So regarding the original question, I'd have to put an estimate because I don't know how many dives I have done, and I'm actually a somewhat compulsive data-logger. I love having dives downloaded from our computers in order to track a number of things - "hey, my RMV changed after I got that new backplate and evened out my trim some more!" However, I only know for certain how many dives I have since switching to computers in 2005.
I started diving a couple of years before getting certified in 1980. In college my wife and I did scuba for all our PE and ended up DM'ing or assistant-instructing on a number of dives that even I didn't log. Then our paper logs were eaten by a hurricane.
But that's not really what matters. As Christi points out, in the absence of documentation you put what realistically reflects roughly the number of times you've managed not to kill or irrevocably damage yourself diving. The operator can use that as a rough guide to place you on a boat with appropriate other divers.
Even then, that's not what matters most. As others have pointed out, number of dives or certification does not equal skill. I've been on boats with "instructors" who've terrified me underwater. I've found myself impressed with young teens on their first OW dives with whom I'd be happy to buddy up.
I have, at this point, not all that many Cozumel dives, 406, over 17 years. Most have been with the same DM/instructor who knows us well enough that he has keys to our houses in both Cozumel and the US. We're only in Cozumel 4-6 times a year at this point, which means we're on surface interval for months at a time. Although I think it's fair to say he's familiar with our skills, the first day of any trip we stick to comfortable sites (no Punta Sur or far north) so we can get everything dialed back in. I'd fully expect Chisti or any other good op to have put us on the beginner boat and have her DM's watch us like hawks before letting us expand to where we could get into more trouble.