Race to the Finish Line: Earth Spirit vs Puck

There were a lot of wild plays at the Chongqing Major, but none so wacky as GH’s Earth Spirit embarking on The Great Escape during Liquid’s match against Vici Gaming.



As you can see GH forced Vici to keep chasing him all the way across the map and while Ori eventually caught him, it made us wonder, “Who would win in a race between Puck and Earth Spirit?” Let’s start by setting some parameters:

• The heroes will be in the same state they were in the clip. That means the same items, levels, and talents.
  
• The distance for the race will be 18000 units. This is roughly the same distance as the entire bottom lane, from the Radiant to Dire Tier 3 Towers.
  
• All inputs will be instant and perfect, for example Puck will always reach the maximum possible distance with Illusory Orb.

With the ground rules set let’s look at the relevant stats and abilities for each hero.

Earth Spirit's Items		Puck's Items

Starting with Earth Spirit, with Tranquil Boots he can move at 366 units per second and can use Rolling Boulder to cover 1600 units (using a Stone Remnant) or 800 units (not using a Stone Remnant) in 1.6 seconds. There are primarily two limiting factors for Rolling Boulder, the cooldown (a very short 4 seconds) and the number of Stone Remnants that Earth Spirit has available. Earth Spirit starts with 7 charges of Stone Remnant and regains one charge every 30 seconds.



Meanwhile Puck has 367 movespeed and has access to both Blink Dagger and Illusory Orb. An important note is that in this scenario Puck has taken his level 20 talent for 40% increased distance and speed on Illusory Orb. This means that he covers 1200 units instantly with Blink Dagger and another 2730 units over 2.995 seconds with Illusory Orb. Blink Dagger has a cooldown of 15 seconds while Illusory Orb’s cooldown is only 10 seconds. Thanks to his Eul’s Scepter, Puck has enough Mana Regen to cast Illusory Orb infinitely with its 10 second cooldown. This means that the only limiting factor to Puck’s movement capabilities are his cooldowns.



Since these heroes have such close movespeeds and great movement abilities, the abilities will entirely determine the outcome of the race. With that in mind let’s look at what the ability usage will look like for each hero.



We can see by comparing these graphs just how significant the cooldowns are in this scenario. The fact that Earth Spirit can get two Rolling Boulders for each Illusory Orb is worrisome enough for Puck, and that’s before accounting for the fact that Rolling Boulder both moves faster and takes less time than Illusory Orb. Blink Dagger’s long cooldown might mean that Puck can’t overcome Earth Spirit’s low cooldown advantage.

So what would this actually look like? Let’s take a look at what exactly Puck and Earth Spirit racing through their abilities would look like. This image shows about how far each hero would make it in around 6 to 8 seconds.



With this graphic we can see just how much farther Puck makes it with his first use of his rotation. This also means that when the cooldowns of both Puck’s Blink Dagger and Illusory Orb line up, he will either overtake Earth Spirit or extend his lead further.

So we’ve looked at the abilities, the cooldowns, the distances. Now all that’s left is to see who actually wins the race.





What a race it ends up being! It’s hard to tell from the graph just how close it is, but Puck ends up winning the race by 0.238 seconds! That’s less than a quarter of a second difference after racing across the entire map. An amazingly close race considering such a long distance. This becomes even more impressive upon realizing that Earth Spirit manages to finish the race just before running out of Stone Remnants. It’s hard to tell from the graph, but Earth Spirit’s last roll actually doesn’t use a Stone Remnant as he’s already run out, meaning that his roll speed has been cut in half (down to 800 units per roll instead of 1600). This means that if the race were to continue past the 30 second mark, Puck would blow Earth Spirit out of the water. By our calculations, Puck is already 3000 units ahead of Earth Spirit by the 45 second mark.

So it looks like GH doesn’t have too much to be worried about, it turns out that he did very well in a race that he was never meant to win.