Quick Math on Movement Speed

FortniteBattleRoyale4 - Quick Math on Movement Speed

Hey guys, Whitesushi here. Almost a month ago, u/dervd made a video testing movement speed numbers in relation to actual in-game performance and concluded (quote)

  • MS seems to be capped via extremely high diminishing returns
  • Close to max MS is reachable via hoverboard or approx 50% MS increase
  • Running animation isn't however, the more movespeed you have the faster the animation it appears

He's almost right, in fact extremely accurate considering the approach he has taken. That said though, I was recently prompted to work out the math behind this mechanic so I would like to add-on to what dervd has discovered as well as to make the conclusion… well… more conclusive. Anyway, let's dive right in

The Method

Like all my math posts, our goal is to determine the formula behind our mechanic, which in this case happens to be movement speed. In order to do this, we need to figure out how movement speed bonus gets translated into actual movement speed in game. Luckily for us, the in-game user interface displays the tiles/second numbers and I was able to more or less confirm this was accurate since

  1. Tile/s displayed matched with my player movement across fixed number of tiles running off the in-game timer
  2. My conclusion was pretty much close to what dervd had determined

Next, we need to break down what exactly is tile/s or more specifically, what is one tile. I can't really remember where in the patch notes this was stated (it was quite a long time back) but the developers basically wrote that a tile in game is 512 units. As such, 1 tile/s essentially means that the player travels 512 units/s. Knowing that, we can then take a guess that the player's movement speed which is by default,

  • 410 for running
  • 550 for sprinting

has something to do with tile/s directly and well, we aren't wrong. If we just take 410/512 and 550/512, we will get 0.801 and 1.074 respectively which you will find rounds to 0.8 and 1.1 displayed in your UI. Once these are out of the way, we just had to determine the formula for bonus movement speed which happened to be

Final Tile/s = Base Movement Speed * ( 1 + Bonus Movement Speed ) / 512 

This formula was of course confirmed through a lengthy verification process where I plugged the formula against actual in game numbers at varying movement speed bonuses to see if they match up and guess what, they did.

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The Results

So what did I discover? Well for a start, I want you guys to look at and understand this table which also happens to be the single most important piece of information from this post. For those who don't really get what all the columns mean…

  • % Bonus : Percentage bonus movement speed total
  • Est. Move : Estimated movement speed according to formula
  • Act. Move : Actual movement speed taken from in-game UI

and of course the last 2 columns are basically just sprint speed instead of movement speed. As you can see, the numbers all add up and more importantly

  • Run (or as I call it move) speed caps out at 63% bonus which is 1.3 tiles/s
  • Sprint speed caps out at 77% bonus which is 1.9 tile/s
  • There isn't really any diminishing returns at all, it's just a hard cap

This cap is further supported by the down arrows displayed in the UI typically used for other stats when they are capped such as F.O.R.T. To put these numbers into perspective, most husks spawn 8 tiles away from the base. To cover a distance of 8 tiles, a player with capped sprint speed of 1.9 t/s will take 4.2s, 3s faster than another player at base sprint speed of 1.1 t/s.

Bonus Information

Did you guys honestly think that was it? Well, here's some other interesting bits of information I found.

  1. Even though Dire is supposed to have 85% movement speed bonus (10% Shinobi + 25% Perk + 50% Unique Perk), I believe he only receives 60% as shown by the in-game numbers of 1.3/1.7. His level 30 perk which was supposed to give an additional 50% bonus is instead replacing the base perk and only giving 50%, thus making it 60% total. This means that the hero, who can otherwise hit sprint speed cap on his own, isn't even able to hit the run speed cap.

  2. BluGlo pylons seem to give 15% movement speed after working backwards using the UI tile/s numbers after the pylon is active. Of course, I even tested this in conjunction with other movement speed bonuses to ensure rounding doesn't throw us off.

  3. Movement speed bonus on sword was throwing my numbers off a little especially running the Lead Sled which was capable of running 2 movement speed perks. I believe this is due to the bonus not actually being 5/7/10/12/14, but rather a decimal number that gets rounded off to them. It is highly like that a number between 2.25 and 2.37 was added to a base of 5 for each perk rarity.

  4. There is no zone downscaling for movement speed… (just in case anyone is wondering)

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Alright, so that's basically it. Hope this post has been helpful in assisting you better plan them movement speed shenanigans. Personally, I find it quite a shame that movement speed caps out in the first place although I must say it feels rather similar to how armour works in the sense that the perk is perfectly fine for regular use and only feels poor when overly and unnecessarily stacked. Feel free to discuss what you think about this movement speed cap in the comments below and or if I left out any bits of information you would like to add on.

TL;DR Run speed caps out at 63% while sprint speed caps out at 85%. Dire's perks are bugged, only giving 60% instead of intended 85% and movespeed pylon gives 15% movement speed.

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