When you do the numbers and they give you an answer, you don't dismiss it as "absurd".
One man's modus ponens is another man's modus tollens. You have amply explained why you reached the conclusion you did based on idiosyncratic personal preferences and constructed an unconvincing model to try to justify it; there are no 'numbers' here, there is only absurd reference class tennis. ('Stratford-on-Avon had 0.0001% of the medieval English population; the odds against the greatest English writer coming from Stratford-on-Avon is astronomically unlikely!') I am perfectly happy saying that the result refute the pseudo-premises - not that you gave a precise model in the first place: I will ask you again, what is the right amount of criticism for Shakespeare that would satisfy you that he really was the greatest writer ever?
My separation of classes chronologically is, like all good models, inspired by observation. In this case, the observation that a statistically-impossible number of the people considered "best in field" came very early in those fields, even in fields like literature where coming early is a disadvantage rather than an advantage as regards the quality or contemporary opinion of your work.
The damning point here is that you are willing to bite the bullet and say it applies to sciences as well, where we would, contrariwise, naturally expect the earlier a scientist to live, the easier it is to make incredible discoveries and pick up low-hanging fruit. Only an early scientists has a hope of discovering, say, gravity. Or an early mathematician something like calculus. You have to live as early as Parmenides if you want to discover something basic and extremely important like 'the moon is illuminated by the sun'.
the earlier a scientist [lives], the easier it is to make incredible discoveries and pick up low-hanging fruit.
You are ignoring the distinction PhilGoetz made in the grandparent comment:
If the claims people made were along the lines of "X was the most influential in his field", we could expect this. But I often hear it stated as absolute ability.
Do you like Shakespeare?
I've been reading the Paris Review interviews with famous authors of the 20th century. Famous authors don't always like other famous authors. Hemingway, Faulkner, Joyce, Fitzgerald — for all of them, you could find some famous author who found them unreadable. (Especially Joyce and Faulkner.)
Except Shakespeare. Everyone loved Shakespeare. In fact, those who mentioned Shakespeare sometimes said he was the best author who has ever lived.
How likely is this?
I have a divergent opinion. I realized this during a performance of A Midsummer Night's Dream. I've seen the play three or four times. Every year, people perform it at Renaissance festivals, in Central Park, and in at least one high school within 5 miles of my house. I was sitting in the audience as they got into the part where Bottom acts like an ass and this is supposed to be funny. I was just waiting for them to get it over with, and then remembered that there was nothing after it in the play that I looked forward to anyway. I suddenly realized, "This... is a bad play." Up until that moment, I had somehow believed that it was one of my favorite plays without actually liking almost anything in it.
A Midsummer Night's Dream is supposed to be a magical romantic comedy. It contains nothing of the magic one finds in a Peter Beagle or Charles de Lint fantasy, less-stirring romances than the average fan-fiction, and less humor than one would find in a randomly-chosen paragraph of Terry Pratchett. It has never made me laugh or cry once. Yet even having read it, and having watched it at least twice, I somehow voluntarily paid to sit and suffer through it again when I still had unread stories by Chekov, Borges, Katherine Anne Porter, and a hundred other worthies whose work seldom failed to move me at least as much as Shakespeare's best.
I have two competing hypotheses. Hypothesis #1 is that Shakespeare was the greatest author who ever lived, or at least in the top 10, whatever that means. You would be hard-pressed to find more than a handful of literary critics who would dispute this. Hypothesis #2 is that something about the time that Shakespeare wrote in made it very likely that we would elevate some writer from that time period to "Greatest Writer Ever". For instance:
I can easily compute how likely it is that one of the Elizabethan authors was the greatest author of all time given that hypothesis 2 is false: It is the number of Elizabethan authors divided by number of authors of all time.
So how many Elizabethan authors were there? This is probably the sort of thing that shouldn't be attempted using Google, but I don't have a university library at hand. Using Google, it appears that we have about 600 plays from that time period. Most of the writing from that time seems to have been by amateur poets, mostly members of the nobility. The number of serious authors during the Elizabethan period — and I'm really guessing here; the number of distinct professional author names I've come across is about a dozen — might be around 100.
How many people write novels in English today? Hard to say, but this web page makes a reasonable case that about 100,000 novels in English are published each year. Publishers accept about one out of every thousand books submitted; it is not unusual for a book to be submitted to 10 different publishers. I will therefore estimate that 10 million novelists write 10 million novels in English every year today. Our first approximation for the prior odds for some Elizabethan author of being the greatest English writer of all time are therefore about one in 100,000. I'm going to multiply this by a factor of 10 to account for the fact that authors in Elizabethan times had no libraries, and few good writings to take as models even if they'd been able to acquire copies. I'm going to multiply by another factor of 10 to account for the strange fact that almost everyone agrees that Shakespeare is the greatest writer of all time, when this is not how appraisals of artistic merit ever work. It is almost never the case that a blinded evaluation of the works of different experts in any kind of art results in a unanimous opinion on which one is the greatest. I suppose Beethoven or Aristotle might be such cases, but I do not find the degree of unanimity regarding their merits versus Bach and Newton that I find on the merits of Shakespeare versus everyone else. This gives prior odds of one in 10 million.
(Yes, I am actually arguing that unanimity of expert opinion in this case makes that expert opinion less likely, because non-merit-based mechanisms produce unanimity much more often than objective evaluations of artistic merit.)
At this point, is there even any need to consider the proposition that Shakespeare was the greatest author of all time? For myself, I think not. There's nothing left to explain away. Sure, there are people claiming that Hamlet or King Lear are masterpieces. But I already know that some weird mechanism is at work that convinces people every day to actually pay money to watch A Comedy of Errors. Whatever that mechanism is, it can also explain our attachment to Hamlet.
Given that I know there's a powerful reality-distortion field around Shakespeare, isn't it more rational to assume that whatever fondness I have for any Shakespeare play is a result of that field, than to try to evaluate the play and trust in my superhuman ability to resist that field's force?
And what do you do if you still feel that you like Shakespeare? If you logically conclude that you've been deceived into over-valuing his work, do you will yourself by force of intellect to stop liking it so much?