Your giving a mathematical exposition on a hypothetical bowling game that just lacks the merit of being realistic.

Having come through every level of bowling I am forced to say that it is extremely unlikely for two bowlers to consistently exhibit the kind of games you are describing. It might be possible for a bowler who is bad to once in his lifetime throw a five bagger ( 5 in a row ). A pro can do that at will.

To throw strikes consistently, you have to roll the ball at the correct speed and the correct number of rotations. You must hit an area around the pocket ( about 2 inches ) from 60 feet away. The bowling ball must not deflect off the headpin in its path through the pins to the gutter. Your timing must be so accurate that your left foot and the ball must reach the foul line at precisely the same time in order to have a powerful release.

For someone to throw 4 strikes in a row and then all gutterballs on a consistent basis is so rare that there is no reason to change the game to suit this hypothetical person. Also such a person would have a score of 90, quite easy to beat by even a 120 average bowler. The four strikes do not nullify the cardinal sin of professional bowling: Never leave an open frame!

]]>Makes

perfect sense to score

consecutive strikes as they do.

No, it's not to me.

Hypothetically, a bowler could get three (or four?) strikes in a row in the

first three (or four ?) frames and then get all gutter balls, showing he

can't maintain. Not only are the points in his frames inconsistent,

he "goes downhill" to 0 on the gutter ball and stays there for the

remaining frames of a game.

While another bowler could throw five strikes about evenly spaced out,

with gutter balls in between, and score less than the previous player.

The points in his frames would have a closer to symmetric form

(a greater relative consistency), and he wouldn't be suffering from a

downward trend of decreasing strikes.

It'd be similar to a student answering the first 3 (or 4?) questions

on a 10 - 12 item multiple-choice quiz correctly (and the rest wrong)

and being awarded more points (a higher grade) than a student

who would get 4 to 6 questions correct in total. And these would

be about evenly spaced out as possible for the questions which

were marked correct.

And, across 3 consecutive games (max. total of 900 points), the

first bowler could bowl 5 strikes in the first 5 frames, and 5 gutter

balls in the last five frames in the first game. And then bowl 4

strikes in the first four frames with 6 gutter balls in the last 6

frames. And in the third (last) game, that bowler could throw 3

strikes in the first 3 frames, with 7 gutter balls in the last

7 frames.

In contrast, the second bowler could bowl more strikes than the

first bowler did in his respective games (the rest gutter balls),

but spaced out with a lower official bowling score per respective

game.) Not only would the second bowlwer be getting more strikes

than the first bowler in each game, but the first bowler's performance

would be getting worse with each successive game.

For the professional or the strong scratch league bowler that is the point. Stringing strikes shows that you are locked in on the lane. That you understand it. That your form ( stroke ) is perfect and in harmony with the lane. That your ball speed and number of rotations is perfect. That you are capable of rolling the same shot over and over, the mark of a pro.

For ordinary bowlers 150 - 160, strikes are a random event, for 180+ bowlers they are the culmination of years of practice. Makes perfect sense to score consecutive strikes as they do.

]]>weight in the total score, in my opinion.]]>