Originally Posted by schmke
I'm a bit confused. The NTRP system does effectively have the 10 levels as there is not a 3.67 level. There is 3.5 and 4.0 and you are one or the other.
But you have to have a way to determine when someone has improved or declined such that they should move into an adjacent level. The NTRP does this through having calculations to the hundredth and established periods at the end of which the rating check and level (re)assignment is done.
In your scenario, how would you calculate when someone should move up or down a level? I think that is what the debate is about, not so much having some reasonable number of levels.
IMHO, you have to go to at a minimum tenths and realistically hundredths to have a reasonable way to calculate ratings based on opponents ratings. Treating all players at a given half-point level the same would not result in an accurate system at all.
You can easily have scenarios where player A, a weak to middle 4.0 plays court 3 and has a good record players just bumped up from 3.5 and gets bumped to 4.5 because he won a lot at 4.0. While player B, a middle to strong 4.0 plays court 1 and loses more than he wins against strong 4.0s just bumped down from 4.5 and gets bumped down to 3.5 because he lost a lot a 4.0. So you have player A, probably not as strong as player B, but A gets bumped up to 4.5 and B down to 3.5, a full 2 levels apart.
As I mentioned in my previous post, what strikes someone as "logical" is going to be based in this case by whether they really believe there is an actual measurable and most of all, reproducable difference between a 3.68 and a 3.69. Obviously anyone can perform the mathematical calculation to come up with such numbers. But is there any data to say that the numbers 3.68 and 3.69 will predict a different outcome in future matchplay (does the 3.69 win more matches)? My guess is there is no such data. Well if there is no difference in matchplay results between 3.68 and 3.69 then from a purely statistical standpoint (this is not my opinion, it is a statistical reality) they should both be 3.7.
In the extreme example of treating all 4.0s exactly the same (1 significant digit), you would use simple won/loss records. It would be an OK system (not great). It wouldn't be very nuanced and would miss outliers who played a skewed set of opponents. But OTOH you wouldn't have cases like a prior thread where some guy goes 9-0 or somesuch and doesn't get bumped. Perhaps that guy played a very odd set of matches, but on the face of it, it looks weird, especially for the next guy who plays him. I gives the impression (perhaps true, perhaps false) that the USTAs system is missing the forest for the trees, or worse.
I get your last paragraph's example, but you know what? The most visible tennis ranking systems in the world (the ATP and WTA) don't use any
opponent ranking information in their calculation of ranking. A trip to the quarters in a 500 level is the same whether you beat the World #1 6-0, 6-0 or if you were LL with three walkovers. You'd think from these boards that the Pro ratings would be all over the place, but except for players coming off of injury, it seems to work just fine.