Removing the Winning Bias from GPM Stats

Last updated 2 years ago


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Published on 2014-12-16 20:33:50

Why is Gold Important

Of all the skills Smite players utilize in game, the ability to generate gold efficiently may be the most important. After all, if two similar players duke it out, the one with the better items will have a clear advantage, and the only way to get those items is to buy them with gold. Not only useful for buying items, gold can also be used to gauge a player’s performance. Almost everything you can do to help your team gives bonus gold. Clear the lane? Have some gold. Knock down a tower? Have some gold. Secure the Fire Giant buff? Have even more gold. That is why this week we will be looking at how well each of the SPL players did at increasing their wealth, specifically their Gold Per Minute (GPM) statistic, during the regular season.

The Problem

There’s a major problem that comes up when you try to compare players using GPM: players on winning teams have bloated statistics. For example, Snoopy averaged 510 GPM this season while Zapman sits at only 475 GPM. You might be tempted to say that Snoopy is better at generating gold than Zapman based on these stats, but there’s one little issue with that statement: Snoopy was on a team that posted a 17-3 record, 6 more wins than Zapman’s Dignitas. Perhaps if Zapman were on a team that won as often as Cognitive Red, his GPM would be similar to Snoopy’s, maybe even better.

Generally speaking, gold leads in MOBAs are part of a positive-feedback system. The team with a gold lead can exert more pressure and clear more neutral camps, which in turn generates an even larger gold lead. This gold advantage cycle continues until there is enough of an item lead to destroy a phoenix or two and take out the Titan. Even games between closely matched teams tend to feature this sort of behaviour with gold leads. There are certainly comebacks, and occasionally teams will even win while still behind on gold, but these situations do not happen on a regular basis. It is therefore common for the winning team, and the players on that team, to have a higher GPM. This is what we call “winning bias.”

The Solution

So how do we remove winning bias? One way to do this is to see what GPM we would expect an average player to achieve with any given record, then compare this to the player of interest’s GPM. I call this value Expected GPM, and because Smite’s players tend to fall into very distinct roles I go a step further and calculate a different Expected GPM for each position. A comparison of a player’s Expected GPM and Actual GPM will give us some idea of how well the player faired. We’ve now got a ratio that we can use to compare any two players at a given position. However, most people might still want a GPM number to make comparisons. To do this, I simply multiplied the ratio of Actual GPM to Expected GPM by the average GPM for that role. Voila! A GPM stat that eliminates winning bias.

So now that I’m through with all the explanation, here are the charts that compare the GPM stats of EU SPL and NA SPL players this season:

EU SPL GPM charts

NA SPL GPM charts

A few quick clarifications. I only displayed the stats for players who played a position more than 10 games, so you won’t see Zimpstar’s stats as ADC or emilitoo as a solo laner. The stats of players with too few games are still counted toward the average GPM, Winning GPM, and Losing GPM of their role. If a player switched teams (e.g. Ninjabobat) midway through the season, only the original team is denoted though all stats from the whole season are included. I also did not count any games that were forfeited for non-gameplay reasons (e.g. the game in which Cognitive Red was disqualified for a combat pause) as the results of these games were not decided by which team knocked out the Titan first.

For this particular article, I wanted to leave the real insights up to you, the reader. However there are a few crucial points I took away from these stats. First, most players seem to be collecting gold at a similar rate. In EU, the biggest differences are in the solo lane where Psiyo and enQu lead the way with Xaliea not far behind. Mid, Jungle, and ADC players all stayed within about 2.5% of their expected GPM. I understand this for Mid and ADC, who typically find themselves clearing lanes and staying safe, but the fact that all the Junglers were also this close surprised me. The story in NA is a little different. Almost every role other than Jungle featured a 5.0% or greater spread between the top and bottom farmers. Of particular note is the consistency of Lassiz in the jungle; while he had the lowest winning GPM, he also had the highest losing GPM, meaning that Lassiz could find farm even in losing situations.

I also made a tab for full team stats. What stood out to me here is the consistency of teams getting 2050 to 2080 GPM in their losing efforts. Only Fnatic and Cognitive Red posted an average losing GPM below 2000 GPM. With the highest winning GPM and the lowest losing GPM, I feel fairly safe in saying that FNC and COGR were the most snowbally teams in the EU and NA, respectively. And just like their Jungler, Dignitas posted the lowest winning GPM but also the highest winning GPM out of either region. This means that Dignitas is one of the most consistent teams when it comes to farming.

As I continue to push toward more fair player comparison metrics, I am always finding new snags that upset the balance. If you go to the GPM vs Game Length tab, you will see that winning players have higher GPMs in short games than in long games. This is to be expected as winning the game later means gold gained from taking towers is stretched over a longer period, leading to lower GPM values. In the future, I would like to go a step further and correct for game length as well. However, there just aren’t enough games in a season to fill up the timeline and create an accurate best fit line for each position.

You’ve been reading jhuns, tune in next time for more mind-blowing stats!

17 December, 2014