Why is scoring a ten so hard?

At the end of an enjoyable morning's shooting yesterday, we got talking about the size of targets. I have covered this subject in an earlier blog post (Small or far Away?), but this time Martin R mused about what proportion of the target face would score a one (imperial scoring) compared with scoring a gold.  Knowing the size of a face, the number of scoring rings and the equation for the area of a circle (I knew that Engineering degree would come in useful one day), I decided to fire-up Excel and see what numbers fell out.  The results surprised me!

Ring	Metric score	Imperial score	Outside dia(cm)	Inside dia(cm)	Area (sq.cm)	%area (metric)	%area (imperial)
Outer white	1	1	122	109.8	2221.07	19%	36%
Inner White	2	1	109.8	97.6	1987.28	17%
Outer black	3	3	97.6	85.4	1753.48	15%	28%
Inner black	4	3	85.4	73.2	1519.68	13%
Outer blue	5	5	73.2	61	1285.89	11%	20%
Inner blue	6	5	61	48.8	1052.09	9%
Outer red	7	7	48.8	36.6	818.29	7%	12%
Inner red	8	7	36.6	24.4	584.49	5%
Outer gold	9	9	24.4	12.2	350.7	3%	4%
Inner gold	10	9	12.2	0	116.9	1%
					11689.87

Before looking at the results, it is worth looking at how the calculations are done.  I decided to work with a 122cm diameter face, the largest in common usage in target archery.  There are, of course, ten scoring rings on a standard face, two each of white, black, blue, red and gold, working from the outside inwards.  Each of these rings is the same width so it is easy to find that for a 122 cm face, each ring is 6.1cm wide (122/20).  The inner gold is the only complete circle, having a diameter of 12.2cm.

To work out the area covered by each of the rings, simply calculate the area of the circle from the outside diameter of the ring then subtract the area of the circle from the inside diameter of the ring.  If you cast your memory back to your schooldays you will recall that the area of a circle is Pi times the radius squared.  Using a spreadsheet means that you can do this fairly easily, but it might help to know that in Excel, the function PI() can be used in a function instead of typing 3.1.4159265.....

The actual areas of each of the rings are shown in the table above.  I then summed them before calculating the percentage of the total target area for each ring.

As I said earlier, the results surprised me.  What immediately stood out was the difference in percentage area of the outer white (19%) and inner gold (1%).  The 19% figure wasn't that much of a shock, but the 1% definitely was.  To score a ten, you need to almost twenty times as accurate as scoring a one.  That probably explains why I get significantly more ones than tens, and has nothing at all to do with my ability!

The other oddity I noticed was that the percentage areas form a linear progression: 1%, 3%, 5%, 7%, 9%, 11%, 13%, 15%, 17% and 19%.  There is probably a sound mathematical reason for this but I cannot work it out.  let me know if you find out!

The above calculations are based on ten-zone, metric scoring, but you can easily find out the area percentages by summing the two figures for each of the coloured scoring zones.  I have included these figures in the table above.

So, what about the smaller targets?  Clearly, the areas will be smaller, but the proportions of each of the scoring rings are identical to the 122cm face, meaning that the percentages will be the same regardless of the overall diameter.

Equipment Failure Annoyance

Mrs EA and I have decided that we are never again going to shoot on the same boss in a competition, if at all possible.  Why?  I hear you ask.

Last Saturday we took part in the King's Cup, an indoor FITA 18 competition run by Chessington Bowmen.  We regularly shoot with them in this venue and had been looking forward to the day for a while.  There were three sessions timetabled during the day and Mrs EA and I were booked into the second of the three.  Because he entered later, EA jnr was shooting in the final session of the day.

We arrived in plenty of time and set up our bows.  During practice Mrs EA found her arrows flying too high and adjusted her sight to compensate.  However, the adjustment didn't seem to be doing anything.  Eventually she realised that turning the adjustment knob did not moved the sight block as expected because the block was not free to move.

The only thing that had changed since the sight's previous outing four days earlier was that I had changed the grub screw securing the sight pin to a more robust, socket-head screw.  As an aside, I had to do this on my own sight a couple of weeks earlier because the sight pin kept shaking loose between ends, and the grub screw did not allow for sufficient tightening without burring the hex socket.  I found a suitable screw (M4) in my box-o-bits (rescued from a dead shower mixer!), but when I tried to replace the same screw in Mrs EA's sight, I found that the thread was different (M3).  They are both SF Elite Carbon sights, but hers is a few years older than mine, and there are a couple of other, minor differences if you look carefully.  I ordered a pack of 10, M3 screws from my favourite eBay supplier and fitted the screw on Friday.  The sight pin has not moved since.

Back to Saturday - Mrs EA was getting more and more frustrated at her sight not being adjustable and it was affecting her performance.  Her blaming me for the problem was affecting mine!  I did manage to moved the sight block enough for her to get some accuracy, but she did not regain her confidence.  I was distracted enough to pull my arrows before scoring on one end! We both ended with our worst-ever scores for the FITA 18 round and the only saving grace is that I didn't come last.  Whilst putting away our kit we noticed that we seemed to be the only couple who were shooting on the same boss, so we have decided to request being separated in future!

Having written-off our session we sat down to watch EA jnr in his.  This was his first time scoring an indoor round shooting compound and he was the only junior compound entry.  The other three compound archers on his boss are all very capable, so any bad shots from him would be apparent.  He ended with a score of 445, which is very creditable given the circumstances, and it put my score of 275 in stark contrast.  As the only competitor in his class, he was awarded gold medals for the session and for the overall competition.  Some might say that he got them by default, but many people were impressed by his performance and were surprised that he had only been shooting compound for less than a month.  Because there are so few junior compound archers around us, he will be setting new club and county records rather than breaking them, but I guess someone has to be the first. Perhaps it may spur other juniors to try compound, too.

Back home after the competition I took a good look at the offending sight and I think the problem was a combination of things.  The previous weekend, Mrs EA had tightened the retaining screws that pass through the block onto the vertical track because the block was wobbling.  This did not cause any problems until the block was moved to the very top of the track, where it wedged.  Any attempt to use the screw adjustment resulted in a click and no movement.  By the liberal application of some WD40 and the use of an old toothbrush, I cleaned out the block and removed a lot of dirt from the threaded rod.  The block now moves freely again.  The prospect of having to buy a replacement sight on top of all of the other changes was not very welcome, but this one is clearly reaching the end of its (reliable) life.   Mrs EA has hinted that it could be a good birthday present, so I have until July to save some pennies.

Domestic bliss has been restored.