Thursday, February 26, 2009

Rare or Impossible Two Pin Leaves in Bowling

Since I started keeping stats on the pins left standing after the first throw, I have recorded 334 pin configurations. Of these, 110 are unique. It is possible to increase this number to 150 with the current count by making a symmetry assumption: if a particular spare combination has been observed, then the mirror image about the midline is also possible. For example, if a 6-7 leave has been observed, then it is assumed that a 4-10 leave is also possible.

To date, I have observed every possible single pin spare opportunity. There are ten of these. Among the bowlers I have observed, the 5 pin is most likely to be left standing when a score of 9 is received on the first ball. A standing 1 pin is the rarest.

This post concerns two pin leaves. There are 45 theoretically possible combinations of two pins remaining after the first ball. Of these, I have recorded a total of 35 when symmetrical pairs are included. I have divided the ten that I have not yet recorded into two groups, symmetrical and asymmetrical. The symmetrical leaves are symmetrical about the midline. The asymmetrical are not:

Symmetrical leaves not observed: 1-5, 2-3, 8-9, 7-10
Asymmetrical leaves not observed: 1-7, 1-10, 2-6, 2-9, 3-4, 3-8

So here’s the question. Have these not been observed because they are impossible to leave, or because they are rare? One of these is obviously possible because we have all seen it, and it is probably the most famous leave in all of bowling, the 7-10 split. It is apparently not particularly common. Is the same true of the others? My hunch is that all of these are possible but one, the 2-3. It is hard to imagine how this could be accomplished without some crazy pin action. Anyone else care to venture a guess? Has anyone seen a 1-5 or an 8-9?


  1. Yet again great research. I truly enjoy the stats you come up with and enjoy visiting the site due to the charts and analysis you come up with. Keep up the good work and good luck on the rest of you season.

  2. Thanks Anonymous! It's good to know that there is somebody out there who appreciates this. Most people who visit this blog do it in a hit and run fashion.

  3. nice, something else to keep an eye out for in my bowling class. we have some pretty lousy bowlers using 6 and 8 pound balls, so I've seen some pretty crazy leaves already, now I know what to look for as rare or unusual.

  4. I have seen the 1-5 left at least a couple of dozen times. Probably the "easiest" way to leave it is to throw a hook and then barely hit the 3-pin on the right side so that it knocks over the 2-pin. I'm not sure if I've ever seen the 8-9, but I have seen the 7-8-9 left a few times.

  5. It is possible to leave a 2-3. I did it once by the five falling into the head pin. Some how when I tried to pick it up I managed to shoot straight through the two pins.

  6. Left the 2-9 last night (and made it). Dropped the ball right of the head pin, left the 1-2-9 (the more reasonable result of the mistake) and a pin on the deck tooko out the head pin.


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