Non tilt window channel

Hello there. It looks like you have either an S380-32 or S385-32. The only difference between these two balances is the bottom shoe depth. See below. Measure your old balance's shoe depth to see what matches best. 

Comparison of the S378, S380 and S385 balance shoes.

You then have to choose a stamp option, which reflects the balance's strength. Your old balance's stamp of 31-9 is from a rating system no longer in use. To know what stamp to pick, weigh the window sash that these balances support. You can then use that exact weight to choose the correct stamp option.