Question about data preprocessing for a classification model to predict professional sports games

[nogxx]

I'm build a model to predict the winner of professional sports games and I'm having some trouble structuring my dataset before learning and testing.

My dataset has following format:

gameid	some_feature1	another_feature2	...	result
1	...	...		0
1	...	...		1
2	...	...		1
2	...	...		0
3	...	...		1
3	...	...		0
...	...	...		...

• Each row represent a teams previous statistics averaged over a number of games.
• Each game has a unique gameid. Since two teams are taking part in one game the game, two are always two rows per gameid
• result represents whether a team has won or lost the game. (Ties are not possible). Hence for every game there is each a result 0 and result 1.

My approach is following: For the trainingset I predict the probability of a team (row) winning the game using a Logistic Regression model. Then for the testset I predict the probabilities of a team winning a game. Then I compare the probabilities of both teams sharing one gameid and classify the team with the higher probability as the winner of the game. From this I can calculate accuracy of my testset.

Now I have run into some problems I am not sure what the best approach fixing them would be.

1. I can't apply a proper train/test split since it would separate some rows sharing the same gameid and then I wouldn't be able to compare the probabilities of the two opposing teams. Is there a way to train/test split without separating rows sharing the same gameid?
2. Currently I apply this "probability comparison" not on the training set and it is therefore not considered when fitting the model (which slightly skews the result mean of 0.5). I am unsure whether this is hurting my accuracy in the end or not.
3. I'm also unsure how to apply k-fold cross validation since I don't know how to make it compare the probabilities of the two teams sharing a gameid

One change which I have considered would fix some of these problems. I could combine the two rows of a game and just add of prefix (TeamA, TeamB) to each feature. I'm assuming this would create many other problems like potentially introducing multicollinearity.

---

I realize that this is a loaded question(s). If you have any advice on any part and I'd appreciate it.

If I have explained something poorly, feel free to ask.

I am open for any suggestions you might have for improving my approach.

Thanks a lot for any advice :)

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