League of Legends

Dr. Mundo Or: How I Learned to Stop Worrying and Surrender


Background

EDIT: This is targeted specifically at the Bronze division. There will be other studies for the other divisions. All commentary is aimed at Bronze, but is entirely based off of the data. I will be making other posts for the subsequent divisons. I started at the bottom and will be working my way up the ladder.

To pre-empt most of the concern, this is not a rage post; it's a data analysis series using the RiotAPI to pull game data and try to tease out how early game states affect end game win probabilities. This was done with one of two things in mind, 1) to better determine if my impulses about surrendering at 15+ were correct when games were significantly skewed, 2) try to determine the cutoffs for when games were winnable to a reasonable margin.

A few days ago I started using the Cassiopeia package for python along with direct calls to the RiotAPI to make data requests. The data I pulled for this came from 10 random summoners in Bronze 1. They were selected with a two criteria in mind: Must have played more than 100 games this season, their relative win/loss must be near within 5% of 50%. This was repeated three times for a total of 30 summoners. 20 games from each player were chosen creating a 600 game database with no shared games. In the future, this will be expanded to be a much larger database.

The majority of the work was data wrangling and cleaning. Currently there is a limitation to using the RiotAPI to determine gold per lane as there is a non-negligible amount of error in the lane data with top laners often being assigned jungle, as such that isn't an option.

I pulled the frame by frame (in the RiotAPI timeline) data to generate a minute by minute snapshot of the game along with some other general statistics. I looked at the game states with particular focus at 15 minutes and 20 minutes and the periods in between. Further I did general stat summaries for other game conditions like first baron, tower, and inhib.

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Data and Analysis

I took the data and calculated some features relative to gold state and then used that to segment game states. In particular, the gold differential at 15 and 20 minutes. I then used the differential in kills between blue and red to come up with a rough approximation of said gold differential. Everything was done in reference to blue. If there is a negative number it means that red is ahead in that category. The gold cutoffs for each team were baskets of:

  • 0-1000 gold
  • 1000-3000 gold
  • 3000-6000 gold
  • 6000-10000 gold

Blue Side

Gold Differential Win Rate @ 15 Win Rate @ 20 Kill Differential @15 Kill Differential @ 20 Occurance Percent @ 20
0-1000 48% 61.7% .18 .088 10%
1000-3000 67.6% 61.1% 2.5 2.5 10.5%
3000-6000 83.3% 78.1% 6.5 7.0 13.5%
6000-10000 100% 93.5% 10.45 11.65 13.8%

Red Side

Gold Differential Win Rate @ 15 Win Rate @ 20 Kill Differential @15 Kill Differential @ 20 Occurance Percent @ 20
0-1000 50% 40.9% -.25 -2.3 6.45%
1000-3000 61.1% 56.2% -2.5 -2.4 10.6%
3000-6000 84.0% 78.3% -5.6 -4.78 13.8%
6000-10000 92.3% 97.6% -10.4 -10.3 12.3%

It's immediately apparent that games which are relatively close in kills at 15 to 20 are entirely winnable and as such should not be surrendered. Also, these account for approximately 40% of all games you will play. The issue here is the final two categories. Together, they constitute over 55% of all games you will play in Bronze I. This means that you will either be given a free win or a free loss about 25% of all games you play.

This brings us to the question of should you ff or not when down by more than 7 kills at 15 minutes. Mathematically, yes. Average game time for the final two categories is about 30 minutes. If you leave the game at 20 minutes, and queue again, there is a greater than 70% chance you will be put into a game with an average chance of victory greater than 50% and a 25% chance of an almost guaranteed win. I am in the process of creating a modeler based off these probabilities to provide concrete examples of this cost benefit analysis.

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Myths

One of the biggest things I see is that at low elo, anyone can throw, and while that is true, it's an exceedingly low number of occurrences. I hear that late game teams scale, and while that is true, every champion in the game scales with gold. The main way to receive gold is via csing, and in bronze csing is almost non-existent. Average cs scores for games in the 40 minute range are routinely below 4-5 cs/m. As such most of the gold is coming from kills and assists which means that leads can get compounded very quickly.

Other metrics people use to determine if a game is "lost" are usually incorrect. If your team loses first baron first tower, you generally have a greater than 35% chance of winning. Though, if your team is the first to lose an inhib, your chance of victory plummets to 15%, but losing an inhib is generally a sign that things have gotten pretty bad for your team whereas losing a tower or baron are much less fatalistic.


Discussion and Limitations

One of the most difficult things in game is accurately determining the gold differential between the two teams. A tower down before 14 and a kill differential greater than 7 would probably be a good marker for a very losable game state. Kills spread out across the team will probably be more conducive to a comeback than most of the kills on one or two people. This is because, from the data, i've noticed that once a player has lots of kills it snowballs very quickly because of the emphasis on fighting and lack of emphasis on csing.

One of the interesting things is the distribution of game times. There are two gaussian distributions of game lengths, one centered around 25 minutes and another at 35 minutes. This probably results from objectives as elder will usually spawn at 35 if one team isn't stomping or fights around baron/dragon soul.

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Evenly matched games in bronze will tend to last a long time as there isn't the decisiveness to end them. This leads to very chaotic behavior later and so I did not attempt to model it or make any sort of statement regarding it.

I have not done anything to try and model team comp or CC abilities, and as such this is a more general study.


Going Forward

If people like this type of analysis i'll probably do the same thing for other divisions up to GM. I know people will either love this or will call me a quitter or that thinking about surrendering a match is a bad mindset, but the data doesn't lie. If you have the time to play several matches, just ffing and going next when you are almost guaranteed a loss is probably going to be more efficient to climbing than trying to duke it out over a statistically lost cause.

Source

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