By quincy0191

Last time I attempted to answer a fairly fundamental question: what are the statistics that correlate most closely to a win? Put in more common terms, what numbers seem to be the most important when determining whether a team will win or not?

The answer was generally not hugely surprising, but it contained a few twists. If you haven’t read the article, I’ll play spoiler: GPM has a very high correlation with wins, XPM has a good correlation, K/D/A are all decent, and CK/CD are not good. So now let’s examine what inputs are most important in gold per minute in order to determine how players generate significant amounts of farm.

1. Experience per Minute (r value 0.92)
XPM correlates highly with GPM, but this is likely an instance where causality flows mostly in one direction, and it’s not the helpful one. No doubt players with a high experience gain will farm more easily as they have more powerful spells and additional stat gain at their disposal. But farming for gold naturally creates a lot of experience as a byproduct. It is worthwhile to note that high-farming heroes are generally a high level as well, but that statement is not exactly groundbreaking, nor is it very helpful.

2. Creep Kills (r value 0.69)
And all of a sudden CK is not only back, it’s second on the list. With wins, creep kills didn’t seem to make much of a difference, and in terms of team gold they don’t correlate very well (r value 0.32). That suggests that creep kills aren’t very important to how a team farms overall. But on an individual player basis, they are the most important thing.

Take a look at the scatter plot and trendline for CK and GPM

It’s mostly a mess of dots early on, but later the trend is a bit more visible, and the red dotted line represents a linear regression (an equation that predicts GPM given CK) clearly heading up. There are a few outliers, like Flensmeister’s 819 GPM performance with less than 100 CK, courtesy of a 22/1/39 line in just over 25 minutes against tUS.

Regardless, effective ricing seems to be the best way to accumulate a high GPM, rather than getting a gank-oriented hero and looking for pickoffs. Or maybe not, based on the next entry

3. Kills (r value 0.68)
Getting hero kills is nearly as effective in generating gold as getting a lot of creep kills. In fact, the difference between the two is just 0.015. For all practical purposes, kills are just as highly correlated with GPM as creep kills. That means we can run a multiple variable regression using K and CK on GPM to figure out how the two of them together explain gold gain.

Just using those statistics we get an r value of 0.78, suggesting that together they do a good job of predicting whether a player has good farm. The r2 value, a measure of how well the line fits, is 0.61 – K and CK explain about 61% of the variance in GPM. Considering those are just two stats, that is a pretty solid correlation. Looking at the K-GPM correlation graph we see something similar to the CK-GPM graph:

4. Creep Denies (r value 0.46)
This is an excellent lesson about the importance of not taking numbers as gospel. Sometimes you will run into weird stuff like the idea that creep denies correlate decently well with farm. Suddenly you’re out there denying every creep you can and expecting to have a high GPM. Well, this is likely coincidence. Or more accurately, players who get a lot of creep kills also deny fairly frequently because they’re more often in a position to do so. CD does correlate decently well with GPM, but that likely does not mean anything.

5. Deaths (r value -0.37)
It is important not to die if you want to maintain your farm. Not only does it prevent you from losing gold, but it represents lost time that could be spent killing heroes or creeps. However, it’s apparently not as critical as one might think. A correlation factor of -0.37 doesn’t really suggest that deaths will have a serious negative impact. They’re certainly not good, but they’re not the end of the world.

6. Assists (r value 0.24)
Here we have the reason why supporting in HoN right now seems like it’s an exercise in sadomasochism. There just isn’t enough gold in it for them. Assists simply do not do a great job of boosting GPM. But if you’re playing a support hero, this is where a lot of your farm is supposed to come from; you can’t take CK away from the carry, you can’t take hero kills away from the carry, you get a little bounty if you threw an autoattack or some spells. Clearly it’s not enough.

7. Time (r value 0.14)
Some people might consider this a surprise, but there’s a good reason for it: late-game, supports still don’t have very much farm. So whether it’s 15 minutes or an hour, you’re likely to have at least three or four heroes in the game around 150 GPM. As the game goes later carries do tend to pick their farm up, and on a team-wide basis there is a stronger relationship between GPM and time. So you should expect to see more efficient farming as the game goes on, with heroes more able to move between camps and lanes as well as clear them more quickly. But that doesn’t mean everyone benefits, and the growing discrepancy prevents a strong relationship between GPM and time.


Conclusion

You might notice that the top r value here of consequence is just 0.69. That is much smaller than the previous high between GPM and wins, 0.85. There’s a good reason for that: we’re missing some critical inputs to GPM. The most obvious among them is towers – I do not include tower kill numbers among my data, as there is no way to reliably get it short of watching the entire replay for every game. That is not always possible even if I wanted to do it, and it means there is a pretty significant source of gold missing.

The other issue is variance. Not all hero and creep kills are made the same – killing a Snotter or a Dragon Master both count as 1 CK, but there’s a pretty big gold gap between them. The same goes for hero kills. So it’s difficult to get the correlation values closer to 1, simply because there are some games where a player will kill a bunch of ancients and other games where a player will kill a bunch of easy camps.

Lastly, let’s use that multiple regression thing again to see how close we can get to fully explaining GPM. Using K/D/A and CK, the most sensible inputs, we achieve an r value of 0.91 and an r2 of 0.82 – those four statistics explain 82% of the variance in GPM, which means that collectively they’re pretty good at telling the story of how a player got their gold. But in all honesty they’re not as good as I expected; one would imagine that the primary inputs to GPM would predict more of the stat. It would appear that tower gold and particularly bounty variance play a larger role than one would initially assume. That does make sense; getting 600 gold for a hero kill instead of 300 is an entire minute of good farm. Still, we can say with a fair degree of confidence that GPM is mostly comprised of hero kills and creep kills, a conclusion that is probably not too shocking, but nice to see legitimized.