The most efficient thermal result when using insulation board in a standard wall used in existing buildings or in new construction is to prevent conduction paths to the outside world.
For my example this thermal modeling uses a wall with 3/4" siding, 1/2" plywood sheathing then 2x4 studs with batt insulation and 1/2" sheetrock inside and is pretty poor if temperatures are extreme, hot or cold outside.
So to improve this same wall, say you get a fixer-upper, is to carefully remove the siding, box out for windows, doors and vents where needed then add 1-1/2" of insulation board on top of the sheathing, it can be thicker for deserts or the Arctic, northern exposure or south. Seal the joints of the board to create a seal, this will cause condensation.
Then add furring strips of ripped 1/2" plywood 1-1/2" wide on top of the board to keep the siding from getting wet from condensation and reinstall the siding.
What this does is stops conduction from the inside, the wind or sun on the siding no longer is touching so greatly reduces that source and most important it turns the existing wall into thermal-mass that keeps the inside in the comfort range with less energy.
This image is a thermal model run of 400-minutes, 20C outdoor (white), 0C (blue) indoor, adding the insulation board & furring triples the thermal resistance so if you had R15 it's about R45 with the board plus the effect of added thermal-mass.
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Standard Wall vs With Insulation Board Thermal Model.
Construction tips:
Use a lot of fresh sharp large mat knives for cutting. The panels tend to crumble when the blades are dull. It is worth the price of the new blades for cleaner cuts. You can use 3" screws to add the furring strips not over studs so that conduction path is stopped better.
