Mapwide resources: Gold and XP

tl;dr Gold appears normally distributed (modulo surrender), and data about xp is a bit hard to access at the moment.

A discussion on twitter this week got me wondering how much gold and xp teams earn. You will remember that it is the official LeagueMath.com position that League of Legends is—in fact—a team game. As is the case when I get to wondering, I immediately dove in to my treasure trove of match data to see what I could find.

Such an open-ended question is bound to have many avenues to explore, so I will begin with the first ideas that came to mind.

I looked at four basic ideas:

1. How much gold does a team earn in any given game?
2. How about gold per minute for a team in a game?
3. How much xp does a team earn in any given game?
4. How about xp per minute for a team in a game?

The interest of these particular statistics can be increased by splitting the data out by league (Bronze, Silver, Gold, Platinum, Diamond, Master, Challenger), and comparing winning and losing teams. That way, we can begin to point at how player skill translates into earning resources and winning games.

The histograms in this post draw data from 1,857,008 recent NA ranked solo-queue matches from the excellent Riot data API. These matches were played by players of all skill levels on patches 5.3-5.11. Now we dispense with further ado.

This first set of charts shows (per league) how much gold is earned by a team over the course of an entire game. On the left is gold earned by winning teams, and on the right is gold earned by losing teams.

There is so much that can be said about a set of charts like this. I invite you to take time and consider them for yourself. But, here are some of my initial thoughts:

• In every league, teams that win typically earn more than 60,000 gold in a game, and teams that lose do not.
• The asymmetry in the left half of most of these plots is likely driven by the game's surrender mechanic. Because teams cannot forfeit before twenty minutes, a game is much more likely to end just after 20 minutes than, say, at 19 minutes.
• As players skill up, they tend to win and lose with slightly less gold. This makes sense in terms of an earlier finding that better players play shorter matches.

I want to move on now to today's first look at differences.

These charts show (again, per league) the gold difference between teams at the end of the game. That is, the gold earned by the winning team minus the gold earned by the losing team.

Again, a lot to think about here, but I have a few quick thoughts:

• Most winning teams have more than 10,000 more gold than their opponents.
• The vertical line in each plot represents a tie (equal gold). Few teams win when they are behind in gold, and as players skill up even fewer teams trailing in gold win.
• The plots also appear to be 'squeezed' horizontally as players skill up. This means that there is less variance in the difference in gold between winning and losing teams in more competitive games.

In these first two sets of charts there is a conflating factor that is unfortunately ignored. Namely, there is no control for varying game length. To address this, we can look at similar charts for gold/min.

These charts show (per league) the average gold earned per minute for winning and losing teams.

Mmm, nice. My thoughts:

• Losing teams tend to earn about 1,500 gold per minute, and winning teams shade more toward 2,000 gold per minute.
• Higher skill players earn more gold per minute both in victory and defeat.
• Anything below 1,500 gold per minute is almost certainly a loss; and it looks like it is hard to lose if your team is exceeding 2,000 gold a minute.

As above, we can take the difference between these pairs.

This set of charts shows (again, per league) the difference in gold earned per minute between winning and losing teams. That is, winning gold/min minus losing gold/min.

Again here, the vertical line on each chart is the point of a tie (winning and losing teams have equal gold/min). The area under each curve to the left of that line is the fraction of games won by the team earning less gold/min. That fraction is tiny.

I also notice here that the gold/min discrepancies are growing as players skill up. Even against equally ranked opponents, better players do better at creating an advantage for their team.

There is, extremely roughly, about 600 gold/min of lane creep spawned by each team (100g/lane every 30s). That is completely insufficient to create the differences we are seeing here in every league. Kills, Baron, and jungle monsters must play a large role. The calculation thereof is left as an exercise for a future post.

Now, to move on to xp.

Edit: I had many more histograms here, with similar analysis to the above but for xp instead of gold. Unfortunately, those charts were wrong; and I have removed them to avoid spreading misleading information.

There was a problem with the data acquisition. And sadly, there is currently no way to get the correct experience data given how I am using the Riot API.

This type of analysis of experience will just have to wait.

If you are reading this now, you are hopefully happy with what we learned about the distribution of gold earned across leagues for winning and losing teams. You are probably also at least mildly disappointed that the promised xp analysis is missing. Take it from me, the defect in xp data acquisition made the deleted plots worse than useless.

I look forward to finding a way to measure experience earned correctly and revisiting this interesting topic.

I am surprised at how narrow the gap is between bronze and diamond in terms of resources earned both per minute and over the course of an entire game. What dependence relation is there here (if any) between resources earned and APM (actions per minute)?

It is worth mentioning that this line of analysis could also be split again along many other dimensions, like team composition, lanes, items, champion tags (tank, assassin, marksman, ...), etc... Collecting lots of resources correlates well with winning, but resources are not collected in a vacuum.

Okay, maybe head back to the index and find an article to read that has not had its second half redacted due to bugs in data acquisition. Then go ahead an subscribe to the rss feed and follow me on twitter. Those are the best way to find out immediately when future articles go live.

A Möbius strip has only one edge and only one side. League and math go together just as inseparably. In three dimensions, what is a side without an edge? Likewise, what is league without LeagueMath.com?

Only my ego was harmed in the making and eventual deletion of the second half of this article.

8)

Peace.