i ask for help with these ball bearings

[iron_mec]

This is not a formula but a complete procedure which also includes the choice of the value of some graph/table coefficients (the result of physical observation).
and this often happens in the engineering field (see for example a verification of a structure according to ntc 2018...).

for other mechanical components, there are dedicated regulations because stresses are different (as is the choice of materials).
the conditions that lead the pitting to be critical for the useful life of a bearing, are exceptional conditions, obviously out of the design conditions: If so it does not mean that something has been neglected during the project.

demanded, for example, because for bearings (excluding particulate cases) a "high chromium" is used and not other types of reclaim steel.

I also imagine why the bearing must hold loads and therefore very stressed to wear and crush and therefore I think it needs high cr to resist better.. the doubt was whether the formulas of calculation of the lube for fatigue life could affect other components to take into account the increase of life hours due to the type of oil, applying the calculation of the formulas of the factor that takes into account the oil seen in the bearings also for other components. . .