Are there any measurable world records from the Elizabethan era that still stand?

I'm not sure what sort of world record you would have in mind, and given the parlous state of science at the time, what world records would you trust? If, for example, I exhibited a Chinaman from the Ming who lived for 231 years, which is surely a world record, you would rightly reject this by saying 'it is much more likely that this world record is inaccurate than he really did live to 231, given how notoriously bad records were at the time, the cultural value set on being the oldest man in the world, etc'.

If Shakespeare got pretty close to the perfect tragedy, but there was a slight refinement of the form from the 19th century that's better (if less significant), surely people would prefer to watch that, and count themselves fans of that author.

If Shakespeare helped define what the perfect tragedy was, and all later tragedies felt the 'anxiety of influence', this isn't so clearcut. See my other comment.

Is that a real distinction? When Shakespeare is the 'most influential', then in some respects, he is setting what it means to be 'able'. He is setting our norms and expectations, laying down the language we think and write in. John Keats: "He has left nothing to say about nothing or any thing." Ralph Waldo Emerson: "His mind is the horizon beyond which at present we do not see."

When a writer is so influencing (should I say, 'distorting'?), is it really meaningful to draw a distinction between 'influential' and 'able'? Like Phil's implicit claim that every writer has an equal chance of being Shakespeare, this is not something I am willing to instantly grant without inspection.

The fact is that across most fields, a statistically-impossible number of those regarded as the greatest practitioners were among the very first practitioners.

Statistically impossible... based on what?

There are numbers; I have provided some in the case of Shakespeare, and you yourself have provided more. If you bothered to compute the odds you would find them astronomical.

Based on what am I computing these odds? What sort of absurd model assigns equal possibility to being Newton in Newton's lifetime and right now?

That's amazing discriminatory power, and it doesn't happen by accident.

I agree that it doesn't happen by accident. And I think there's many alternate explanations besides the one you seem to hew to.

Have you considered that greatness may simply come and go with periods of particular ferment? Look at the plots over time in Human Accomplishment: clumpiness is common, but other than that, there's no particular rhyme or reason. Arab literature clumps at a different time from Chinese painting which clumps at different times than Western Philosophy, and so on. All of this massively violates a naive model 'everyone has an equal chance to be Newton, therefore isn't it really suspicious that Newton was so early on'; am I supposed to believe that 1000 years later, Arab poetry is still biased by random canonizations? And the same bias hit Japanese literature for a different clump of writers? And hit a later still clump of English writers?

(This is reminding me of anthropic reasoning. 'We get these absurd consequences from SSA/SIA! Clearly the Great Filter is near and we are doomed to die in the next 50 years!' 'Or maybe your theories of anthropics are filled with holes and problems, and you've nicely demonstrated their absurdities.')

You listed the top-regarded practitioners in fields I didn't mention, and they followed the same pattern.

Yes... So what's simpler, that in all fields there are conspiracies to canonize random early participants, or that early participants really are not identical to later participants?

It may be worth noting that there's a fair bit of evidence that over the long-term, only some literary wors get a lot of attention, and this does not seem to be closely correlated with what at a specific time is widely read or considered great literature. Much of what we consider great works of literature from the 19th century were not as widely regarded as they are today, while other works have fallen by the wayside. Similar examples show up elsewhere and elsewhen. For example, The Tale of Genji was written in the middle of the Heian era when a lot of different literary experimentation was going on, and it took time for it to be recognized.

It may make sense therefore to use a test of time as a way of determining literary merit. This isn't ideal: it is possible that once a work is sufficiently well-done, the actual level of acclaim more closely resembles a random walk. I'm not sure how to test that hypothesis.