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Wrap Around Scoring for Bowling

no need for specialness of first and tenth frames
  (+11, -2)(+11, -2)
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In standard ten pin bowling, each game consists of ten frames. In each frame, the bowler can achieve an open frame, a spare, or a strike. An open frame is achieved when the bowler fails to fell all ten pins in two throws, and the score is the number of pins that were felled. A spare is achieved when the bowler takes two throws to fell all ten pins, and the score is ten points plus the number of pins that the bowler fells in their next throw. A strike is achieved when the bowler fells all ten pins in the first throw of the frame, and the score is ten points plus the number of pins that the bowler fells in their next two throws. In order to make the tenth frame equal to the others in possible points, the bowler can make one or two extra throws if they achieve a spare or a strike in that frame; and the pins felled in those extra throws only count as the bonus points for that spare or strike, and not as points in their own right.

As a consequence of this scoring method, there are a couple of side effects that I think are undesirable. The first is that it makes the first frame "special" in that any kind of spare achieved in it is worth exactly the same. For example, if a bowler achieves a spare in all ten frames, there would be ten total first-throws, only nine of which would count as bonus points. Lets say the first throw in the first frame is one pin, and then in every other frame the first throw is nine pins. The bowler's total score would be 190. But if that one-spare occurred instead in any other frame, their score would be 182.

The second problem is that the tenth frame is "special". Besides the obvious point that there can be three throws in the tenth frame, and only two in the others, we have the problem that a failure to fell all of the remaining pins in the third throw of the tenth frame has much less significance than such a failure in any other bowling situation. For example, if a bowler is looking at a 4-7- 10 split in the third throw of their tenth frame, they would be motivated to just fell the 4 and 7 pins and not worry about the 10 pin, because going for the spare would put them at risk of missing completely and the possible reward would be small, just one point. However in any other frame, they would be motivated to try for the spare, because there would be another throw right after it and the reward could be larger, up to eleven points.

Therefore I suggest a simple adjustment. Make the tenth frame the same as all the others, and wrap around the scoring. For example, if a bowler achieves a strike in the tenth frame, let them count the number of pins felled in their first two throws of the game as bonus points. If a bowler achieves a spare in the tenth frame, let them count the number of pins felled in their first throw of the game as bonus points. This solves both of the above mentioned problems, and I think it is more elegant.

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Edit:

The only drawback that occurs to me is that it makes it easier to bowl a perfect game, because you would only need ten strikes in a row instead of twelve. One way of dealing with that would be to have twelve frames, a perfect score would be 360, and you would need to throw twelve strikes to achieve it.

JakePatterson, Aug 14 2008

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       Excellent idea.[+]
imaginality, Aug 14 2008
  

       You hit the bun pin on this one! Excellent, wonderfully sensible idea.
phundug, Aug 15 2008
  

       What happens if it's a tournament, head to head? Does a player get to carry those extra pins into the next game against a new opponent? You're describing a system that works pretty well in multi-game matches or league play, but in an elimination style tournament it doesn't.
Noexit, Aug 15 2008
  

       [Noexit] No, no points would carry over into another game. To clarify, if a bowler achieves a strike in the tenth frame, that would be the last throw they make for the game. The bonus points would be figured from the first two throws that they made in the game, which would be from way back in the first (and possibly the second) frames. As a result, the value of the first throw in the first frame matters.
JakePatterson, Aug 15 2008
  

       Ok, thanks for the clarification. [+]. It's been too long since I league bowled to figure out how this would actually work out, but it'd be fun to give it a whirl. Should be pretty easy to experiment with using manual score keeping.
Noexit, Aug 15 2008
  

       Another possibility is you bowl 15 frames ("Amish style" for those who've seen "Kingpin"), and you take the maximum of any 10 in a row as your score.
phundug, Aug 15 2008
  

       Bowling for Buns.   

       [+]
Giblet, Aug 15 2008
  
      
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