Back Timers and Power Spikes

15 min readSep 13, 2017

In our first article, we saw how gold and XP differences could help define the strengths and weaknesses of each role. In our second article, we focused on the Jungler, and tried to understand how Junglers used their innate early game advantage to apply pressure all over the map. In our third article, we left the early game to focus on the mid game and worked out what teams tended to focus in priority. We also saw that the patterns of the Jungler in the early game had effects onto which objective was focused.

In this article, we’ll go back to the early game and take a more general look at the strengths and weaknesses of each role, rather than just the Jungler. To do so, we’ll take a look into when players usually do their backs, depending on their role, and see what that entails in terms of itemization and power spikes.

Caveats

Most of what will be talked about in this article is stuff most people already intuitively know. This article just reinforces this intuition by putting numbers on it.

The data we are using is from high ELO players (dia2+), who *may* be more efficient and more knowledgeable about the game than the average player.

This is aggregated data. The findings presented in this article are not to be taken as gospel, but rather as a general rule of thumb.

TL;DR

Toplaners back around 4:45, then around 8:20 and then around 12:00
Midlaners back around 4:45, then around 8:00, and then around 11:00
Botlaners back around 5:10, then around 9:00, and then around 12:45
Junglers back around 4:30, then around 7:30, and then around 11:15
Lanes are 5.5–9% more likely to stay in lane if there’s a cannon in the wave.
Toplaners have around 1400 total gold on their first back, 2600 total gold on their second, and around 4000 on their third back. These values include the 500 gold from the start.
Midlaners have around 1450 total gold on their 1st back, 2600 total gold on their 2nd, and around 3700 on their 3rd. These values include the 500 gold from the start.
ADCs have around 1650 total gold on their 1st back, 3000 total gold on their 2nd, and around 4500 on their 3rd. These values include the 500 gold from the start.
Supports have around 1200 total gold on their first back, 2100 total gold on their 2nd, and around 3200 on their 3rd. These values include the 500 gold from the start.
Junglers have around 1500 total gold on their first back, 2450 total gold on their 2nd, and around 3800 on their 3rd. These values include the 500 gold from the start.
ADCs must stay 1–2 wave longer in lane to get a B.F. sword but usually have enough for zeal or vamp scepter + boots.

When do players back?

This is actually a pretty difficult question to answer. There’s no event called “PLAYER_RECALL” or similar in the data that Riot provides to 3rd party. This means that there’s no clear way to know when a player goes back to base. So how does one look for something one can’t see?

Correlated Signals

When trying to find something you have no way of measuring directly, you have to look at measurable events that only appear when that event occurs. For instance, astronomers can’t really see planets orbiting far away stars, they’re just too far away! However, by looking at how brightly a star shines over a period of time, if they see small regular variations over years, they can guess that this star has a planet orbiting around it and that it’s blocking the part of the light of the star.

Another example is Mendeleev, who was particularly good at inferring the nature of matter. The guy predicted the existence, as well the mass and behavior of certain atoms that were undiscovered at the time, just because otherwise there were gaps in the table of elements he was constructing.

Finally, most people are using inferred signals every day: When you’re looking for someone that could be in multiple places, you won’t look for them in places that are not lit, because no lights usually mean nobody is there. Or when you cook pasta, you don’t dip your hand in the water to test if it’s hot enough, rather you wait for the moment when bubbles are forming in the water.

Recall Correlated Signals

In League of Legends, there are also related signals, and maybe that in the subset of events that we have access to, there are types of events that can be used to infer the occurrence of the missing “recall” event. So what are the events we have access to? Well, there’s champion kills, monster kills, tower kills, wards placed, ward kills, item purchases and sells, and skill level up. Out of this small list of events, there’s only one type of events that can help us model recalls, and that’s item purchases. Indeed, the only place where people can buy items is at the base and using the reasonable assumption that people back using recall, and don’t like to sit in base doing nothing, we can suppose that players do their purchases in the next dozen of seconds after their back or so.

Looking at item purchases as a way to look into when players go back to base is probably a good place to start. However, there is a possible issue with this. Some players may back and not buy anything. This is a valid point of criticism of this model, and we have no way of proving that there is a bias, but we can argue that this almost never happens in the early game, as players are likely to buy consumables to help them last during the laning phase. So the number of recalls that we’re missing by looking at item purchases should be fairly small. A second argument to justify the validity of item purchases as recalls can be that even if the number of no-buy recalls is sufficiently large to matter, there may not be sufficiently many differences in terms of behavior compared to buy-recalls so that the overall recall behavior is still very similar to the one from buy-recalls.

For the rest of this article, we’ll assume a 15 second lag between recall and purchase. This is completely arbitrary.

Multiple Purchases for a single Recall

Another issue that crops up when using Item Purchases to model backs is that players more often than not buy more than just one item when they go back to base. This means that you cannot just look at the item purchases dataset directly, but you first need to group item purchases together depending on how closely they happened in time. We decided to choose a 45s window for grouping purchases together. This means that we only consider purchases that are at least 45s apart. For instance, if we have the following purchases events happening at 4:45, 4:50, 5:05 and 6:40, we’ll discard the 4:50 and 5:05 events as part of the same recall as the one for 4:45. (This is trickier to implement than it looks).

When do Players Back?

We’ll start our analysis by taking a look at how item purchases evolve over time by lane.

This is not really looking good. Apart from the Jungler role, which has a much higher amount item purchases around the 4–5:30 minute, we don’t really see much differences between lanes. By looking carefully, we can probably conjecture that the botlane is the last to do its first back, but that’s pretty much it in terms of first back analysis. We also notice a periodicity of about 1:30, which could indicate how often players back. However, this can also be explained by the fact that the cannon minion spawns every 90 seconds. And having a 90-second periodicity for the backs would clash with our previous estimation using the average current gold in the pocket of a player, which put it at around 3:30.

Cannon Waves

Cannon waves spawn every 3 waves, which makes the second cannon wave arrive mid around 4:05, and slightly later bot and top (~4:20). This corresponds to a noticeable dip in item purchases in the 4:30–5:00 window for every lane, which suggests fewer backs in the 10–15s prior, with an increase in backs on the next wave. This pattern repeats itself over for the next 4 and a half minutes, with fairly identical dips. We can better deconstruct this pattern by analyzing how much of the backs on cannon waves are transferred to the next wave and the previous wave.

It seems that on average, from 5.5 to 9% of backs take into account the presence of a cannon wave. However, the behavior does not look like players realize that there’s a cannon in the wave and decide to stay longer, rather that they know when cannon minion waves are and pace their backs accordingly. Indeed, if this behavior was purely reactive, we’d see the backs being transferred onto the next wave, with little of it being transferred to the wave before cannon.

Now that we’ve established the impact of cannon waves on backs, we’ll first try to see what it looks like when the 90-second periodicity is smoothed out, as this should bring out the underlying signal and help us understand our graph a little more.

Decomposing the signal — First Back

Alright, this didn’t get us very far. Maybe the approach is not the correct one. Instead of looking at all backs, let’s focus on the first back instead. When does the first back happen? Well, we don’t know. However, what we know for sure is that the first back should represent nearly all of the beginning of our curve representing all backs, as you can’t really do your second back before you do your first. So, let’s zoom in.

Wow, these curves actually look an awful lot like the left side of Gaussian curves. This is great news because it actually makes sense! If people usually go back around a certain time, they won’t back exactly at that precise moment every game, rather, in some game they’ll go back slightly early, in some other games, they’ll go back slightly later, and in very few games they’ll stay in lane for a very long time, or go back almost immediately. This means that we can model our first back as normal distribution centered around the average time for the first back.

Decomposing the signal — Jungler

We’ll start with analyzing the beginning of the Jungler item purchase curve. As we’ve seen previously, we can model the first back with a normal distribution, so let’s plot how this distribution fits into the total backs over time.

Alright, this is pretty cool. We have a clear distribution for the first back, we can get the average time of the back, as well as the standard deviation around that average. Now what? How do we go from there to finding when the second back happens? Well, we can start by removing the backs that were attributed to the first back from the total backs and see what our new curve looks like.

We know for sure that the beginning of this curve should be composed almost only of second backs, as we removed the first backs, and you can’t do your third back before doing your second. We also see that the beginning of the curve looks a lot like a Gaussian curve. This is all starting to sound pretty familiar! It’s what we did for the first back. So let’s do exactly like we did for the first back.

As you may have already guessed, we can repeat our process for the 3rd back, and so on. So let’s do just that.

This is incredible! Just to make you realize how awesome that is. We went from that pretty unhelpful graph to this amazing decomposition:

It’s like black magic! We basically take what is a bump followed by a nearly straight line and transform it into a set of nice curves, just because the bump looked like a Gaussian curve. How insane is that! This is basically saying “give me a straight line and I’ll tell you when people back”. Maths is just fucking amazing.

Decomposing the signal — Bot

What we did with the Jungler, we can do with the ADC, Mid, and Top. I’ll spare you the details and give you the 2 core charts instead.

Decomposing the signal — Mid

Decomposing the Signal — Top

Back Timers

Alright, we now have beautiful curves for every back of every lane, which is pretty cool in its own way. However, this isn’t exactly what interests us. What we want are cold hard numbers that we can use and not just look at. The following table describes the average time at which each lane usually backs and also includes the standard deviation from the mean for each back.

From the point of view of Junglers, this provides a lot of information into when lanes are weak and strong. Indeed, a lane that just backed and purchased items is stronger than one that did not. Additionally, a lane that is about to back is likely to be low in HP and Mana. Therefore, as a jungler, you should probably aim at ganking lanes right before they attempt to back. Past level 6, this strategy can also apply to roaming midlaners. So what this table is actually not just a table of when players go back to base, but also a table of when each lane is vulnerable or strong. Using this table, we should probably be able to construct ganking pattern that leverages these weaknesses and strengths.

We can also see that our previous estimate of about 3:30 minutes spent in lane between backs was actually pretty good! This general rule of thumb is also something that can be used to track the moment a player is weak or strong. Indeed, imagine botlane does a late first back, let’s say around 6:00. Their next back may not be centered around 9:00, but rather around 9:45, depending on whether they want to match their opponents’ back or prefer to have a sizable amount of gold before going back.

Purchasing Power

Another information we can derive from this table is the purchasing power, a player has when he backs. We define the purchasing power as how much gold a player has earned at that point in time, rather than how much gold he has on himself at the moment of the back, as this value is dependent on the build order as well as when previous backs happened and is therefore unreliable compared to a simple “Total Gold” metric. Note that this table is still aggregated data, which means that the average gold values account for players that got kills before their back, and is, therefore, a bit higher than the gold these roles usually have when they don’t get kills.

This gold table should be extremely important when trying to evaluate a build order, as backs constrain greatly which items a player has for the next few minutes. Indeed, imagine that you found out that a Bilgewater Cutlass start is the best start for Vayne. You’d still need to factor in the fact that it costs 1500 gold, on top of the 500 gold spent on a Doran + pot. That brings this start to 2000 gold, which is a pretty late first back. This means that if the other ADC backs as usual, he will have a 1k gold advantage over you until you yourself back. This means that, depending on the state of the wave, he can either freeze and zone you out, or push and set up a dive with the help of his Jungler; and what was supposed to be a great build, in theory, turns out to be painful to play in practice. And that’s without taking into account that this disadvantage will repeat itself until both sides backs at the same time, which could put the progress of the build in an awkward position. This does not mean that the build should be dismissed, but rather that certain build orders have price points that are not perfectly suited for the current meta, which can negatively impact the performance of the build, and that this should be taken into account when evaluating the quality of a build.

Another interesting observation we can make from this table is that more often than not, ADCs do not have enough gold for B.F. when they back, which could make AD reliant champions less appealing than their counterparts that work well with the cheaper Attack Speed items.

Finally, we can see that although Junglers are the first to back, they still hold a total gold advantage against solo laners for their first purchase.

The Ornn Factor

Riot recently revealed the next champion that will hit the Rift. His name is Ornn and what interests us here is his passive, Living Forge which states:

Ornn can spend gold to forge non-consumable items anywhere. […] Additionally, Ornn and each of his teammates can purchase MASTERWORK upgrades.

Some people have already done some analysis of the Masterwork part of the passive, which would make teams stronger in the late game, as players would get a higher slot efficiency. Most of these analyses were using something called the “gold value per stat point”, which states for instance that 1 AD is worth 35g, while 1AP is worth 21.75g. I outright reject the methodology used to calculate these values, and the concept of “gold efficiency” as it used right now, but I’ll expand on this in a future article, maybe.

What interests me in this passive is not really the Masterwork part, but rather the “purchase anywhere” part. In 4 seconds, Ornn can do what takes most people over 30 seconds, which is to back, buy and go back to lane. This gives Ornn a massive advantage in early game, most notably as a Jungler, as he can transform his gold advantage into an item advantage immediately before ganking. This passive moves all of his power spikes earlier, and could, therefore, increase his early ganks impact. Having an extra long sword before minute 4 is insanely strong, as this represents a buff of over 12–16% in auto attack damage at that point in time, depending on runes. On the other hand, having an extra cloth armor means an extra 15 armor at a time where it is standard to have around 30–40. However, this advantage is partially lost if Ornn does not act during this window of time, and stays in his jungle. All in all, this passive, combined with what we’ve learned in this article, suggests that Ornn could be the king of early ganks. It’s all guesswork, though, and I could very well be very wrong. This also does not take into account any of the other abilities of Ornn, which could be terrible for ganks, nor does it make any statement about Ornn’s ability to win games.

Conclusion

In our article about the early game focus of junglers on lanes, we’ve fleshed out some potential patterns Junglers follow in general. In this article, we’ve extracted when each role backs from relatively unhelpful data and saw when each lane was strongest and weakest in general. This, in turn, could help us find exploitable patterns that Junglers can abuse. We now have a lot of pieces that we can use to craft smart and efficient jungling patterns. There’s, however, one additional piece of information that we can use to measure the strengths and weaknesses of each lane, and that’s vision gaps.