Score of Demarcation

[Mike White]

Standard statistical rules:
* 67% of all results will be within one standard deviation (98% within two standard deviations)
* That is ~17% cut off of the high and low ends

Most statistical process control systems use 1 standard deviation to indicate where normal lower boundaries should be set. If you are outside the boundaries once an adjustment should be made. If twice in a row then something is terribly wrong.

you may comment that this requires a normal distribution. Bowling scores are actually log-normal but if you look at the distributions the normal curve effectively describes the distribution. By putting the boundaries based on rank order of scores this works for log normal and other similarly skewed distributions.

The point is that by knowing where you normally score you set a realistic floor to be upset about and a realistic threshold for a great game to be happy with. At the 17% boundaries, for me that is a low game of <151 and a high game >192. Without that knowledge I tend to fixate on the few games >210 and think that I should be doing that all the time. And i hope to improve so that is the case. but right now I should be happy with a 195 as that is better than normal. I also shouldn't be too bummed out about rolling a 168. while it is more than 10 pins below average for me, it is normal. I track and adjust my limits as the season goes on. That way changes (whether to my bowling or the scoring environment) keep me properly assessing my results.

That was a much more knowledgeable response than I expected.

However, by selecting a value you estimate will be about one standard deviation below average, you are setting a threshold that you would expect to meet or exceed 84% of the time..

"If you wanted to do it right, you would bowl at least 30 games whatever the 6th worst score is is where you you expect to normally be above (standard statistical rules)."

Is there a defined percentage value indicated when using the word "normally" as you have?

To me, normally, would be similar to usually, or more often than not.

Those imply a probability value of 50%

You could select your average, and assume you will meet or exceed that value, but that depends on your distribution of scores.

Using standard statistical rules, your best estimate would be the median of scores previously shot.

By the definition of the median, you have met or exceeded that value 50+% of the scores achieved.

median:
noun
1. Arithmetic, Statistics. the middle number in a given sequence of numbers, taken as the average of the two middle numbers when the sequence has an even number of numbers:
4 is the median of 1, 3, 4, 8, 9.

[Amyers]

Thank you guys for turning the post into statistics 101. lol

[JJKinGA]

Mike, as far as normal - i would say that you would disqualify if you were hurt, overly tired, not trying your best, bowling when you know the pattern is unusual (like the Sunday after Thanksgiving when there hasn't been a cleaning/re-oiling for three days). Pretty much anything that makes you certain that regular variation is not happening. If brought that up only because there are times that it is obviously not normal. If you try and rig the system you won't get good results from the math. Garbage in = garbage out.

You are also right that you could double that reduction from your average and get close to the OP request for absolutely should not cross line. (But everyone knows they suck if they are 50 pins below average).

[JJKinGA]

BTW, the overly tired comment is a true experience. One week I had an issue with a home invasion threat and went to league the following night on about 2 hours of sleep. I didn't break 400. It was apparent mid-way through the first game that I just could not focus enough to bowl well (not only sleepy but emotionally drained). My teammates asked me to hang in there and do my best. In reality I should have just taken the blind score. I was in no shape to bowl.

[2handedsniper]

400 for me

[Mike White]

Mike, as far as normal - i would say that you would disqualify if you were hurt, overly tired, not trying your best, bowling when you know the pattern is unusual (like the Sunday after Thanksgiving when there hasn't been a cleaning/re-oiling for three days). Pretty much anything that makes you certain that regular variation is not happening. If brought that up only because there are times that it is obviously not normal. If you try and rig the system you won't get good results from the math. Garbage in = garbage out.

You are also right that you could double that reduction from your average and get close to the OP request for absolutely should not cross line. (But everyone knows they suck if they are 50 pins below average).

Your full sample size should include times when you were hurt, tired, etc.

If you know know the situation ahead of time, you can only include in your calculations those previous times where the situation matched the current situation.

This is why football has injury reports.

Bookmakers use this knowledge of altered situations to recompute the new expectations.

But that really doesn't address the OP's question.

What the OP's question does, is show that the statistical model is the wrong tool to answer the OP's question.

The OP wants to NEVER go below some threshold.

That would mean you would need an amount of standard deviations that covers not 68%, but all 100%.

Mathematically, that would be infinite standard deviations.

What we do know is the absolute minimum score in bowling is 0.

So it looks like 0 would be the threshold to never cross below.

Using another line of reasoning...

If you pick an arbitrary number such as 130, and ask yourself, how bad does things have to be to achieve 130, and then how much worse does it have to get to achieve 129.

Clearly if you can get down to 130, you can get to 129.

Repeating the same logic, you can get to 128, 127, etc.

Therefore, the obvious answer remains 0.

If you shoot a 110 game, it's part of who you are.

Popeye, and Forrest Gump's Mama probably put it best.

"I am what I am", and "Stupid is as stupid does"

[fordman1]

If memory serves correctly from 25 years ago at work we used 3 standard deviations.
No computers just a calculator and a paper chart.
We plotted the readings (game scores) and after 30 games put in a line with the average. Say 200
Then on the bottom we put in the difference from game to game say 180-176-222-211-230-200 etc
Then got a average of the differences 4-46-11-19-30 the avg. would be 22
Then mult. by 3.27 and got so the difference would no more than 72
Then the top was by 2.66 meaning no score would vary more than 53 pins son between 253 and 147.
I haven't done it in years but that might be close.

[billf]

Acceptable low score? It doesn't matter as it is what it is. If I throw the ball like crap then I expect to score like crap. Of course there are times when you score well but throw it horribly. I'm learning to only worry about what I can control. Focus on proper execution each and eery shot and hopefully the scores will take care of themselves. Getting too high or especially too low due to score doesn't help anyone.
"What do I need to do to win this frame?" Before you realize it higher games and series start to follow. ****If you have any talent of athletic ability. I don't have any bowling talent other than coaching some damn good athletes****

[Tony]

Bowling is first and foremost a contest, so taking that as the critical factor in all of this wouldn't the minimum acceptable score be one pin more than your opponent.

[Tony]

On the sidebar of being able to score bowling, I began bowling in the dark ages before automatic scoring systems, we were glad to get the overhead projector with transparent plastic sheets allowed the scores to be read without walking up to the scoring table and looking at the paper sheet.
I also bowled with a couple of crazy engineers, who thought that scoring the night using roman numerals would be a fun idea, to keep it symmetrical we also scored the other teams sheet, I lost interest somewhere along the line but I do recall it being a challenge to keep everything in roman numerals.