Applying an algorithm on it's own training data for descriptive purposes?
can you apply a trained algorithm / model on its own training data if my interest is not in predicting forward but evaluating success vs likelihood of success (and still yield useful information)?

Yes, absolutely. There are quite a few cases where applying a model on the training data is useful. The most common is probably to detect overfitting: a high difference in performance between the training and test set is a sign of overfitting. In general it can also be useful to know how the model performs on the training set in order to obtain an upper baseline for the performance.
Everybody says &quot;don't predict on the training set&quot; simply because it's a simple rule to remember and such an easy mistake to make for beginners. But as long as one understands what they are doing and knows that obviously the predictions obtained on the training set are biased, there's no problem.
The task described in the question makes sense to me, you have my permission to predict on the training set ;)
Just one more remark: there might be a bias in the training data itself, in the sense that if success for an event is very unlikely then the event will fail more often than suceed even when the condition of its success are satisfied. If the data contains this kind of cases, it means that the model is trained to predict &quot;fail&quot; for potentially successful features. Whether or not this impacts the model depends on whether there are enough similar but successful events in the data, I think.