Bayesian models are working fine when you have few datas, and I have used the last conclaves ballots number to "train" that. It was mostly a toy project to understand better how a Bayesian model is working.

You can build a model, but is there any reason to assume it can predict what you want it to predict?

A very rudimentary process for a conclave election can be modeled by a geometric distribution. So using a bayesian model to estimate that can be appropriate. Of course, if you want a better estimation you need a more complex model, but I repeat, for a toy project it would be interesting.

Anyway, at least the real election at 4th ballot was inside the confidence interval predicted by my model.