Trevor,
If you think I am misunderstanding your argument, than make your argument clearly and concisely. As far as I can tell from some of your prior postings, you seem to think there is something wrong in the way the sim generates the random numbers moreso than the fact that they are generated, which is really an entirely different issue altogether (technique v. theory). That certainly isn't the issue that others are raising or that I am defending. Maybe you are right about your allegations, but given that you are complaining about methods that are behind the scenes and you don't have access to, I'm yet to be convinced that you really even know what you are talking about, let alone that you are right.
I do think you are confusing the issue relating to the real life player versus the stat table. The stat table is made up of the varying performances of the real life player, and these performances should probably be viewed in terms of possessions rather than in terms of games, or even minutes. By necessity, there is variation among possessions (make or miss, rebound or don't, turnover or don't), and these are used to determine various percentages of certain things occurring, which when matched against similar percentages derived from the other players on the court and certain other inputs (tempo, defensive positioning, doubling, etc.) determine the odds of certain things happening in a given possession. Yes, the stat table has a static probability of a certain result given control of all other inputs (which are substantial) while a real player's probability of a certain result would be fluctuating constantly. However, over the period of the stats that the real player generates, he is no more random that the stat table generated because once generated, the stats don't change.
Obviously, it is too complicated to incorporate every variable that impacts a real player so using the actually generated stats incorporates all of those variables in shorthand. No, it isn't exactly the same, but then most of us just want a playable game, not a simulation that is able to faithfully recreate some player's off night on the twenty-third game of the season.
Your last points are rambling. The game has gotten progressively worse? Well, I'd agree that the last major changes were a step in the wrong direction, but that has nothing to do with randomness. Many have cited bizarre/unjust results? Perhaps, but most bizarre results have a limited impact on the results of a season, and "unjust" is a subjective term. That is due to extreme randomness? Sure, some of the complaints are about randomness, and the majority of these come across to me as someone complaining because they didn't win. It isn't that they never win since they win often (as Ash so vehemently points out in his last post), but they didn't win this time so the sim must be broken. Personally, that all comes off to me as "sour grapes". But even you can't pretend that that is the only complaint ever voiced since you back off and admit there are "other arguments and reasons to leave". So much for your proof, let alone speaking for those who don't ever give an indication why they are no longer playing.