Archer assessment sheet
An A4 sheet to take to the range: each of the archer's numbers is set against a reference for the level, and each change against the swing of chance, before any conclusion is drawn.
This sheet is for assessing an archer on the range with pen and paper, and it answers two questions: where each of the archer's numbers sits against what is normal at that level, and whether a change between before and after is bigger than the swing of chance. It holds the reference tables (the floor by level, the rounds it takes to confirm a difference, the expected percentage of Xs), a box for working out signal or noise by hand, the directional test and space for three training priorities.
It prints on a single A4 sheet, and only the sheet comes out, without the rest of the page. Straight after it you will find two calculators that do the same sums on screen, with the working shown step by step; further down, how each part works, how to read the results and where the limits are. Everything stays in your browser: no data leaves your device.
Range assessment
Archer assessment sheet
Every number is set against a reference for the level; every judgement, against the noise of chance.
Reference tables
| Average level | Pure bell curve | Model with tails |
|---|---|---|
| 600 | 9.9 | 10.9 |
| 630 | 8.1 | 8.8 |
| 660 | 6.4 | 6.8 |
| 690 | 4.6 | 4.8 |
Between two single rounds the typical gap due to chance is about 1.4 times the floor (√2): two scores closer than that tell you nothing. Compound and barebow: use your personal floor.
| Difference | 3 points | 5 points | 8 points | 12 points | 20 points |
|---|---|---|---|---|---|
| Rounds per period | 67 | 24 | 10 | 5 | 2 |
| Level | ~520 | ~560 | ~600 | ~640 | ~680 |
|---|---|---|---|---|---|
| Recurve | 2.8% | 4.1% | 6.8% | 11.4% | 16.5% |
| Compound | 3.6% | 4.8% | 7.7% | 14.6% | 27.6% |
Signal or noise
| Average before (M₁) | Rounds before (n₁) | Average after (M₂) | Rounds after (n₂) | Floor |
|---|---|---|---|---|
- Difference |M₂ − M₁| =
- Threshold = 2 × floor × √(1/n₁ + 1/n₂) =
- Outcome:shownnot shown yet
If the difference is above the threshold, the change is shown. If it is not, the change is not shown yet: you need more rounds, as many as the rounds-needed table says.
Directional test (clock method)
For each arrow, before pulling it: its clock direction from the centre of that end's group (12 up, 6 down, 3 right, 9 left) and its distance in rings. At least 12 ends, which is 72 arrows. Then count the vertical arrows (near 12 or 6) and the horizontal ones (near 3 or 9).
| Vertical arrows (12/6) | Horizontal arrows (3/9) | V/H ratio | Group offset |
|---|---|---|---|
V/H above 1: vertical error dominates (release, draw length, clicker). V/H below 1: horizontal error dominates (alignment, torque).
Training priorities (three at most)
Golden rule. The sheet does not add up to a single mark: two archers of the same level can have opposite sheets, and the right training for one is not the right training for the other. No decision is taken on differences that sit inside the floor. · matteocampagna.com
Signal or noise: the sum on screen
If you would rather not work it out by hand, enter the numbers from the box here and press Calculate. The starting values come from an example: floor 9, three rounds before averaging 625, three rounds after averaging 632.
The vertical to horizontal ratio
The same for the directional test: enter how many arrows you counted as vertical and how many as horizontal, and press Calculate.
How it works
The sheet
The sheet is designed for an assessment day with pen and paper: you print it, fill in the header and, during the day, complete the boxes as you run the tests. The tables printed at the top let you read the numbers on the spot, with nothing else to hand. At the end you choose three training priorities at most, starting from whatever came out weakest.
The floor
The floor is the standard deviation of the total of a 72-arrow round when the archer's form does not change: it measures how much the score swings by pure chance from one round to the next. It comes down as the level goes up, because archers who group tighter swing less: for recurve at 70 m, according to the table in the essay Il pavimento (The floor), it lies between 9.9 and 10.9 points at 600, between 8.1 and 8.8 at 630, between 6.4 and 6.8 at 660 and between 4.6 and 4.8 at 690. The two numbers in each row are the essay's two scenarios: in the pure bell curve every arrow comes from the same group, in the model with tails a few arrows leave the group and weigh on the total more than their number suggests. When a single number is needed the second is the one to use, because it makes a change harder to declare. Your personal floor comes from the totals of at least six recent rounds shot in the same conditions, meaning the same distance and the same format: it is their standard deviation, which a spreadsheet gives you with the STDEV function.
The signal or noise calculation
The average of several rounds swings less than a single round: with n rounds, the floor is divided by the square root of n. When you compare the average of n₁ rounds before a change with the average of n₂ rounds after it, the two swings add up as squares, which is how chance swings combine, and the difference between the averages swings by floor × √(1/n₁ + 1/n₂). The sheet's threshold is twice that value:
threshold = 2 × floor × √(1/n₁ + 1/n₂)
The factor of 2 means that chance alone rarely goes beyond the threshold: about one time in twenty. With the example's numbers, floor 9 and three rounds before averaging 625 against three after averaging 632, the threshold is 2 × 9 × √(1/3 + 1/3) = 2 × 9 × 0.82, about 14.7 points. The difference is 7 points, below the threshold, so the improvement is not shown yet.
The rounds needed
The second table is the same rule read the other way round: instead of asking whether a difference is above the threshold, it asks how many rounds you need, before and after, for a difference of a given size to clear it. The sum is n = 2 × (1.96 × floor / difference)², where 1.96 is the value that corresponds to 95% confidence. With the floor of a 630 recurve archer in the model with tails, 8.8 points, it gives 66.11 rounds for 3 points, 23.80 for 5, 9.30 for 8, 4.13 for 12 and 1.49 for 20, which the table shows as 67, 24, 10, 5 and 2: the figure is always rounded up, as the calculator above does, because you cannot shoot half a round. Read it as a minimum: this rule uses 1.96, the sheet's threshold a round 2, and clearing that one too takes about 4% more rounds.
The percentage of Xs
The third table shows how many arrows in a hundred land in the X, the inner 10, at each level: for a 640 recurve archer it is 11.4 on average, for a compound archer at the same level 14.6. To compare yourself, count your Xs over at least five rounds, divide by the arrows shot and set the percentage next to the value for your level.
The directional test
The directional test looks for the axis on which the error is largest, using the clock method. After each end, before pulling the arrows, you judge by eye the centre of that end's group; then for each arrow you note its direction from that centre, like the hours on a clock face (12 up, 6 down, 3 right, 9 left), and its distance in rings (0 on the group centre, 1 one ring further out, and so on). You repeat this for at least 12 ends, which is 72 arrows. At the end you count the arrows that sit mainly on the vertical, near 12 or 6, and those that sit mainly on the horizontal, near 3 or 9: the ratio between the two counts, V/H, is a rough estimate of which axis dominates the error. Separately, you look at where the whole group sits relative to the centre of the target face, which is its offset.
How to read it
The two calculators above also do this reading for you: below the result, the box headed "What your numbers say" takes the values you entered, says what they mean and points to the next step.
Your personal floor
If your personal floor is close to the table value for your level, you are already at the minimum of noise: the swings from one round to the next are almost all chance. If it is much higher, part of the variation does not come from chance (unstable form, conditions, the mind), and that is where there is work to do. A score less than one floor away from your average is a perfectly ordinary round, and even a gap of two floors happens by pure chance about once every twenty rounds.
Two single rounds
Between two single rounds the typical gap due to chance is about 1.4 times the floor (√2 × floor): it is not the floor, it is how far apart two rounds usually end up when nothing has changed, and two scores closer than that tell you nothing about a change. A 630 recurve archer who shoots 638 and then 622 has not improved and then got worse: with a floor of 8.8 points, a swing of 16 points is inside the noise. To declare a change by comparing one round with one round, the sheet's threshold is higher still, 2 × √2, about 2.8 times the floor: for the same archer, about 25 points.
Signal or noise
If the difference between the averages is above the threshold, the change is shown: it is unlikely to be just the floor moving about. If it is not, the change is not shown, which does not mean it is not there: it means those rounds cannot reveal it. The right response then is to wait and collect more rounds, as many as the rounds-needed table says, before changing anything else. It is the calculation that prevents the most common mistake in coaching, which is reacting to noise and chasing swings that are only chance with technical changes.
The percentage of Xs
If you shoot fewer Xs than expected for your score, your group is good but not well centred, and the margin lies in fine aiming and tuning. If you shoot more, fine aiming is a strength and the margin lies in cutting down the low arrows. These are the two levers of the score, grouping tight and centring fine, and the comparison tells you which of the two is further behind.
The V/H ratio
A ratio above 1 says that vertical error dominates, which is usually linked to the release, draw length and the clicker: that is where the technical work goes, not into alignment. Below 1, horizontal error dominates, which is linked to alignment and torque. The group offset is read separately: a group sitting all high or all to the right points to a tuning or aiming problem on that axis, not to spread.
The priorities
There are three priorities at most, chosen from the weakest points. The sheet does not add up to a single mark: two archers of the same level can have opposite sheets, one precise but fragile and the other solid but with a strong vertical error, and the right training is different for each. In every case, no decision is taken on differences that sit inside the floor.
Limits
The sheet is paper and does not calculate anything by itself: the sums are done by hand or with the two calculators on this page. The floor table comes from a model, the one in the essay Il pavimento, and holds for recurve at 70 m on the 122 cm face. For compound and barebow the essay says the curves have to be measured, and the sheet does not make them up: for those divisions only the personal floor counts. The X table, on the other hand, comes from an analysis of an archive of competition results carried out for an earlier project, which is not published: read it as a rough guide to what is typical at a given level, not as a forecast for a single archer, who can depart from it for perfectly good reasons.
The other tools on the site use the same floor, and their numbers can differ slightly for reasons that can be stated. The floor calculator uses the same table, but gives higher numbers than the sheet for the rounds needed (49 rather than 24 for 5 points at 630), because it also asks for an 80% chance of seeing the difference when it is there, while the sheet's rule stops at the threshold. The score gap calculator uses the pure bell curve alone, calibrated on the published tables of the essay on the set system, and a one-sided 95% threshold.
The signal or noise calculation is only as reliable as the floor you put into it. The table floor measures chance alone, with form held constant; in real life sleep, the day, the mind and the wind come on top and widen the swing. With the table value, then, the threshold comes out a little lower than it should and the verdict more optimistic, which is why it is better to use your personal floor, measured over at least six rounds. The rounds also need to be comparable, at the same distance and in the same format, because mixing 18 and 70 metres breaks the comparison. Finally, the baseline has to come from a block of rounds before the change: if it is worked out on rounds that have already improved, the comparison is skewed from the start.
The directional test gives up precision so that it needs no equipment: the group centre and the direction of each arrow are judged by eye, and the V/H ratio is a rough estimate. The method sets no threshold beyond which the ratio counts, so a value close to 1 should be read with caution, and you need at least 72 arrows. If you want more, you can mark each arrow with the tap target or on the plotting sheet, which give the axis ratio from the coordinates, or photograph the target face after each end from a fixed position, with reference marks in the frame.
Finally, the sheet covers only part of an assessment: the level, the floor, the comparison between before and after, fine aiming and the direction of the error. Holding up under pressure, endurance and the warm-up need tests of their own, which are not included here.
For the sums the sheet does by hand there are also dedicated tools: the floor calculator for the floor and the rounds needed, Did I really improve? for comparing two rounds from their ring counts, the change detector for following your rounds one at a time after a change and the group size calculator for the size of the group and the X rate.