In your opinion, what is the difference between the tournament bowler who averages 190 on an off day as compared to the tournament bowler who averages 200, even 210 on an off day?

As with dmonroe814, I'm a little confused with the question, but will take a stab.

My observation would be that the higher average bowler is probably more consistent at converting spares.  Maybe he's more consistent on his first ball accuracy, and thus leaving easier spares; or maybe he's better at reading ball reaction and chooses a ball that has a higher carry percentage.  The potential options are too many.

What seems to be proven is that day in and day out he scores a little higher than the other, thus the higher average.  Over a period of time an average is a fairly true picture rather than an anomaly. 

Lane conditions bowled on are another factor.  Perhaps one bowler competes on more forgiving conditions... 

I do believe that good spare shooters do get their fair share of strikes, because the same accuracy required to be a good spare shooter can be applied to their first ball.   

This may, or may not, be of help with your question, but it's a stab.

It depends on what causes the " off day".  If you are talking about bowling on house shots, I would just say the guy averaging higher on the bad day is simply more consistent in his execution.  It isn't about versatility on house shots.   

One thing I do remember from about 15 years ago when I set a city average record of 237 ( it didn't last very long ).  I always thought the difference between me and 3 or 4 other guys who were at 230+ was that my bad nights were never below 640 or 650, partly because I was a very good spare shooter.  Lots of nights I would have a little 200 with several corners in the first or second game, but if I stayed clean there always seemed to be a 250 or 260 before the night was out.