Machine LoLing

Don’t worry, we scale: a vignette on champion scaling

by Joseph Zinski

We scale bro. My champ has a mid game power spike. A mid game power trough. You’ve looked on lolalytics. You’ve seen what their win rate is in games of a given length. It uhh… kinda sorta shows some trends.

But can we do it better? With the data I scraped from split 1? What about the data I will be scraping split 2? Let’s explore.

Gold Leads and Win Rates

So what are we trying to do? We want a proxy for the likelihood a team will win a game in a given game state. Gold lead is a good place to start, and this post will focus on that variable.

First, let’s just look at the mean gold lead of teams when a champion is on their team. We can look at support as a case study. Each line is a support, say Elise, and the mean gold lead she generates for her team over the opposing team. We do this rather than individual gold lead because some champions generate gold for their friends more than for themselves.

I’ve divided them into clusters for ease of viewing. We can see that some champions tend to gain a gold lead early and some tend to lose it early. Then, later in the game, almost all regress back to the mean of 0. Champions that gain gold late and lose it early are the scaling champions.

Also, note that there are cheaters like Pyke. He cheats with his gold passive, and thus his team’s mean gold is artificially inflated. Draven, TF, GP, and others also cheat. I don’t correct for that here. Those champions need that extra gold to be balanced. Their kits require it.

Converting to Win Rate

That’s cool, but let’s go one tiny step forward and try to get a better proxy for win rate. What we really want to ask is how strong a champion is in a neutral game state. If everything is tied, how likely is that champion to win? That will give us a good idea of champion scaling.

In my last post, I showed how gold lead relates to win rate in roughly even game states which I defined as having a gold lead or deficit within 500 of 0, 0 grub lead, and 0 drake lead. This worked well for the first 20 minutes or so, but after that Atakhans, barons, souls, inhibs, and towers are rarely balanced. Balancing all neutrals, towers, and inhibs matters because even if we have a Kayle and a Draven each at even gold at 40 minutes, the Draven team is more likely to have secured more of the non-gold objectives earlier that game due to his early strength. That will remain a caveat because here I will be using gold lead as a perfect proxy for game state. Its not a perfect proxy, I know, and ignoring all the objectives is a big caveat.

Interpreting this caveat:

  • If we find that Kayle has a 55% WR at 30 minutes in “parity” games (games where gold is even), that’s probably an underestimation. In reality her WR is probably even higher if all neutrals are also roughly even, but they probably aren’t because she is weaker early.
  • If a Draven has a 45% WR at 30 minutes in “parity” games (games where gold is even), that’s probably an overestimation. Draven is strong early, so if the neutrals are also even, his WR would be even worse.

Below we find champion’s win rates in games where gold is nearly at parity. They are grouped by role and separated using k-means in 5 groups for visual clarity. If you’re doing math that’s 25 plots so buckle up.

Support

Adc

Mid

Jungle

Top

These plots largely speak for themselves. I think they are very cool.

Comparing Gold and XP Parity

I have the same set of graphs for games at XP Parity. They are largely the same with a few outliers. Gold tends to correlate with XP as I mentioned in my last post. However, some champs cheat XP like Nilah or Zilean.

Interestingly, some non-cheating champs are just more reliant on gold than XP, and we can see that when we compare the gold and XP parity WRs. Below, I compare the win rates of champions at 20 minutes at gold or XP parity. (Some champs are off the scale, I thought is was funny so I didn’t adjust the axis)

Future Improvements

So, what are the limitations of this analysis? Obviously assuming XP or gold is a perfect proxy for win rate was not ideal, especially because their value becomes very low after 30 minutes. I attempted a model relating the neutral objectives and gold to win%, but it didn’t work well. Why? Well I haven’t put too much effort into yet for one, and for two, I did not scrape inhibitor or turret data for split 1. The late game really requires that info to make a decent model. I am pulling all the needed data right now in split 2, so we will revisit the concept of an equation that translates all game-state data into win% once I have it.

For now that’s all! My next post will explore which individual champions benefit most from a 1k gold infusion at 5, 10, 15 minutes. I assume it would be the scaling champions, but maybe it’s Draven. I’m interesting to find out!

Comments

7 responses to “Don’t worry, we scale: a vignette on champion scaling”

  1. Andrew Avatar
    Andrew

    I noticed on your final graph showing the EXP vs Gold dependency, Brand seems to be missing from it.

    Reply
    1. sparkimusmaximus Avatar
      sparkimusmaximus

      Taric too, I think I set my games played limit too stringently. I’ll fix after work today.

      Reply
      1. test Avatar
        test

        Also no illaoi

      2. MachineLoling Avatar
        MachineLoling

        Fixed!

  2. Val Avatar
    Val

    I do not understand the last 5 graphs. If there is a gold parity at 20 minutes, then if we take Nasus as an example because it is simple, he has around a 55% winrate. So if the gold is even, he is winning. If there is an XP parity at 20 minutes, he has around a 50-51% winrate. So if the XP is even, he is tied. So why is Nasus an XP dependent champ if he wins more when gold is even?

    Reply
    1. Cpt Lancia Avatar
      Cpt Lancia

      I like to think about it like this. How far behind can the champ be in XP or Gold to still be considered winning.

      In Nasus’ example, he must be even in XP to be winning. Whilst with gold, he wins hard at even gold, so he can afford to lose a decent amount of gold to still be winning.

      Also, any way we can get these updated for newer champs like Yunara? 😉

      Reply
    2. fabian Avatar
      fabian

      This is a discombobulating question

      1. Dependency
      If you need a lot of a resource to get THE reward => you are more dependent on the resource.

      Efficiency
      If you need little of a resource to get THE reward => you are using it efficiently.
      AND if you have two resources you could spend on with different efficiency, it would be BETTER to spend it on the more efficient resource => you are more dependent on the efficient resource.

      I think the second way of saying depend is more correct in this situation(I disagree with the plots).

      2. (Incoherent rambling)
      If a champion is scaling it should be weak first 20 minutes => it gain a gold/xp deficit first 20 minutes.
      If this deficit is large while still maintaining a 50% wr the champion scales good.
      If this champion is in parity with opponent and higher than 50% wr then it means the champion is accelerated(gained a lead). Vice versa below 50% would mean champion is decelerated(not gained a lead).

      Depending on how efficient a champions uses gold or xp, the spread of wr when ahead/behind in resource is tighter(inefficient) or wider(efficient).
      So assuming a scaling champion should be in a (equal gold and xp)deficit at 20 minutes, if a champions wr is close to 50% gold/xp -parity wr, I would conclude that resource is not efficient. (this data does not explicitly exists in plots)
      But if a champion has high wr at parity, that resource is probably efficient.

      Good luck

      Reply

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