Scoring Spread v. Skill Level: A Theory
I was reviewing my scores and those of all the rest of the gutty and brave souls participating in this DM Holiday bravery exhibition....
Let me warn you now, this is going to get a little geek-like
, but there's this theory I have. If someone in the group is a statistician, please feel free to evaluate this theory for its validity. If it is valid, then a predictive model could be built...well, more on that concept later.
The Cardinal's Theory of Relative Consistency:
When you first start playing, you will be consistent - consistently bad; all your racks will be close together in scores of 0,1,2,3,4, or 5. You just cannot shoot well enough to score above a few balls consecutively.
As you improve, your scores will become inconsistant...the consistency will evaporate because - on occaision - you can string together a few balls, and get a higher score, maybe even in the double digits - so the "spread" of your scores will be greater. This will last a long time as you progress.
As you further improve, the consistency of your scores will further decline as you gain the (shooting and positioning) skills necessary to run out from time to time - so you'll have the occasional 18 or 20 on a rack, but, just as often you'll have a 0,1, or a 2...and pretty much everything in-between. As a middling player, the dispersion of scores would be the greatest around both sides of the mean value....
You improve some more, and the incidence of 0,1,2 scores starts to decline, so the dispersion is actually starting to narrow - you are getting more consistent. Mentally though, you are probably starting to get really distressed about these low scores "ruining" your average / total score. I kind of think many of us are in this phase in this tournament (from "Advanced" to "Semi Pro" levels). I am for sure. I feel that I ought to knock off at least 10 balls
every rack - but I don't really, I average 10 - and I do get some 20s - so that means I gotta have some zero to 7 scores too (and, yeah I do, including that one damn 00 which really pissed me off
until I realized a minus 1 was possible!
).
At the higher regions of skill (where I am not, but aspire to be), say averaging 15 per rack, the consistency of scores starts to come together again; but now the spread is tight around a high level. The low end of scores has come up - players of this caliber just don't score below 5; if they do its a real unusual occurance, an outlyer.
And, then at the nirvana levels, the consistency is super tight around the mean again (as it was for the beginner), but of course around a very high average like 18.
So what? So, for the most of us toiling in the 7 to 14 average per rack range, you should expect a certain number of very low scores - and you'll also have some 18's & 20's - that's how you average in this range. There's no real reason to be upset that you are inconsistant. You are, by definition.
And, now, that would make me think I could potentially spot a dissembler...
Consider these two outcomes:
14, 04, 06, 20, 00, 14, 12, 14, 06, 10 = 100
10, 09, 09, 11, 12, 10, 09, 08, 12, 10 = 100
The first set of 10 racks is, I think, pretty legit; players good enough to average 10 are - by definition - good enough to run out every so often, but not good enough to avoid dreadfully low scores either.
The second set of scores is just
too consistent around the mean average of 10 - nothing lower than an 8, nothing higher than a 12. If you are good enough to average 10, well then every once in a while you ought to be able to score high in the teens! Put another way - if you are good enough to avoid
ever scoring below 5 or 6, then you are definitely good enough to run out every so often.
I conclude the second set of scores are suspicious, and probably come from someone who is jiving.
Any statistics mavens out there could use the scores from this year to test my theory; quantify the expected variances vs averages, build the model....
