From: Near Portland, OR
A given hex may have a base in it, but it would be very rare that a base would take up anything close to the entire hex. It is possible that Los Angeles today is geographically the largest metro area on Earth. (Urban sprawl has enabled it to eat up a large chunk of Southern California.) According to Wikipedia, the Los Angeles metro area today (which includes Los Angeles county, Orange county, Ventura county, parts of Riverside county, and parts of San Bernardino county) is 4850 square miles. That is a little bigger than one hex, which is 3600 square miles.
During the time period of the game, Los Angeles is far, far smaller, much less than 1000 square miles, less than 1/4 of a hex. And that it a major US city. The island of Singapore is only 253 square miles, 7% of one hex. The majority of that hex is open water.
Fighters on CAP over Singapore are going to be over the city. They aren't going to be cruising around in the Straits unless they are protecting a convoy. Enemy aircraft just passing through the hex where Singapore is are going to avoid passing directly over the island and risk being attacked. Because the game's granularity is a 60 mile hex, it looks like they are passing right over the base, but they could be 30 or even 50 miles away.
Fighters flying CAP might see enemy planes passing 30 miles away, but it is doubtful they would intercept them. First off, the fighters on CAP would probably have orders to not leave their station unless they are engaging enemy planes that pose a risk to the base or other target being protected. Secondly, unless the fighters have one hell of a speed advantage (such as flying Me-262), they won't be able to catch enemy aircraft in a tail chase in any reasonable time.
If they are chasing the enemy and have a 50 mph speed advantage, it would take almost 40 minutes to catch the enemy.
Fighters are tactically offensive weapons, but strategically, they are defensive weapons. Fighters are not much use as pure fighters unless they have something to defend. Historically, when somebody gets air spurpemacy, fighters are assigned attack plane roles to give them something to do such as strafing ground targets or ground support. When the tide turned for the Allies in the Solomons, Corsairs got bomb racks.
Fighters flying in the fighter role are assigned to defend something. They are escorting bombers, flying CAP over a base or convoy, or they are waiting for the call to fly up as interceptors. Fighters defending something may go chasing off after something, but if they are, they are usually disobeying orders.
Fighter sweeps are sometimes flown, but the fighters are usually tasked with shooting up ground targets if enemy fighters don't appear. Unless air defenses are very strong, the defending side usually won't send up fighters to intercept a fighter sweep. When the RAF was conducting fighter sweeps of occupied France, the Germans rarely sent up fighters once they figured out what was going on. The British lost a lot of experienced pilots to flak on those missions and the Germans lost little.
Shattered Sword does document that poor Japanese CAP doctrine and discipline contributed to the loss of their carriers. Their fighters tended to concentrate on the first threat they became aware of and there was little fighter direction. That meant that the fighters were engaged chasing American torpedo planes when the SBDs showed up.
Even with such poor fighter discipline, the Japanese fighters were not wandering too far from their carriers. The arc covered was probably about 100 square miles (2.8% of a hex) maximum. Probably less than that.
With long range radar and sophisticated ground control procedures, the capability of CAP greatly improved. By the late war carrier battles, US ships had radar that could cover more than an entire hex. That enabled people in a ship's CIC to vector fighters to the enemy so they were in the right position at the right time. That's a very different situation than an early war scenario where fighters are defending a base and somebody flies through 30 miles away. In the latter case, by the time the enemy was spotted, it was usually too late to do anything about it unless they were coming at you.
As far as air battles over the Eastern Front. Much of the air action there was concentrated over the front lines, or over bases just behind the front lines. Fighters would be covering the air space over their troops or base and the other side would be trying to get attack planes through to attack the enemy troops. If a pure fighter battle broke out, it would most likely be when to opposing CAPs encountered one another.
WitP AE - Test team lead, programmer