good way to model y=f(x1)+f(x2)+...+f(x30)? In a football manager game, there are many players as in this screenshot:

My y is the average rating of a player, my sample size N is big enough, and
x1,x2,x3,...,x30 are the attributes like finishing, acceleration and pace (which can take values from 1 to 20). No attribute has a negative effect.
Can I use regression or another technique to find parameters such as:
y=f(x1)+f(x2)+...+f(x30)

In other words, after sampling N players, I want to know which attribute has the most effect in average rating, and which the least, and a scale to know how much more important is one attribute compared to the least important one.
 A: First you should graph the correlation between the average rating and each of the variables separately to get an idea of the data. You also want to check the amount of variation in your Y variable (you don't want too much) and the variation in your X variable (you want a lot). 
Next run a linear regression. You said in the comments that the coefficients were negative, but what were the standard errors? I am guessing the variables are correlated so you may suffer from multicollinearity making inference about specific coefficients difficult. Just because the coefficients aren't what you ``want'' at first glance doesn't mean the functional form is wrong. 
Next, consider grouping the categories into larger categories and doing tests of joint significance for the larger categories. Or you could try other kinds of functional forms like squaring your variables to bring out more variation. 
Also check the R^2 to see if your RHS is getting at most of the variation in Y. If it is low, while the marginal effects may be meaningful, there is much more determining Y than what you are estimating. 
