Good questions, I mean good questions, young man. I'll answer them as I am able.
There's only one Roshambollah in the world, and I am he. Challenge forthcoming.
I could not disagree more as to your premise that Roshambull stats would be complementary to live tourney data. The overall throw distribution may be similar, but a mere tally of throws does not take into account qualititative analyis. I don't have anything against online fantasy RPS, but there are a distressing number of players who are starting to confuse it with the real thing. It's like comparing a futbol simulation (say, a video game) with a real match. The rules may be the same, player stats may be similar, game scores may be similar, even the "look and feel" may be similar. But at the end of the day, it's just a video game. It resembles the real thing, but it's not the real thing. Online RPS is a fun social game for some, and can be a useful adjunct for beta-testing strategies "in a vaccum" if you will, but that's about it.
You make a couple of assumptions about real-life RPS tournaments. The first is that all players present are fully aware of Game Theory and how it relates to RPS. No, most players just show up because it's a fun social activity, and there's the chance to win some money. Fair enough, but these players are the "bread and butter" of Pro Players. It does not occur to such players that they have to work in order to "play randomly"; they think they're already playing randomly, but they do have certain statistical tendencies (I could tell you what they are, but I'd rather sign you up to Roshambollah Learning Systems - the game is to be sold, not to be told.)
You are correct in your assumption that many players do indeed play pre-determined throws, but not just for the reason you mention, e.g., average players trying to get a leg up on the Pros. Professional Players such as "The Legend" C. Urbanus also use "scripting" as it is the ultimate in non-reactive play.
It is true that average or sub-par players can improve their performance by adopting a random or pseudo-random approach instead of playing reactively. However, not only does random play not improve your chances above 1/3 in the long run, there is also a strategy that works against random play, without cheating. I have been meaning to write a treatise on this strategy for some time, but for now I'll just refer to it by its proper name: Precog, short for "Precognitive Play." Precog is one of the highest levels of RPS strategy, but an advanced practitioner can use it to trump random much of the time. An active application of Precog ("Mind Control") can be used to force another player to change his or her throws, even if that player is following a random script. I realize that occult manifestations may not fit into your academic data model, but no true Pro Player doubts its existence. "He who has the how is careless of the why."
You may indeed find correlations between Real Professional RPS players and their performance in fake online RPS; indeed, on Roshambull, several names in the Top 10 are are not unfamiliar to students of the sport. Expert and Master level Pro Players may use their advanced knowledge of RPS Game Theory to gain an edge in fantasy online RPS (in much the same way that some National Football League players also "manage" fantasy football teams.) However, there is no real causal relationship, especially when one considers the fact that fake online fantasy RPS players are completely unknown in Professional circles.
Again, and I can not say this too firmly, Real RPS and online rps are two different animals. I would be very wary of making too many connections between the two. If you do, you run the risk of "creating the data" and forcing it to fit the model you have already determined, anathema to true academic excellence.
There is more to RPS than mere "physical" and "predictive" aspects. To continue with the use of words that start with "p", there are also the "precognitive" and "paranormal" aspects.
Not to mention that there are also metagame concerns; a Real RPS Pro may happily lose a few matches on purpose, even tournament matches, in order to maneuver for a greater win later. This is so common an occurence, it barely deserves mentioning...
Still, we Pro RPS Players love academics; Don McKeown, graduate student of Sociology at U Calgary, is currently working on a study involving the sociology of RPS as an emerging sport. He is a thoughtful student, and he picks up a mean bar tab. RPS, by its very nature, is more suited to the soft sciences. Still, many Pro Players may hope that if the results of your study are publicized, they will be able to gain a further edge over the average player by inverting expectations. For this, and many other reasons, I wish you the best of luck with your study. If you have any further questions, do not hesitate to ask.