.
 

Damage Rating

Damage per minute (DMG/M) has always been one of those stats that isn’t entirely informative without the proper context. So we wanted to create a damage metric which would take into account champion picks, frequency played as well as wins and losses.

We landed on a metric that would show how well a player is dealing damage in comparison to their expected DMG/M. The formula for the expected DMG/M is shown below:

1

It seems a bit daunting but essentially it just looks at a player’s champion pool and takes the weighted average of the Professional DMG/M in wins and losses for those champions. Sample size is important here, so in order to get the Professional DMG/M we also included NA LCS and LCK data. Only champions with three or more games in a win or a loss are included as otherwise the player’s own performance on that champion skews the Professional DMG/M far too much.

Now that we have the expected DMG/M based on champion pool, frequency and wins and losses we can compare this to a player’s actual DMG/M.

2

To make this clearer let’s run through an example with the King of the Top Lane - Viziscasci. Let’s take a look at the champions he’s played this split:

Champion

Wins

Losses

Professional DMG/M in wins

Professional DMG/M in losses

Camille

1

0

476

288

Gangplank

2

0

690

505

Gnar

0

1

643

386

Jayce

0

1

648

550

Maokai

1

0

386

379

Poppy

2

1

405

343

Renekton

2

0

419

320

Shen

6

2

369

267

Trundle

1

2

417

317


If we plug these numbers into the expected DMG/M formula we get:

3

This comes to 409.67, now that we have these numbers we can look at Viziscscasi’s actual DMG/M which is 486. When we take the percentage difference we get 19%, which means Vizicsacsi does 19% more damage than would have been expected given the champions he has played.
 

Overall ranking

Due to the complexity of the game there are so many different variables that can affect every single one of the metrics we look at to evaluate performance. Even the most fundamental stats can be affected by a bunch of different things. Take kills for example - it is way easier to pick up kills on a Riven than a Poppy. Also maybe you’re just a make peace not war kind of person, if we look at Misfits they have the lowest combined kills per minute out of all teams. Just because they don’t always go for the kill it doesn’t mean that Misfits are a bad team!

That being said, we shouldn’t just throw these stats out of the window, they’re still useful in our aggregated ranking. We should just recognize that some stats are better than others, and whilst the EU stats team are highly opinionated when it comes to our stats tier list it would be kind of arbitrary for us to just create a weighting out of thin air.

So first we made a list of all the stats that we felt were relevant for top laners. And then we sent a survey out to all our casters and top laners, asking them to rank how important they felt each stat was. For each individual survey we created a weighting based on the responses and then averaged them out to get our final weighting - here are the results of the survey:

Isolated deaths

13.36%

Jungle Proximity Difference

11.78%

CSD@10

10.98%

Kill Participation

9.69%

Deaths

9.50%

Damage Rating

9.40%

CSD@15

9.06%

Kills + Assist @ 15

8.40%

Assists

7.59%

CS per minute

7.23%

Kills

6.46%

Before we talk about how we brought everything together we should look at Jungle Proximity Difference. The idea here is to take into account that having additional jungle pressure above your opponent could also have an effect on how well you’re doing vs. your opponent in lane. Getting a positive CS Differential (CSD)  is a lot easier if your opponent is too afraid of ganks to farm! But we should also take into account that regardless of your jungle proximity difference you might just be a super good farmer. So we looked into the correlation coefficient between jungle proximity difference and CSD@10 as well as CSD@15 - which averaged out to 0.47. We’ll use this number as a modifier when docking off points to offset the effect of the jungler.

OK, deep breath - time for the homestretch. Bringing it all together is actually pretty simple. For each stat we took the player ranking and multiplied it by the relevant weighting. Let’s use isolated deaths as an example:

 

Isolated Deaths

Rank

Expect

0.45

1

Cabochard

0.62

2

Alphari

0.76

3

sOAZ

0.88

4

Wunder

1.10

5

Odoamne

1.10

6

Flaxxish

1.17

7

Vizicsacsi

1.23

8

Phaxi

1.38

9

Satorius

1.45

10


The weighting for isolated deaths is 13.36%, we multiply this number by the respective top laner’s ranking in this category. So for sOAZ we would multiply 13.36 by 4 to get 53.44. We do this for every stat, making sure we apply the modifier for Jungle Proximity Difference. Then we just add all the positive stats and subtract all the negative ones (deaths, isolated deaths and although it isn’t negative per se, Jungle Proximity Difference).

And now a drumroll for the final rankings:

Vizicsacsi

437.7

Odoamne

412.6

Wunder

375.9

Alphari

321.6

Expect

289.5

Cabochard

253.7

sOAZ

213.2

Flaxxish

32.4

Satorius

10.1

Phaxi

-41.9


Congratulations, we made it! Now stay tuned for more Top Lane Week content, it’ll be lighter on the numbers - promise!