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The Hardest Shot in Bowling (slate.com)
58 points by mhb on Mar 10, 2015 | hide | past | web | favorite | 15 comments

Nice article, but the nitpicker/mathematician (is there a difference?) in me spots a flaw in its logic. Maybe, the reason for the low success rate on the 4-6-7-9-10 split is because the really good pros rarely end up with it.

Also, I would like to see a comparison using mirror images for left-handen players.


Also, it's often better to just take the easy 3 pins from the greek church (especially after a strike) instead of risking a complete miss by trying to cover it. Covering the 3 after a strike is +6...missing completely is +0.

Exactly. The author's difficulty scores are not adjusted for risk.

Admittedly, maybe pro bowlers aren't familiar with this one configuration. However, they are incredibly familiar with every aspect of bowling, so if the great majority of them cannot (or will not attempt to) make this shot, it's probably pretty telling regarding degree of difficulty.

Of course they will attempt to make that shot, if they get it, and the game calls for it (extreme example: if they need only 3 pins to win a match, no sane pro would attempt to get a difficult spare of 4 pins that has an easy 3 pin subset)

On the other hand, if you are behind with only a few turns to go, taking the risk of taking on the more difficult throw will be the right choice.

The issue is that the distribution of plays that good players get on their second throw is different from that that bad players get. Let's exaggerate to show why:

Collect all throws on a random bowling alley for a year. I predict that the 1-2-3-4-5-6-7-8-9-10 configuration as the first throw has a higher success rate than as a second throw.

Reason? Players who end up with that second shot must have completely missed the first shot. Good players will occasionally get there (if you wait long enough you will even find a pro throwing it, maybe because he suffers a stroke during play), but bad players will get there disproportionally more often. Of all such second shots, 90+% may be played by the bottom 50% of players.

Similarly, I think the 7-8-9-10 that isn't in this dataset isn't impossible. I would guess children who are barely strong enough to throw the ball will occasionally throw it.

Thinking of it, bowling would get way more interesting if one could get more points for difficult combinations. Let's say you announce "I'll leave the 7 and 10 pins standing and take them out with my second ball", and go on to do that. Surely, that's worth more than a dull strike?

I have seen a 7-8-9-10 both left, and amazingly, picked up. Weird stuff happens when people don't throw the ball hard. This particular feat was by a friend's wife. If you throw directly in the middle of the 8-9 they will fall sideways and get the 7 and 10.

No pro will ever leave this though. Not possible throwing at normal speeds.

How do you choose to not make a shot like that? Every bowler wants to get a strike, and if you fail to get that strike you're not choosing what setup you end up with. If you could choose, you would have gotten that strike.

Edit: Or are you trying to say they aren't going for the conversion, just for knocking down as many pins as they can, when they get there? Does the article's data include whether the bowler was attempting the conversion? My expectation is no, the data covers all frames that include that split, without excluding ones where the bowler has indicated that they're not attempting the conversion.

I'm not a good bowler but I have made the 6,7,10. I think the problem with the "Greek Church" is that you've got the 6,9,10 setup and you're trying to just nick the 6 to send it to the opposite side to hit the 4,7. If you do that, the ball probably sends the 10 to the right of the 9 and you just don't get all 3 on the right side. The mirror image setup is completed far more often because a right handed bowler is aiming at the set of 2 pins (6,10) and the 6 can take out all the ones on the other side while the ball gets the 10. I wonder if the data included which pins were left standing after the failures.

The hardest shot in our local bowling alley is the two lane bounce (onto someone else's game) followed by the car park sprint to avoid the beating that follows such an audacious shot.

Very few make it.

How common are cases like this "Greek Church"? Part of the reason the 7-10 split is iconic is that it's something a beginner sees pretty often.

The rectangle that says "The Spare Success Machine" is interactive. Select the pins and it will give you statistics on that configuration. "Out of 149 times this occurred in the sample of PBA competitions it was converted to a spare 2 times." From a collection of 180,000 non-strike frames.

I am really interested in seeing the rate at which all of those combinations occur in some sort of chart rather than just small text under the calculator.

The 7-10 split occurred 3069 times in comparison to the 785 times of 4-6-7-9-10. The mirrored one only occurred 149 times but was converted the same number of times.

Is there really enough occurrences of these to determine which is hardest?

The numbers aren't good enough to say that any of the five hardest shots is significantly more difficult than the others.

Part of the problem with these stats is that depending on the state of the game the person might not even be trying to pick it up. If you need 2 pins to win, get the 2 easy pins instead of trying to pick up the hard spare where you might miss.

The other thing is that pros don't leave something like the greek church very often. It was left 785 times in 447k frames. The data on picking it up just isn't that significant. It also means it isn't going to get practiced nearly as much as something more common.

Also, there are more right handed people than left, and it shows in the data. mirror image shots aren't "easier," they are just easier for a certain handed player. As most are right handed, the shots that are easier for them will show up as easier in the stats.

It's interesting that the mirror-image Greek Church is converted 1.6% of the time, some eight times more often. One has to wonder, if the stats could be distinguished by left and right-handed players, would the numbers be opposite.

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