There is a bowler today with talent to compete at the pro ranks. How many bowling balls are required by that person to purchase  in order for he/she to compete and be successful on the pro tour?  8, 9, 10, 15, or 20 plus?

Much depends on what one views as their definition of "compete" and "be successful." At that level, I would put those terms in the context of making more money in the way of income than is being spent on expenses...and the relationship one has with their equipment becomes far more critical. 

I had regional events where I was in the building with a total of eight balls and I had national events where I travelled with close to 20...and in each instance, I could tell you the relationship between each piece of equipment so that a change in the middle of a game didn't cost me multiple frames trying to get dialed in. 

However, the more you have at an event, the more critical the practice blocks became, as did the winnowing-out process so you knew what to take back to the car/truck compared to what was able to be kept in the paddock (since there was often a limit on what could be in the building outside of the practice block).

There are also going to be those who are in a position to drill up new stuff every week.  Not everyone can afford that since many were going out of their own pockets.  Which brings it back to knowing your equipment...if you don't know your equipment and you cannot pull any ball out and be lined up on the first-shot, it doesn't matter if you only had three balls or if you had 20 to choose from.  But when your livelihood depends on the equipment, you want to be in a position to maximize the prospects of success, and with bowling, that can mean more is better even if only a few actually see action in a given tournament...

And FWIW, I still own most of what I ever acquired, even going back to the late 80's when I first started competing in tournaments...and I have some of my Roto gear that STILL has fewer than 20 games on it even though I carried it for a few years of regional and national competition. 

6 at the most. Surface being one of the biggest factors. You know the patterns for the tournament in advance so making sure you have a good arsenal for that condition shouldn't be too hard. Many bowling balls can be used on several different conditions with the adjustments being to ball surface.

Trying to bowl and be competitive on the PBA Tour with 6 balls would be like someone getting their PGA Tour card and thinking they could compete with Tiger with 6 clubs.

+1

Others have said it, but I will reiterate it, the actual # isn't the answer, it's knowing how they fit into your game and the differences between those balls. You need a progression of equipment and drillings from a piece designed to hook early to ones with more midlane, to ones with extreme length skid/flip. You should know how each ball relates to the others no matter what the surface. When bowling professionally, 2-3 pins can mean the difference between cashing and not cashing, between making match play or not, between making the TV show or not, so you can't take a couple or even 1 frame to get lined up after a ball change.
 
Taking that into account, and thinkign about the different patterns in the PBA today (not including the new animal patterns for the Summer Series, which I don't think are released yet), I would think you would need probably 10-15 balls to cover everything, making surface changes as needed.

There aren't too many guys with tour level talent that pay for equipment.

If you travel with 20 you can probably narrow it down to 8 or so to practice with.  Once practice is over you're probably down to less than 3 or 4 that will actually be usable.  Then you're probably headed to the truck to drill a couple more.  That's just the reality of how it works.  Then there's the guys that want a fresh cover every chance they get. 

Surface is one of the biggest factors in what the bowling ball will do. I've seen and used to be one that was hung up on a drilling that will work magic on this condition or that when used with the right bowling ball.

It isn't that nearly as much as it is the bowling ball and the bowling ball coverstock. Todays bowling balls our literally idiot drill proof.(almost lol) Demo days is a great example, granted normally on a THS, have you ever noticed how great a bowling ball rolls for so many bowlers when tested at a demo day event where the ball is not specifially drilled for one specific person?


Simple question just for fun. Do you think the reaction difference in a bowling ball for a given bowler with a pin 3" from the pap versus 5" from their pap will have a big difference on the lane?

What about moving the MB instead, say near the thumb versus near the players track?

(All bowling balls above would use the same layout specs, only with a different pin to pap in the first example, or a different mb angle in the second, all other information would remain the same.)

Many people do when laying out a bowling ball, or having multiple bowling balls for a given condition.