Authorization rate
The share of card authorizations the issuer approves, and the number heads of payments watch most closely.
In a shop with chip and PIN almost everything goes through. Online the figure is noticeably lower, and for a large merchant a couple of percentage points can be worth as much as an entire product line. Declines come from empty accounts, expired cards and issuers that simply don't trust the transaction. So the work is mostly about giving the issuer more to go on: network tokens instead of raw card numbers, updated card details, correct flagging of recurring charges and a frictionless 3DS authentication.
The metric is easy to improve the wrong way. Resubmitting the same declined card over and over will eventually raise the approved count, but the card networks charge fees for excessive retries. And the ratio says nothing about the customers who never made it as far as the payment step.