Debatable new measures of champion difficulty

tl;dr It may be the case that champions you like are harder to play than you think.

As usual here at LeagueMath.com, we (you and I, dear reader) begin with a question. Which of the 125 current champions in League of Legends is the easiest to play?

Riot helpfully(?) provides a ranking for each champion on a scale of 1-10 for difficulty. It is presented in the champion info in the client as a meter with a staircase icon, and can be accessed through the excellent Riot data API as champion.info.difficulty, but is otherwise hidden in places like the champion pages on the website.

Looking at the ratings Riot gave to each champion for difficulty, they seem a bit arbitrary, and they do not always align with my intuition about how tough it actually is to play each champion. Is Morgana really a 1/10 in terms of difficulty? Is Swain really an 8/10?

I could arbitrarily assign my own difficulty ratings to each champion, but where is the fun in that? Much better would be to use math and data to try and devise a measure based in objective reality. Like Quell said, "Face the facts. Then act on them."

I used the 2,097,222 recent ranked NA solo-queue matches in my database to boil each champion down to a difficulty rating. The database contains matches played on patches 5.3-5.12 by players of all skill levels and so serves as a reasonable backdrop for this type of work.

Here is the procedure I used to calculate my difficulty rating:

1. For each champion, calculate the win percentage for teams with that champion in each league (Bronze, Silver, Gold, Platinum, Diamond, Master, Challenger).
2. Plot those win percentages from left to right with Bronze on the left and Challenger on the right.
3. Fit a nice regression line through the points.
4. Measure the slope of that regression line.
5. Normalize (on a one to ten scale for comparison with the Riot difficulties).
6. Sort the list of normalized slopes, and make a table.

Think about it. A steep positive slope indicates that skilled players win more with that champion than unskilled players do. That likely has some sort of dependence relationship with how difficult a champion is to play. A flat slope indicates that skilled and unskilled players win about as often with that champion, which may (to a sufficiently deranged individual) indicate moderate difficulty. And a negative slope means better players lose less frequently to that particular champion. One could (if one were so inclined) read this as that champion not having a high skill-cap; better players more regularly beat that champion because that champion allows for relatively fewer high-skill game-changing plays.

Anyway, this is—as the title of this post indicates—all very highly debatable; but, it is the procedure I invented and followed, and you are going to stare at this table with the same morbid curiosity I did. Ha!

Heimerdinger at the top and Nidalee at the bottom... /me drops the mic.

There are many interesting questions to ask at this point, and almost all of them are of the form "but Harold, why do you think A is so much less difficult than B?" But every question of that form must immediately be reformulated as "Why do players win with B more often as they skill up, and relatively less often with A?" Then, you will (as I did) pick pairs of champs off this list, essentially at random, and start rationalizing all kinds of fun thoughts.

A few other quick observations of mine here:

• By this measure, Quinn is by far the least difficult ranged AD, and Miss Fourtune (Riot ranks her as a 1/10) comes next with a difficulty just over 5.
• Nidalee, Jayce, Kalista, Elise, and Lee Sin (champs with super mechanically-intense kits) are all near the bottom. So, there may be some merit to this measure.
• Vel'Koz is about a 3.3/10 on this measure, and I have never personally tried him, but on paper, and having played against him, he seems harder than that. Maybe his skill-cap is not that high?
• This measure agrees perfectly with Riot that Nami is a 5/10. There must be some deep significance here.

This particular measure of difficulty was fun to conceive, implement, and analyze. Take a few tens of millions of data points, slice them up and project them onto a super low-dimensional space, fit a silly line through the resulting points, normalize, sort, and call it a day.

But maybe it was too fancy.

Here is a simpler measure. Bronze win rate.

Could it be a good proxy or predictor for difficulty?

Here is the table:

Ha! A few things to say here before I leave you.

Spam Heimerdinger if you want to get out of Bronze.

At first it may seem like a neat coincidence that these two tables are so similar. It is no coincidence at all. Bronze win rate was the left-most point in the curve fit. A nice high Bronze win-rate sets a champion up for a good shot at a shallow or negative slope on that line. It is perhaps interesting that the tables are not identical. I guess there is more to a champion than their performance in ranked matches played at the Bronze level.

I think a lot of players pick up new champions after seeing them perform well in LCS matches. This is likely a critical error for most players. A champion's performance at the highest level of play in an artfully designed team composition reflects your performance with that champion in solo-queue approximately not at all. Ha! I am off to go practice Darius (jk).

I know you can think of a better measure of champion difficulty. Tweet me about it. Is tweet a verb like that?

Today the US takes on Japan in the Fifa Women's World Cup 2015 final. Such finality is a metaphor for you and I together here at the end of this post. Chances are, by the time you read this that match will have been played, and the world champions of women's soccer will have been crowned. But, I predict that the debate about which champion is easiest/hardest will rage on. Why else were you searching?

Whether or not anything was decided about champion difficulty today, there is nothing useful left here. Be brave, return to the index. Indulge in the warmth of more League and more Math. Finally, if it is your kind of thing, subscribe to the rss feed, there is simply no better way to be notified when new articles arise.

Linear regression is a fun way to smash a bunch of data points down to just a few. The shortest distance between two points is a straight line (assuming a sufficiently simple geometry), and the most direct connection between League and Math is LeagueMath.com.

No feelings of Heimerdinger mains stuck in Bronze were harmed in the making of this article.

Peace.