MCC34 PKW scoring moment

I started with the assumption that the scoring would be C1+(C1+C2+C3+C4)*(M1+M2+M3+M4)*W1/(W1+W2+W3+W4); pretty much the only other assumption that could make sense is that the scoring is C1+C1*(M1+M2+M3+M4)*x+M1*(C1+C2+C3+C4)*(1-x) for some value of x, but a short look at the scores shows that they are way too coinsplit for that to be the case. Finding how to calculate W was pretty hard however.

 

I quickly noticed that (medium-dnf)/(easy-dnf) is about 5, and after a bit of thinking I realized that adding 0.1 for DNF, 0.15 for easy and 0.35 for medium is a very logical way to achieve that. 0.8 for hard seemed to match up with that as well. Now I had the idea that W1=A1+x for some x, but I didn't know how to calculate it, only that it depended on the team's multiplier(no other way of calculating x would make sense). Using the sheet mentioned in the post, I assumed that everything was divisible by 0.05, so I looked for the values of x that made the individual scores line up with reality for each team and, if a is DNF, b is easy, c is medium and d is hard I found the following:

 

2a+2c=1 or 1.05

b+3c=1.3, 1.35 or 1.4

a+2b+c=0.9 or 0.95

2b+2c=1.05, 1.1, 1.15 or 1.2

a+b+c+d=1.45

a+b+2c=1.1 or 1.15

a+3c=1.25 or 1.3

 

We can divide the first equation by 2 to get a+c=0.5 or 0.525. The latter isn't divisible by 0.05, so a+c=0.5. From a+3c=1.25 or 1.3 and a+c=0.5 a+3c-a-c=2c must be 0.75 or 0.8, so c must be 0.375 or 0.4. The former isn't divisible by 0.05, so c=0.4 and a=0.1. Similarly, a+2b+c=0.9 or 0.95 shows 2b=0.4 or 0.45, so b=0.2. From a+b+c+d=1.45 d must be 0.75.