How should we convert sports results data to perform a valid logistical regression? Say we want to perform a logistical regression analysis (although my question pertains to regressions in general) on sports results to determine the effects of various factors on who wins and who loses.  We have the background information we want on the teams and players and now just need a random sample.
So we decide to take the published results over the past couple of years as our sample.  The sample we collect is in the following form:
Result, Team 1, Team 2, ...
The result is always 0-1 or 1-0 (no draws).  We can start preparing the data by converting Result into a binary variable:
Result = 1 if Team 1 wins, = 0 if Team 2 wins.
The problem is that this doesn't give us a valid regression.  The reason will take a bit of explaining.  Say one of our observations is:
Result = 1; Team 1 = Man.U.; Team 2 = Chelsea
This observation can be rewritten:
Result = 0; Team 1 = Chelsea; Team 2 = Man.U.
And it is the exact same observation and all the information is still the same and perfectly correct.
And this actually changes the results of our regression!  One quick way to prove this is to consider what happens if we rewrite all of the observations so that Team 1 always wins.  Then our dependent variable will always be Result = 1.  Thus Var(Result) = 0 and the estimates for our parameters will all be 0 (except for the constant, of course).  If we flip half of the observations so that half the time Result = 1 and half the time Result = 0 and we run the regression on that, we will get non-zero estimates for our parameters.
This bothers me because we are regressing the same data but getting wildly different results based on the order the teams are written in.  If our results can change based on the order we decided to put the teams down when recording our observations, then they can't be valid.
So what is the best way to prepare this data for analysis so that we can get valid results?
 A: Rather using trying logistic regression, I would consider trying the techniques in

Dixon, M.J. and S.G. Coles, 1997.
  Modelling Association Football Scores
  and Inefficiencies in the Football
  Betting Market. Applied
  Statistics.

In this paper, they use Poisson regression to model football scores. Basically, the number of goals a team can score is modelled using a Poisson distribution,  adjusted for:


*

*a home advantage

*an attack rating

*a defence rating



For non-British readers: football == soccer.
A: A simple solution is to incorporate the hometown advantage (that is if your data holds this info). This makes it possible to give a definite meaning to your outcome. So if you have that data, it'll likely be a better model and solves your problem: go there!
Right now, your outcome's definition depend on the order, but your data doesn't.
A possible solution (though I haven't checked this completely) would be to duplicate every record in your data, but change the order and the outcome (so for every observation, both representations are in your dataset), and then do a weighted logistic regression, giving every observation a weight of 1/2 (I think this correctly adjusts your variances, but I'd have to check)
Another option is to change your outcome so it is not dependent on the order anymore (i.e.: the alphabetically former team wins or not), or to always code your two teams in a steady order (i.e. make that the alphabetically former team is always in column 1).
These things are bound to be a bit harder to interpret, though...
A: I would be tempted to use a resampling approach, were in each iteration the presentation of each observation is chosen randomly.  That way the data for each model is still i.i.d. and the uncertainty due to the presentation of the observations is taken into account by the averaging over the resampled datasest.  You can then look at the distribution of parameter values to get an idea of the importance of the explanatory variables.
