Feet on the Mountain, Head in the Clouds: Comprehensive measurement of elemental drake value

Tim Sevenhuysen is the founder of OraclesElixir.com and Head of Esports Data Science for Esports One. He led Shadow.gg from 2017-19 and was Statistical Consultant for Fnatic in 2015.

I’ve investigated the relative value of different elemental drake types in the past, and the topic has continued to fascinate me as LoL has evolved over time, with both direct and indirect changes to the elemental drake buffs. With the development of new, more comprehensive LoL win probability models, which I’ve been building for Esports One, there’s a better toolset than ever for diving deeper into the elemental drake question.

Since Riot recently revealed that the dragon system is getting a big overhaul for 2020, there will never be a better time to share some findings about the current iteration of the system! In future, this will give us a comparison point, so we can conduct similar analysis on the new dragon system and see how much has changed.

The analysis below extends my previous work on the statistical value of elemental drakes. I’ve come away with the following main findings:

  • Mountain drakes are the only drake type to gain in value as more game time passes.
  • Infernal drakes have the most direct value at almost all stages of the game.
  • Cloud drakes start out as the most directly valuable type, but their value falls off more compared to infernals.
  • Ocean drakes have the least overall value, from the very start of the game onwards.

Details and discussion below!

Notes on Statistical Methods
Notes for Interpretation
Statistical Value of Elemental Drakes

Notes on Statistical Methods

The machine learning and statistical modeling underlying this analysis is proprietary for now, since it stems from work I’m doing for Esports One. I can’t go into too much detail about the machine learning techniques we’re applying, or the feature selection for the models, etc., but here are a few points of note.

The drake values reported below show the change in win probability when a team is assigned one more drake of each type while the rest of the model is held at “zero.” So it is the increased probability of victory when gold and all other objectives and factors in the model are equal.

The win probability models take a game state–for example, the gold difference between the two teams, the number of drakes held by each, the status of inhibitors and other major objectives, and so on–and calculate the probability of each team winning, based on historical data from pro LoL. The specific models that informed this post used pro data from Summer 2019.

Multivariate modeling “controls” for the relationships between the independent variables. That means that we don’t have to hand-wave about whether teams only kill cloud drakes while they have a gold lead (which would appear to inflate the statistical value of cloud drakes), or other questions about the effects of context on the drakes. Those kinds of factors can still have influence, but as a footnote rather than a primary discussion point. There is other important context that shapes our interpretations, which I’ll discuss next, but we’ve covered the most basic set of objections through multivariate statistics.

Notes for Interpretation

Before jumping into the direct statistical comparisons of dragons’ value in predicting game outcomes, it’s important to recognize that each dragon type expresses its value in different ways, depending on how much of the dragon’s value is inherent in its buff, and how much that value gets “siphoned off” into other predictors (specifically, gold).

At the most basic level, we can group the dragons into pairs: infernal and cloud drakes express the most direct value, while mountain and ocean drakes are more indirect, with a greater part of their value coming through the gold they generate. Another way to say it is that infernal and cloud drakes do more to imitate gold spent, while mountain and ocean drakes do more to generate gold.

Bear in mind: all four dragon types help teams generate more gold, and therefore have some of their value siphoned off! But that relationship is more pronounced for mountain and ocean drakes than it is for infernal and cloud drakes.

Let’s go ahead and look at the numbers for each dragon type and apply some sound theory to our interpretations.

Statistical Value of Elemental Drakes

The table below shows how much a team’s win probability increases (in percentage points) for holding +1 drake of each type at the given minute mark, with a comparison point at +1k gold for context.

We’ll first interpret the numbers for individual drake types, and then I have some thoughts on making comparisons, and specifically how we can benchmark the amount of gold a mountain drake has to help a team earn in order to be as valuable as an infernal drake.

Mountain Drake

As already noted, mountain drake is the only one where the value increases later in the game. The predictive power of every other dragon type falls off later in games, but mountain drakes become more and more influential as Baron Nashor, Inhibitors, and Elder Dragon begin to come into play.

In the first 20 minutes, though, mountain drakes come across as surprisingly low value. That’s because a mountain drake’s value comes from the objectives it enables you to secure that you would not have secured otherwise, either due to chipping down towers more quickly or having the confidence and kill speed to secure a Baron or future dragons. In other words, part of a mountain dragon’s value must be measured through the objectives it has helped, or will help, a team earn, rather than the inherent stats buff it provides.

In win probability models, that means that if we hold other factors steady (such as setting the gold difference to zero, as we’ve done in the table above), we will see a smaller effect from the mountain drake itself. If the mountain drake has helped the team earn an extra 1,000 gold, we won’t see that effect within the mountain drake—we’ll see it through the predictive power of the gold difference. And if we anticipate, statistically, that having a mountain drake is going to generate some amount of additional gold over the rest of the game, some of that value will be sucked into the gold difference metric, as well.

Another aspect of interpreting mountain drakes, as I’ve discussed before, is that a mountain drake buff can’t be brought to bear unless the team is in position to actually reach an objective they want to secure. This is a core piece of why I’ve always felt mountain drakes are overrated: they mostly benefit teams that are even or ahead in map control, and offer minimal comeback value.

All of this being said, it’s reasonable to assert that mountain drakes are “worth” more than the numbers in the table show. I don’t believe the hidden value can close the gap between mountain and infernal, but more on that later. We have to bear in mind that the higher complexity around measuring mountain drakes doesn’t mean there is no context for infernal or cloud drakes: the buffs from those drakes also help teams earn more gold, reducing their direct value by some amount. So while we shouldn’t undervalue mountain drakes based solely on the models below, we also shouldn’t overcompensate, either.

Ocean Drake

Ocean drakes, like mountain drakes, have more conditional value than inherent value. The reason pro teams are so deeply in love with first-spawn ocean drakes is that the health and mana regen allows them to win their lanes. With an ocean drake, every team member can cast their skills more freely to win damage trades or clear minion waves faster to gain more freedom of movement on the map, and they can stay in lane longer before having to recall. Winning your lane obviously generates gold and experience advantages, which leads to a better chance of winning. But if a team takes early ocean drakes and can’t leverage the regen into gold and xp, then the dragon itself provides very minimal value later in the game.

It’s not surprising that ocean drake has the lowest statistical value, but it’s somewhat surprising that the value of ocean drakes is so low pre-10:00. Possibly the ocean drake’s value is more heavily indexed into gold generation than even the mountain drake’s. Even so, we wouldn’t expect ocean drake to start out at the lowest value from the very earliest phase of the game. It’s entirely fair to argue that early-game ocean drakes are worth more than these stats suggest, due to indirect effects, but overall… ocean drakes suck.

Infernal and Cloud Drake

Infernal and cloud drakes are different than mountains and oceans: their value is more direct. These dragons directly increase the players’ strength levels in meaningful stat categories, making them more closely equivalent to holding more items, rather than being useful in obtaining more actual items. As I’ve noted, there are still indirect aspects, because a cloud drake speed buff might allow faster rotation between lanes to create a positional advantage that nets a tower kill, or the extra combat power of an infernal drake might scare off the opponent from a team fight, earning a free objective. Those gains are ultimately gold gains, similarly to how a mountain drake can lead to an extra tower or Baron kill.

While infernal and cloud drakes start out with very similar statistical value (cloud drake is even slightly higher!), infernal drakes hold their value better as time goes on. A likely explanation is that cloud drakes are highly beneficial for mid-game ganks, roams, and tempo plays. It’s similar to a mid laner or support buying Boots of Mobility: they do it so they can show up in another lane unexpectedly for a gank or a tower dive. By 30:00, the game is much more about positioning minion waves and vision to gain forward control, and less about making quick, decisive plays, so the map mobility aspect of cloud drake’s influence is reduced, and it becomes more about in-combat movement speed or sometimes pick plays onto side lanes.

Infernal drake’s value has never really been questioned. It is always highly influential, at any stage of the game.

Concluding Thoughts

There may not be anything earth-shattering in this analysis, but that’s partly because it’s an extension and improvement of past work rather than something completely novel.

It shouldn’t be a surprise that cloud drakes are much more valuable than some common narratives would have you believe. I actually believed cloud drakes were stronger than this final modeling has revealed, but I still feel they’re undervalued by a good portion of the community.

Mountain drakes have been overrated ever since elemental drakes were introduced, but they are also somewhat misunderstood. A mountain drake is an investment in the late game, but still primarily as a close-out mechanic rather than a comeback mechanic.

Infernal drakes are great.

Ocean drakes are not.

The changes coming for 2020 will be a fairly dramatic shift, and will require some changes to analysis in order to capture not only the number of drakes of each type a team has killed, but also whether or not the team has captured a Dragon Soul. Elder Dragon is being simplified, which will make modeling easier because we don’t have to try to account for the number of elemental drakes that are being empowered by the Elder Dragon.

It’s going to be an interesting new world. I’m looking forward to applying statistical analysis like this to help pro teams navigate the changes.

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