Luck and League: Measuring Ideal Season Length in LoL

Angus Lockhart is a consultant at a market research firm in Toronto, Canada, and holds a Masters of Arts in Political Science. He has been playing League of Legends since season 2.


What is the ideal number of games to play in a season? To many fans and analysts, an ideal season has to be long enough that the best teams reliably come out on top, while the weaker teams fall to the bottom of the standings, but not so long that there is no real room for upsets and unpredictability. Based on that definition, sports analytics provide tools for answering that exact question.

The longer a season, the more likely it is that the best teams float to the top. We’d all agree that a four game season is probably too few, but a hundred game season is probably too many. How do we know what is right?

At 18 games, the LCS and LEC have only two more games than the NFL and significantly fewer games than the NBA (82) the NHL (82) and MLB (150). Is that too fed, or is it appropriate given the nature of League of Legends?

Before seeking an answer, we must acknowledge that when it comes to creating a schedule and a season length, many different factors are important: viewership, burnout, skill expression, and more. The focus of this analysis is “skill expression”, meaning the ability of a team to demonstrate its quality with minimal influence from random or uncontrollable factors. But skill expression is naturally not the only consideration, since teams and Riot have an incentive to maximize profit and to limit playing time to prevent burnout. Statistics, however, can’t say much about these other factors, so a broader discussion of the “best” season length must be left to a different context.

The Data

The math behind this analysis comes from Tom Tango’s “True talent replacement level for sports leagues”, via a Neil Paine article on 538. Their previous analysis provides a framework for understanding how much luck contributes to a team’s score after any number of games.

The following analyses use the LCS and LEC records for teams since the beginning of franchising. This provides a stable period with consistent teams playing in a consistent format. While adding in data from the LCK and LPL would increase the sample size, both use best of threes for their regular season and so they are inherently not comparable.

The Math

The variance in winning records that we observe over a season [var(observed)] is a function of the true variance in a team’s skill and the natural random variance that comes from sampling a limited number of games. We can express that as follows:

𝑣𝑎𝑟(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑)=𝑣𝑎𝑟(𝑡𝑟𝑢𝑒)+𝑣𝑎𝑟(𝑟𝑎𝑛𝑑𝑜𝑚)

We can then calculate var(random) as follows, where n is the number of games played. The more games that are played, the smaller that var(random) becomes, and, conversely, with a smaller sample, var(random) will be larger.

𝑣𝑎𝑟(𝑟𝑎𝑛𝑑𝑜𝑚)=𝑠𝑞𝑟𝑡(0.5∗0.5𝑛)

Using a large enough sample of data (in our case the results of a total of 6 splits of play) we can can calculate var(observed) by just taking the variance in the observed records over that period and using that data we can solve for var(true).

𝑣𝑎𝑟(𝑡𝑟𝑢𝑒)=𝑣𝑎𝑟(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑)−𝑣𝑎𝑟(𝑟𝑎𝑛𝑑𝑜𝑚)

To figure out when a teams record is half skill and half luck, all we have to do is set var(random) equal to var(true). Then we solve for the number of games (n) to see where that is. This gives us the equation below.

𝑏𝑟𝑒𝑎𝑘𝑝𝑜𝑖𝑛𝑡=0.25𝑣𝑎𝑟(𝑡𝑟𝑢𝑒)2

Then, plugging in our calculated value of var(true) we find the breakeven point is slightly over 16 games.

The Results

So it takes 16 games for a team’s record to be half luck and half skill, but what does that mean? The easiest way to understand it is to put it in the context of other professional leagues. Thanks to the work of Neil Paine at 538, we know the comparable number of games (i.e. the breakeven point) for the NFL is 11, for the NBA it’s 12, and for MLB it is 67. That situates League of Legends right in the centre of these sports – slightly more random than basketball and football, but significantly more skill-expressive than baseball.

LoL Football Basketball Baseball
Breakeven Point 16 11 12 67
Season Length 18 16 82 162

The LCS and LEC splits last only 2 more games after hitting the breakeven point, by far the fewest of any league shown.

What should we do about this?

Before reading any meaning into these results, it’s important to contextualize them. League of Legends as a game suffers from more structural randomness than other sports because the game itself changes over time and those changes can benefit or hurt individual teams.

It seems fairly clear that the length of each split is too short to truly tell the skill of teams. While it would likely not be reasonable to play the same number of games that the NBA plays, to even reach the same level of skill expression as the NFL has would require at least a half dozen more games.

One obvious solution to this problem would be – instead of increasing the number of games in a split – to eliminate splits entirely and have one combined season lasting 36 games. This again has advantages and disadvantages from a broadcasting standpoint but it would be effective in reducing the impact of luck and increasing the importance of skill in the standings.

Another solution might be to switch from the best of one format that both leagues under discussion use and instead play best of threes like the LCK and LPL play. This begs the obvious question of how that change would impact skill expression and one that could be investigated in exactly the same way as this in the future.

Either way, it seems obvious that there is a need for more games in the LCS and LEC to truly make sure the best teams can rise to the top.

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