poisson loss fits log(input) to a poisson rate, so exp(input) should be used to recover [positive] rates. And I’m not sure how good these metrics are with a poisson distribution.



 ErikVats:

If I should reformulate the task as a classification task, how would this look? The goal of my task is to get a measure of how much each event affects injurytime.


For that goal, maybe it is not that good, as per category coefficients would be introduced.



 ErikVats:

Would a neural network give a better estimate?


Without hidden layers, it is worse than a least squares minimizer, as the latter instantly gets the global minimum. (and I don’t think a hidden layer will help in your case, as your feature space is too small).
It is actually possible that your initial result converged and the fit line is as good as you can get (with weak predictors). Big MSE is to be expected with separated targets.