Modeling number of spectators in football

Question

Can anyone give ideas on the possible best way forward to solve this specific machine learning problem for sports analytics?

Data set looks like:

HomeTeam             AwayTeam                NoOfSpectators
AC Milan             FC Barcelona              56900
Real Madrid          Bayern Munchen            78900

The outcome variable is NoOfSpectators but there are many levels in both HomeTeam and AwayTeam.

There are about 50 levels in both HomeTeam and AwayTeam. I know you can do OneHot encoding or Label encoding but what other options are worth trying?

For example use RandomForest or LightGBM that can automatically handle categorical / factor variable?

Also since for example: HomeTeam AwayTeam NoOfSpectators AC Milan FC Barcelona 56900

is the same as: HomeTeam AwayTeam NoOfSpectators FC Barcelona AC Milan 56900

How do you suggest that the data set should be structured / modeled before input to a ML model?

Answer 1

Some ideas for modeling: You should definitely not start with some complicated black-box model like RandomForest, you should start with simpler models like linear models which can give some understanding (and serve as a reference if you later decide to try RandomForest etc).

But I think you should start with a better variable encoding. A linear additive model like ~ \text{HomeTeam} + \text{AwayTeam} will not really use the information that A is Home and B is Away, since A+B = B+A. Adding an interaction term will not change that. So you need a better encoding. Add a third variable HomeStadion, which you can code from the information that you have. Then you can try a model like $$ \text{NoOfSpectators} = \beta_0+ \beta_1 \text{HomeStadion} + \beta_2 \text{HomeTeam} +\beta_3 \text{AwayTeam} + \epsilon $$ or you could try to include an interaction term ($\beta_1$ can be interpreted as "HomeTeam advantage"). But with an interaction term the number of parameters will be very large (about 50x50=2500) so will need very large sample size, or you must use regularization. See the discussion in Principled way of collapsing categorical variables with many levels?. It could maybe be useful to use different penalization's for main effects and interactions? It could be that the most important effect of interaction is an "star meeting" effect, so most interaction parameters could be close to zero. That could be represented via lasso, giving sparsity, while the additive parameter could use ridge penalty.

EDIT

answer to new question in comments: The factor variables should be represented by dummy variables, which can be used directly. Good software should construct the dummys for you. But, if you use regularization, note that you should not leave out one "reference level" as usually is done, as it changes the model when regularization is done. See Dropping one of the columns when using one-hot encoding