How much do coins help?

Question

As mentioned in an another Q&A, in Mario Kart 8 coins help to increase your speed. However I'd like to take this a level deeper and ask: How much do they help? and in what manner?

For example, suppose I have a base speed of 3.5, what would my speed be at 10 coins? How much did each individual coin contribute? and did they all contribute equally, or was there a scaling pattern?

Answer 1

Interesting forum post by Nefos @ http://mkboards.com/forums/threads/coin-count-and-performance.8777/

He's done a fair amount of research. Doesn't seem to have a corresponding figure to the speed values used in the game though.

Data from post(s)

I present you evidence of the efficiency of 10 coins against none. I started clocking in 2 specific spots in MKS. The pair 1 shows the spots on the tests with 10 coins. The pair 2 shows the spots on the tests with no coins. They are pretty much the same. The combo I used is Mach 8 + GLA Wheels + Parafoil

So, clocking frame by frame (in slow motion) gave me the following results (I recorded on 30fps): Pair 1 (10 coins): start: 15.90s end: 67.50 interval: 51.60s -> 1548 frames

Pair 2 (0 coins): start: 90.40s end: 144.86666666...s interval: 54.46666666...s -> 1634 frames

So, with 5.25 speed, the increase of speed is of (1634 / 1548 - 1) * 100 = 5.5555555%, or 1/18 faster. This result is way different from my older test. Considering I did that one with a 4.5 speed combo and the relative difference was bigger, it's safe to say that the coins increase speed in the same rate regardless of speed. Also, assuming each coin gives the same amount of speed, we can obviously conclude each coin will contribute to 1/10 of that value.

Now, what does this means in terms of the speed factor used in the game? No idea. I'll have to compare different speed combos and normalize the result to those standards and then we'll be able to see the accurate increase in speed that the coins give.

Hmm, for those standards, an increase of 0.5555...% (1 coin) for a 5.25 combo will be faster by 60 - 60 / (1 + 1/180) =~ 0.3315 seconds, or 3.315 seconds with 10 coins. But actually, there are 2 ways of doing this, either considering the slower took 60 seconds or the faster. So it could also be 60 * (1 + 1/180) - 60 = 1/3 of a second, or 3 and 1/3 of a second with 10 coins.

I'll take that pyro used the second, so I'll calculate the increase of speed following that number: 60 * (1 + x) - 60 = 1/4 x = 1/240

Assuming 10 coins gives the same amount of boost regardless of the base speed, it's possible to calculate the difference of speed from a 5.25 to a 5.75 combo, as the following: (CB -> 1 Coin Boost; FTFSP -> 5.25 Speed; FSFSP -> 5.75 Speed) CB = FTFSP * 1/180 CB = FSFSP * 1/240 FTFSP * 1/180 = FSFSP * 1/240 FTFSP = 3/4 FSFSP

But that would mean 5.75 is 33% faster than 5.25, which doesn't make any sense. The amount given by coins to a 5.75 combo should be greater than that.

I found the following times: 4.75 (0 coins): 2219 frames (corrected from 2220) 5.25 (0 coins): 2206 frames 5.25 (10 coins): 2082 frames 5.75 (0 coins): 2193 frames 5.75 (5 coins): 2131 frames (corrected from 2134) 5.75 (10 coins): 2069 frames (corrected from 2071)

It's clear that the difference between speed tiers are constant: 0 coins: 4.75 -(+13 frames)-> 5.25 -(+13 frames)-> 5.75

And that the difference remains the same regardless of the coins, making the coin boost constant: 10 coins: 5.25 -(+13 frames)-> 5.75

And also that that each coin adds the same amount of boost: 0 coins -(+62 frames)-> 5 coins -(+62 frames)-> 10 coins

Now, to determine how much a coin improve considering speed tiers we should get the difference in frames from 10 coins to 0 and divide by the difference between 2 tiers, let's say between 4.75 and 5.75: 124 / 26 =~ 4.769 In other words, 10 coins would have an impact in the speed tier of about 4.769 times the difference between tier 4.75 and tier 5.75, or simply 4.769. Which means that a combo with speed 1 with 10 coins should have about the same speed of a top speed tier without coins, 5.769.

But then again, there were a lot of inaccuracies in the measurings, so my opinion is that the correct numbers could have been 125 and 25 instead of 124 and 26 (I don't think Nintendo would make the numbers so incompatible, it's probably simpler to use a generic speed boost and it's multiples for anything, this case being the generic speed boost 0.25). That would result in a coin causing an increase of exactly 0.5 in speed, meaning that you'll only need 1 coin with a 5.25 combo to have the same speed of a 5.75 combo.

Oh, and every coin have an impact of about .350 per minute, at least in a straight line.