I have no background in math, so excuse me if the answer to this is straightforward.

I'm trying to build a model that predicts the outcome probabilities of a football game. According to the model, the probabilities for win, draw and loss depend on the Poisson distributed expected goals of both, Home and Away Team. After doing some research, I came across this paper, where the authors extend this basic model by a function that gives more weight to certain outcomes (https://www.researchgate.net/publication/279122210_Beating_the_bookie_A_look_at_statistical_models_for_prediction_of_football_matches).

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(For understanding: x and y refer to goals scored by home and away team respectively)

While I understand the basic intuition behind adding this function, I can't really imagine what happens inside of it. How would one accomplish this slight modification to the distribution? Please let me know if my question is unclear. Thanks in advance.


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