During the short time that Morphy played public chess (loosely, about 1.5 yrs. from the Amer. congress to his retirement), he was untouchable. Most players in Morphy's day and before were amateurs in the truest sense of the word and tournament play was in its infancy. Their catalogue of games as a rule was far, far less than that of later players because they had other professions or interests, there were few tournaments (and travel itself was an expensive and time-consuming thing), and there was generally no time controls, so games sometimes went on forever. The paucity of games isn't as frustrating as the worthy opponents Morphy didn't play. The fact that nearly a century and a half later we're discussing Morphy is telling in itself.
Question about Paul Morphy

A study that analizes levels of play using some function of computer engine evaluations rates him around 2300 elo by today's standards. I find the study reliable myself, and the number seems pretty realistic.

The greatest American player ever? By quality of play, no. By dominance over peers definitely (you couldn't really even call them peers).
Arguably the greatest natural talent (in no small way because such a thing is impossible to quantify -- there have been and continue to be many tremendous talents in chess).
But as batgirl said, the fact that we talk about him today is testament itself. Although not objectively the best ever seen, his play was great and tremendously better than anyone who came before him.
I haven't seen the games used in the study philidor_position mentioned, but they would have had to have been careful not to use any wild sacrificial games. Moves he may not have believed were best, but as was the custom of the day were valued due to aesthetics (a beautiful sacrifice no matter how sound) -- moves that engines would disagree with.
For what it's worth I think of him as ~2400 strength.

Such studies, if they even exist, are rather pointless and possibly even biased. Even trying to compare a 19th century play against current standards is totally flawed in so many ways it doesn't even deserve consideration. It's enough to realize that Morphy outclassed his competition to a degree seldom approached since. The only problem lies in the the fact that he never played many of the outstanding players of his day such as Dubois, Petrov, Lange v.d Lasa, Kolisch, a stronger Paulsen and others.

Such studies, if they even exist, are rather pointless and possibly even biased. Even trying to compare a 19th century play against current standards is totally flawed in so many ways it doesn't even deserve consideration.
They do exist, I'm looking at the pdf file now, I can mail it to you if you wish.I believe I'd posted a screen shot or something in some other Morphy forum.
It can more or less assess the level of play according only to the moves played on the board, so the era, opponents etc. are not relevant.
It helps breaking bubbles. Some people here on planet earth still think he was the strongest player that has ever lived. This study convincingly shows he was not even close. That's good enough for me.
You may find them pointless, I don't.

So, if we have the time for the fastest runner in 1900 at 100 meters, we can compare his time against the fastest runner today at 100 meters and make a value judgement?
I would find that pointless in the extreme.

Not sure what you mean with "value judgement", but it would certainly mean today's runners are much faster. As I said, some people still share the opinion that the 1900 guy is the fastest runner to have ever lived. That'a simply far away from reality, and that's just what I want to emphasize.

Objectively, there is no way that a mid-nineteenth century master could compare with a master of today, regardless of his talent or ability. But just as the training methods, even the genetics perhaps, have improved for athletes, the variables (the differences) for play, and not just theory- which itself has been immense- are as complex as they are numerous. So, while you can compare them based on agreement with computer moves, it doesn't mean what some might believe to mean and leaves us with a similar sense of unreality.

This issue having come up in exhaustive number already, I would recall a comparison between Newton (or Leibniz if you prefer) and a student taking calculus today. The student is able to do more than Newton ever did, with a method more rigorous than Newton ever used. But who is the genius?

Thanks, ivandh. That's sort of my point. Not necessarily to say that Morphy was greater than anyone, but merely that such objective measurements, even if they are unbiased, don't reveal what they might seems to indicate. Such as with the first person who broke the 4 min. mile is a greater runner in my opinion than those after him who have to run faster than that just to compete, although objectively he was slower.

Heh, if I ever got to a 5 minute mile I'd be very proud of myself... you have to get 4:xx nowadays before even being considered competition worthy? Wow

Speaking of Newton, he has a fairly famous quote on this very topic:
"Morphy is the best chess player ever to have played the game." - Issac Newton
Hmmm....
Wait -- here's the quote I was looking for:
"If I have seen a little further it is by standing on the shoulders of Giants." - Issac Newton

A capacity which has allowed humans to thrive as much as we have. We don't have to discover things for ourselves to believe them as true and can even work on from those points toward further improvements.
In fact we're tuned to absorb so effectively, that as teenagers when we first consider scrutinizing something an authoritative figure has said it's thought of as a novel and exciting idea.
Ok a bit off topic, but it's something that interests me. I think it takes a certain level of energy to be able to scrutinize new information (obviously no one has enough time or energy to scrutinize it all) and so even as adults we constantly make assumptions about things we physically/mentally aren't able to verify ourselves.
As a philosophy gal, I'm sure Trysts could go on about Epistemology.

Hm... but then again, Morphy's greatness (defined as being an outstanding player in his day) would seem to have been primarily due to natural talent, in some combination with having had a wealthy and chess-friendly family, or am I wrong about this ?

I used to run up until just a couple years ago, for fun not competitively, and certainly not for speed and never timed myself. But I doubt I could have even approached a 5 min. mile, maybe 7, but probably closer to 8 or slower.

What does wealth have to do with it? Most amateurs, not all of course, of that time had money in order to have the leisure time for chess. Talent has been debated ad nauseum. I won't even get into that.. but Morphy was blessed with an incredible memory and a fertile mind, inside chess and outside chess. Having a chess-friendly family is always a plus- but one the other hand, it was his family to a great degree that dictated his premature departure from chess. Morphy's greatness was predominately that his understanding of chess was clearer than his contemporaries, coupled with his fearlessness OTB.

I used to run up until just a couple years ago, for fun not competitively, and certainly not for speed and never timed myself. But I doubt I could have even approached a 5 min. mile, maybe 7, but probably closer to 8 or slower.
The crazy thing is those Olympic marathon runners are basically running 26 6-7 minute miles back to back.
I meet people claimed he who claimed he was the strongest American player to ever live. What always bothered me about this statement is how few games he played nor do i have any idea how good was his opponets over all
My basicx question is for that time period just how do we rate Morphy or the others