I don't agree with the conclusion that a kid in a sub-optimal learning situation would do better on say an Explore test at 13, then they would at 12 while having been in a closer to optimal learning situation. Now if they had an extra year in an optimal environment, then sure. But the presumption is we skip because that optimal opportunity doesn't exist.
I guess I want to clarify what I meant by talking about my son's Explore scores. If I look at his scores he got as a grade-skipped 4th grader, but compared them to the 3rd graders who took the test (my son by age should have been a 3rd grader when he took the test), then his scores look a lot better. Of course I can't say that he would have gotten the same scores if he had not skipped in the first place, but who knows.
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But here's what I think is an important distinction that is often overlooked by parents of grade skipped children. (not singling you out SPG, just using your situation as a hypothetical case). Average 4th graders score higher than average 3rd graders. As they should, since these tests are mostly acheivement and grade level based. So of course a grade skipped 4th grader will do better than a 3rd grader of the same age - because he/she is already in the 4th grade. We can't possibly know how a child would have scored if he/she had never been accelerated and given the opportunity to learn higher level material.
When we gradeskip our children to x grade, they become x graders. We shouldn't (in my opinion) compare to "what would have been" in the previous grade. The grade skip allows our children to become even further accelerated. Trying to compare based on age at that point does not make sense. Comparisons should be made only to other x graders.
This is one of things I really like about college and even moreso in grad school. Age is not a factor. If you want to get into a top grad school in your field, you had better know your stuff. No school will accept you with lesser credentials just because you got to that point quicker than someone else.
