I've always wondered this myself. I'm no genius or anything but I possibly could do it if given the time (or not). Tnosrac had a good answer and pointed out some facts that cleared things up. So for example (going off the assumption people gain what others lose) if you were in a room with five 9999 VR players and magically you could go over 9999 as well as winning over someone gives you +13, would 1st player gain 52, 2nd player 26, 3rd player 0, 4th player -26, and 5th -52? It seems inaccurate and scaled but is this what happens when you have a room of all equal vr? Or is there a much more complex system?
*sigh* The day a Funrooms VR system is the same as a WW's is the day we have all our answers.
I think I might have it. If you're not keen on long-winded mathematical explanations, skip to the bottom.
If I'm right in my guess that the formula for points exchange is exponential, then we get:
x = a e^(km)
where x = points exchanged; m = the margin between the two players (I'll assume that the higher rated player winning gives a negative margin) and a&k are both constants. e is Euler's number, (about 2.7)
Substituting in the case where both players are rated equally and exchanging 13 points, we get:
13 = a e^0
13 = a
Now comes the hard part. After searching youtube for a bit, I couldn't find many worldwide 1v1s, but I did find this one:
The problem here is their margin is fairly small, only +287. This might introduce some errors in the calculation of k. Anyway, substituting this into the equation gives:
15 = 13e^(287k)
If you rearrange this, you eventually get k being very very close to 1/2000, which is the value I've used from now on. Now to check this, I've used the same data as Yoshifan314, at 9:51 in Astro Star's video:
From this, we can see that before the race started, Skittles had margins of -37, -848, +196, +472, -2377, +472, -2000, -1976, +122, -1480, as you read down the results screen (remember, negative margins mean the higher rated player won). Putting all these numbers into the equation above yields (1 decimal place): 12.7, 8.5, 14.3, 16.5, 4.0, 16.5, 4.8, 4.8, 13.8, 6.2. These add up to 102.1, quite close to the true total of 107. Possibly, the error came from rounding, the fact that I could only find a race with a small margin to calculate k from.
Thus, I'd conclude that the VR exchange formula is very close to:
x = 13e^(m/2000)
Last edited by Tnosrac; 09-18-2011 at 09:23 AM.
Reason: Broken Spoilers
Just one question: The formula is x = 13e^(m/2000). Let's take the margin +472. So x = 13e^(472/2000), right? However, 13e^(472/2000) = 13e^(0.236) = 2.315. How did you get 16.5? Am I doing this wrong?
I uploaded some snapshots from some PROs I've beat months ago, take a look at my profile if you want to check them, and I brought some info.
I think that it's about this (because Nintendo doesn't have defined exact values to this):
5000 wins 300+, 9999 loses 200~400
9999 wins 0~7, 5000 loses abour 10~20
The loser loses not much, about 20
1 wins 600+, 9999 loses about 300
1 - Both 2nd and 3rd place loses VR, cause they lost for a 5000 player.
2 - Usually, if you're a 7500 and beats a 9999, you usually around 150~200.
3 - If you lose for a 5000 (without 9999 on your back), you lose about 80~140, but, if you lose for a 5000 with a 9999 on your back, then you'll lose around 20~50.
4 - If 1-point comes in 1st place by beating a 5000 and a 9999, he'll probably get a true VR Jackpot, winning around 500~900. Yes - he beat a 5000, but the 9999 was in last place, so this factor help noobs gaining VR if you get noob-raped.
The more complicated question:
It all depends of the bottom players' VR. If they have more, they'll give more for the 1st place (depending of his VR too - if he's a lucky 5000 that beat 11 9999's, he'll probably get around 500~600, while everyone in the rool will lose AT LEAST 300 VR).
Oddball ratings: 8454 vs 9361
Well, I'm not sure, but I think that it works that way:
1 - If the 8454 beats the 9361 real hardly, he'll porobably gain around 70~140, while the 9361 will lose around 100~150.
2 - It's quite confuse, but I could notice that another factor that affects your VR/BR earnings/losses is how you beat the other(s) player(s). For example: I'm a 5000. If I beat a 9999 like he was nothing (a big advantage, almost half track, for example), I'll gain 200~400 VR/BR, while he'll lose 300~500.
I think that the VR/BR results are quite predictable at all. It all depends of the players' ratings, how they win/lose, and for who they beat/for who they lose.
I come here to not see my math homework, AND I END UP SEEING MY MATH HOME WORK.
This is my place to relax, :).
Nice work both of you guys, your math seems to be sound from what my 13 year old brain can understand...
I noted this morning a result from a 1v1v1 race:
I noted it because both players lose exact amount of vr. But when I apply your formula for the 8822vr guy:
which gives him a loss of 11 vr and a gain of 54vr. 54-11=43. Not 8 :s
I think Tnosrac's formula is very close, however it still needs work. Take a 1 vs 1 with a 5000 and a 9999. So m = 4999. x = 13e^(4999/2000) = 13e^2.5 = 7300! Since a 7300 pt gain is inplausible, the formula still needs a little tweaking.
If Mkwii uses the Elo rating system, which I think is true, they probably tweaked it a bit. The original Elo formulae can be found here: http://math.bu.edu/people/mg/ratings/approx/approx.html It's rather mathy, but sheds some light on the subject. If we can find the tweaks, we can find the formula. Thanks, Astro, for making this thread, because now I can't stop thinking about it! Anyone have some race results to upload? If we can get enough of those, maybe we can find a pattern.
Last edited by yoshifan314; 09-18-2011 at 03:58 PM.