The numbers game

[Mufti]

Thanks for all the input, revised spreadsheet now created.
In order to keep it small I have created good and bad day charts.

Luckily (I am not sure it was by design) a good day boosts each distance by 12 (not 10) per dozen and almost matches the reconing of ASW1973.
The bad days boost by 8 per dozen at each distance.

Currently I hope to shoot approx 1000 made up of 450, 350 and 200.

So to sum up :- shoot 6 arrows at 100 yds find an average match on the left and look across to the right to find a hopeful total score for the day (either good or bad)

Link again http://www.angelfire.com/planet/mufti/Spreadsheet.htm

[LineCutter]

Originally Posted by Mufti

Thanks for all the input, revised spreadsheet now created.

Not wanting to blow my own trumpet (or maybe I do), but have you tried FullMonte?? (You'll have to head back to page 1)

[Mufti]

Originally Posted by GeoffT

20 handicap (compound MB) 94, 100, 105, 107

28 handicap (c bowman, r MB) 83, 92, 100, 103

36 handicap (r bowman) 68, 81, 92, 97

44 handicap (r 1st class) 47, 64, 81, 89

50 handicap (r 2nd class) 30, 48, 69, 80


None of these approximate to 10 points per distance

Really useful numbers when you haven't any handicap figures - thanks!
r MB numbers improve by 8 per dozen at each distance.
r B numbers improve by 12 per dozen at each distance.

Wouldn't mind betting that 1st class is 16 per dozen at each distance?

now on my chart..

[Mufti]

"I will shoot all Master Bowman scores this season".
Not a bad aspiration one would think.

What do I have to score to meet this goal?
Look it up in a chart of some sort, but what do i have to do with my arrows I ask myself?

I would have to shrink my group size to something less than I did to achieve my Bowman qualification.
So far so good, but how much smaller?

Can I reverse-engineer it?
What size group did I have to shoot to get Bowman?

So many questions!

We know the size of a target.
We know the size of the colour rings.

Can we also assume that all groups are centered on the gold?
Can we also assume that all arrows are scattered at random within this group?

We can? Then onward!

Let's take an example group of arrows.
The diameter of this group is the same as the outer ring of the red zone on a target (all arrows will be scoring 9 or 7)

Given that we know the size of the gold and the size of the red we can calculate it's average score if they are randomly positioned.
The area of the inner and outer red zones on a target is 3 times that of the gold - amazing eh?
For every 4 arrows shot, 3 will be reds and the fourth one a gold.

Given that a Master Bowman's score increases by 8 per dozen arrows with the decreasing distance on a York round.
(I will grant you this is a lot of givens!)
We can deduce what size group I would need to shoot at 100 yards to achieve a Master Bowman's score!

Not only that!

Once we have calculated all the areas of each colour we can work out required group sizes for ALL classifications.

If only we could centre on the gold and shoot arrows at random within exact group sizes every time!
Being human we have good shots and bad shots throughout a competition, wouldn't these average out to the same thing?

So I set about my task:

Calculator at the ready I worked out all the areas for each colour on a target
(I didn't really, I drew circles on a computer and got the software to tell me the numbers).

Did you know there are over one million square millimeters on a target face?
I have always had trouble imagining a million of something, at least now I have something physical to look at!

Then I took percentages and worked out what an average arrow would score within a given group size.
Then multiplied that by 6 dozen (York first distance).
Then added my 8 per dozen increase for a Master Bowman and worked out totals for a full York round.
Then dismissed the obvious nonsense scores (Master Bowman score is between 1065 and 1134 currently).
Then I ran my numbers back from the score to the original group size that generated it and Voilà!

I have to score 26 per arrow at 100 yards! ha ha, no I'm j/k.

Maximum group size at 100 yards to achieve a Master Bowman score is "inner blue".
Maximum group size at 100 yards to achieve a Bowman score is "inner black".
Maximum group size at 100 yards to achieve a 1st class score is "inner white".

We knew this already - or at least guessed it, but now I have proven it with numbers.

http://www.angelfire.com/planet/mufti/groupsizes.htm


I really must get out more.

[LineCutter]

Originally Posted by Mufti

"I will shoot all Master Bowman scores this season".
...
I really must get out more.

You forgot the normal distribution, which can be approximated using your computer's random number generator & central limit theorem. [e.g. plot a histogram of the outcomes of: sum(12*R)-6, where R=Random number from 0 to 1]

[Mufti]

Did I?

Sometimes we get a good shot off (a 9) others may be a white or black.

The average group size would resolve itself (assuming you get more higher scoring arrows than lower ones) into a group size dependant on your skill and therefor class.

If I were to score a 3 or a 1 you can be sure I would shake myself down and shoot 2 or more really good arrows to make up for it and thus maintain my average group size.

Or at least try to

[LineCutter]

Originally Posted by Mufti

Can we also assume that all arrows are scattered at random within this group?
We can? Then onward!

This is the bit I was disagreeing with (& that you said you would not accept in yourself).

Originally Posted by Mufti

The average group size would resolve itself (assuming you get more higher scoring arrows than lower ones) into a group size dependant on your skill and therefore class.

The average score may well work out that way (but that's a matter of taking the qualifying score & dividing by the number of arrows), but the distribution of the group should be centre biased. That's what we're aiming to do after all. So a group consisting of mostly golds with a few blacks & a miss may well make GMB, whereas a group with a perfect circle of blues would not.

The maths isn't that important - get the smallest group you can, get the highest score you can & then work out what it means for the classification.

BTW does anyone find it strange that if a score is tied it's the one who has the worst consistency who gets the win?? (i.e. the most golds, despite the scores being equal)

[Mufti]

Yes, I have thought long and hard on this and tried to relate it back to longbow/older style scorings. It just doesn't make sense.

I have always disagreed with it.

[Mufti]

Originally Posted by LineCutter

... whereas a group with a perfect circle of blues would not.

And I tried to go for the RANDOM effect to avoid the "all blues" scenario.