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Real world too hard? Stay in statistical fantasy land if you must. But while so doing, you might look up the distance to targets in a couple of other real world carrier battles and see if you can draw comfort from them.

You claim only "real world" numbers mean anything, then fail to cite any to prove your point; is the real world too hard for you, as well? I cited sources, but I'm not claiming they are infallible, only that they are all I have. Given the land-based planes available to Midway's air group, I find it difficult to believe that any informed person could seriously think Kido Butai's planes could attack Midway from outside Midway's reach. Can you name a real world event where the Japanese were able to take advantage of their alleged carrier strike aircraft "range advantage" and hit a target without being attacked in return?

It has been observed (by you possibly) that there was no knowledge of what airplanes were there. Probably true in the details, but surely there was an educated guess.

Well, if there was, what was it? What did Nagumo and his air staff think they knew, or could guess, about Midway's air defenses? Maybe that's the answer to the question; Nagumo didn't try to stay outside Midway's range because he intuited that he would be attacked at any distance at which he could reasonably launch his own strike. I don't know and neither, apparently, do you. I think it had to do with lack of intelligence on what types of aircraft were actually on Midway, a feeling that he couldn't possibly out-range land-based aircraft, and possibly the fact that Nagumo's force was a day late compared to the invasion force. I know if I was in Nagumo's place, I certainly wouldn't want to make a costly long range attack; I'd try to preserve my strike and fighter aircraft as much as possible for the carrier battle that was scripted in Yamamoto's plan.

The issue was, IIRC, why did not the IJN sit outside the range of Midway aircraft rather than sit waiting to be attacked.

It's instructive to read the Nagumo Report in this regard.

http://www.history.navy.mil/library/special/midway.htm#p11

It states that, " (g) The enemy's attempt to counterattack with use of shore based aircraft could be neutralized by our cover fighters and AA fire."

The Japanese estimated the air defenses of Midway as follows;

" Estimate of existing conditions there were as follows:
(a) Air strength: ¹
Recco. Flying Boats 2 squadrons.
Army Bombers 1 squadron.
Fighters 1 squadron.
The above estimated strength could be doubled in an emergency."

This was fairly accurate. "Actually there were at Midway on June 3d 30 PBY's; representing two and a half squadrons, one Marine Fighting Squadron of 28 planes, and one Marine Dive Bombing Squadron of 34 planes, plus 21 Army bombers (4 B-26's and 17 B-17's) and 6 Navy TBF's, which had been brought up from Hawaii."

But the Japanese also realized that Midway's air defenses could be quickly reinforced from Hawaii,

"g) Air strength in the Hawaii area was estimated to be as follows:
Flying Boats About 60.
Bombers About 100.
Fighters About 200.

These could be used for the speedy reinforcement of Midway."

The Japanese planes knew that they had an appreciable advantage in strike range and were used to making long range strikes, yet Nagumo moved his fleet to within range of Midway's planes and thus had to defend itself from a strike when it really didn't have to. Why did Nagumo do this when he could have just as well waited until after his first strike had returned from taking out Midway's airfacilities (and thus crippled Midway's offensive capabilities) before exposing his fleet (and its air operations) to the bother of a potencial strike from Midway?

John Prados, in "Combined Fleet Decoded" page 316, mentions a radio message sent by Nagumo to Combined Fleet on May 16, stating his intention to close Midway and begin air attacks two days before the scheduled invasion, "from a point fifty miles northwest of "MI". "MI" was the Japanese code designator for Midway during the operation. The message was intercepted and decoded by Nimitz's intelligence people at Pearl Harbor. If this is accurate, then it becomes obvious that Nagumo's air staff felt that, when it came to launching air strikes, the closer the better, and they discounted any real, or perceived, "range advantage" in favor of the advantages of short range air strikes. This accords with the later US practice relative to carrier air support of invasions, of positioning the close air support carriers just over the horizon from the invasion target. Of course, by that time, the USN had the luxury of using CVE's for close support and keeping it's fleet carriers much further out to sea.