Variables theory is pure statistics... Physics modelling means experimental validation more than everything else (including naturally both mathematical and statistical validation).
If you realy believe you know everything about modelling, why do you ask something? Statistics means good methodology. Mathematics is just the language of modelling ... but Physics means modelling based on reality laws... even myself, as statistician, I believe statistics as science offer methods to modelling and not the essence of the model. What means science for you indeed ? What do you realy need to define a science? Which science is more comprehensive?
There is no absolute “better” model—mathematical models are ideal for systems governed by exact laws, while statistical models are better suited for analyzing uncertain or data-rich environments. In real life, we rely on both: mathematical models guide engineering and physics, while statistical models drive AI, healthcare, and business decisions. Each plays a vital, complementary role in solving practical problems.