What model of window balance is this?

Thanks for writing in. This looks like either an S380-15 or S385-15 Channel Balance. The only difference between these two balances is the depth of the bottom nylon shoe, but the 'heel-to-toe' measurement. See the diagram below for reference. Compare both balances with your old hardware to see what matches best. For a stamp option choose 1450.

Comparison of the S378, S380 and S385 balance shoes.