OK.
Let's say that I say "if you shoot an enemy airplane out of a fight, and he does not retun to that fight, you get a victory."
IMO, if you were credited in wartime with the victory, you get the victory. The actual losses are a separate number, which can be calculated different ways (and this is definitely not how I would do that, but how to make that determination is up for debate). Just knowing the actual losses vs the credited claims, tells us as historians and amateur enthusiasts a lot about what really happened during the war. Because even if we used your criteria, the actual loss numbers are always
far different from the claims.
But as long as you pick a criteria and stick with it, that part is simple.
Reconciling the two (credited victories vs actual losses by the other side) is going to be tricky, and I don't think fully resolvable.
In other words, if a P-38 squadron and two F4U squadrons and a P-39 squadron and two Wildcat squadrons and two different P-40 units engaged a large number of A6Ms and G4Ms over the same little island, and claimed 25 victories (confirmed / credited), but the actual losses were 7 A6M and 7 G4M for 14 total, as happened in one of the battles in the Pacific Adversaries book that Jobbin was talking about, then we know something new about what happened. And to me that is very interesting. Determining which of those units deserve the credit is a lot trickier in that kind of complex situation.
On the other hand, if a P-38 squadron engaged with an A6M squadron and claimed 10 but only 3 A6M were lost, we do know which unit got them, though we will still probably never know which pilot really deserves the credit. For this reason I think we should just maintain the two different numbers in the record. Currently we focus on the claims and mostly ignore the real losses which i think it incorrect, but increasingly I'm seeing some analysis (including in film and videos) where the actual losses are mentioned, so the reader or viewer can kind of mentally reconcile these in their own mind.
You shoot 3 airplanes out of a fight. They went down below the cloud layer smoking, didn't crash, but left trailing smoke and flew back top their base without ever returning to the fight. One of them is written off for spares, but made it home, and so was never put on anyloss list, but it doesn't reutrn to combat. The other two are repaired and return the next day to fight, but obviously are also not on any loss list fromn the day before, despite being shot out of the fight.
Those will be noted. What also happens is that a fighter pilot shot at an enemy plane, later saw it or quite possibly another plane smoking, and maybe later sees a mysterious circular splash shape in the sea. Claims it as a victory. So does another pilot from the same unit. And so does the AAA gunners on a ship down below. And so do the defensive gunners on a bomber that plane was attacking. In reality, that aircraft may have gone down in the battle area (and possibly due to gunfire from any combination of the four parties that made a claim on it), it may have returned to base damaged, it may have returned and then been written off right away, or it may have been smoking just because it the pilot was firewalling the throttle trying to escape. He may have left the fight because he was low on ammunition or because he was outnumbered and feared for his life. I don't think you can automatically assign a victory in that circumstance, though I also don't believe it changes the numbers as much as you may think it does which means it's not as significant as you may assume.
By my definition, the pilot had 3 victories, but the enemy admited no losses and, 70 years later, YOU are telling ME that there were no losses while I am happy to award 3 victories by my definition of a vcitory.
It happened almost exactly tghat way in many cases.
It happened that in many cases, the pilots on the other side returned to base with no or very minimal damage and their planes were flying again the next day. This, by the way, also works both ways. It's not just Allied pilots who overclaimed.
I would say if you want to keep damaged aircraft in mind, you can do that and keep it as part of the story: "25 were claimed, 14 were really lost, 3 damaged". You can also, if you really want to, trace the ultimate fate of these aircraft in many cases because they had serial numbers and these were traced. I think going that route gets a bit too complicated and introduces too many variables but if you wanted to you could do it, and nobody should try to force you not to.
Forgive me if I'm reading too much into your posts, but it seems like you are tying to find a way to dismiss this type of data, when I think you might find that embracing and exploring it will be very rewarding and interesting. The book has not in fact been closed on this war like some thought or claimed it has. The story is much more complex and interesting.