Nowadays individual servings of butter come wrapped in foil, in what are essentially half-tablespoon size rectangles (or 1-1/2 teaspoon, whichever way you want to look at it). Or it comes in little plastic cups with little foil covers, in 1 and 2 teaspoon sizes.
We don't even know where to get a pat of butter these days, but we well recall the little flat of cardboard with the strips on either side that could be folded up, the square of butter, and the thin sheet of coated paper that covered the butter. The sides of the butter were totally exposed to the elements, so it is no wonder butter is now completely encased in foil or cups. Perhaps pats of butter are still available here and there, but we haven't seen one in at least ten years.
We believe that there were 48 pats to the pound, meaning that nothing has really changed – a pat was 1/2 tablespoon, 1-1/2 teaspoons, 1/3 of an ounce, or 9 grams.
If you are using a recipe that calls for measuring butter by the pat, it's a quirky one. Did the writer intend for you to steal your butter pat by pat from the local diner? Does it also call for little containers of grape jelly and packets of Sweet'N Low? We'd think about finding another recipe….