Almost none. It functions primarily as a draft stop. If you eliminate drafts, an old house can feel warmer but there is almost no R value to be considered.

For comparison, most foam panels for sheathing application are worth R3.5 to 7.2 per inch of thickness. So your foam for vinyl might average R-1

Piffin, are you saying it's a waste of time? I would think it's a cheap investment to stop the drafts as you say. And since richierennie is going to redo the outside shouldn't he do this as well?

Devildog

It should be done for several reasons. stopping draft is one of them. Supporting the shape of the siding is another. providing a barrier against moisture is another.

but insulation value is a pure bonus for what little it is. If I were doing it for insulation value, I would be more likely to add an inch or 1/2" of foil faced foam instead of or in addition to the meager piece included with the siding.

it doesn't hurt a thiung but there isbn't much to count on for R-Value.