regression - given model, assess probability of results


(It's many, many years since my last foray into statistics so please be gentle..)

In its simplest form my question is this: I have developed a model using regression analysis that provides a good fit to my data, using multiple input variables. Given all the information I have from the regression model, given two sets of independent variables to use as inputs, how do I calculate the probabililty of one real observation being greater than another real observation?

I searched the forum and the internet, and the closest I have to an answer is along the lines of (from this forum):

Compute the difference distribution and determine the probability that it has a value of < 0.
mean of difference distribution = mean1 - mean2
std dev of difference distribution = sqrt(var1 + var2)
note--> var = (std dev)^2

however, I'm not sure how to implement this, as it implies that I have data about two distributions, but the regression analysis I have done only seeks to fit one distribution, or am I confused...?

Please help; I think what is underlying my question is a lack of understanding around some basic concepts, so I would be keen to learn as much as possible and correct these.

Ok, maybe it will help if I add some context...

The model I've developed attempts to provide an estimate a golfer's next round performance, relative to all those other golfers playing the same course on the same day, same competition etc..

Prior to play, for all those golfers playing on the particular day I will have sets of independent variables, one set for each golfer. Using these sets of independent variables and my model, I will be able to calculate an estimate of the performance of that golfer relative to the field for that day.

What I'd like know, is, given the model, given the sets of independent variables, how do I calculate the probability that one golfer from the field will post a score better than another golfer?

Hope that provides a frame of context that will allow someone to nudge me in the right direction - thanks!