What does "rigor of Silver’s hand-tuned models" mean in this extract?

The key to understanding this is to understand model or, in particular, a statistical model.

A model describes a set of data or observations. To take a trivially easy example, if we have a set of data {1,2,3,4,5}, one model is to say that the average is 3.

This might lead a naive modeller to predict that the next observation is likely to be around 3.

A shrewder modeller would see that the data are increasing steadily and predict that the likely next value is 6.

This is the story of Silver. He had a skill in data modelling that was not bound by simple or conventional statistical methods. His models are described as hand-tuned because he developed his own techniques rather than just using conventional models. The conventional models are described in the text as having methodological rigor, meaning that they were standard techniques applicable to many circumstances. The mention of debate means that Silver was criticised for not sticking to the conventionally approved methods. These methods, having been formally and carefully developed, would have been regarded as having intellectual or mathematical rigor.

Rigor = strict precision : EXACTNESS logical rigor

”Tentatively one might suggest that what characterizes science is the rigor of its methodology”

Merriam Webster

But Silver was able to see patterns in data that the conventional methods and others did not see, giving his models a predictive force better than others. And with better prediction comes better economic advantage.