ASAIK the US Navy claims and losses for the Marianas are as follows:
Looks like the U.S. Navy aircraft outnumbered the Japanese aircraft that they egaged by an average of 12.5 : 1, and shot down a claimed 51.2% of them. We had 22,432 action sorties, engaged 1,791 enemy aircraft (12.5 ; 1), lost 65 in the air to enemy aircraft, another 203 to enemy A/A, and another 223 operationally not attributable to enemy causes.
We claimed 917 shot down in the air and 306 destroyed on the ground for a total of 1,223 enemy aircraft destroyed.
In the strikes from 7/1 through 8/1/44, we outnumbered the enemy aircraft we engaged in the air by 532.5 : 1 (7,455 action sorties versus 14 enemy aircraft engaged.
I have never seen the Japanese equivalent report, so I don't know the numbers from their side.
I have some reservations about claiming 51.2% of the enemy aircraft engaged ... but ... (1) it was late in the war, (2) we had a large cadre of combat veterans and (3) we outnumbered them by an average of 12.5 : 1 in the air.
I have nothing to say about the accuracy of the numbers as I have not tried to verify any of them against anything. I don't have the USN combat reports or the IJN combat reports. It is interesting that we had 83% as many operational losses as losses to enemy A/A and A/C combined. I do not know if a significant percent ran out of fuel, were lost to mechanical / electrical causes, or what.
If anyone has the Japanese numbers, please post them. It would be very interesting, for instance, to know how many sorties the Japanese launched since we only engaged 1,791 total aircraft in 22,432 sorties (12.5 : 1).
These data come from "Naval Aviation Combat Statistics of WW II," otherwise identified as "Opnav-P-23W" dated 17 June 1946.