The runs behind the figure

Every figure on a card is an average of something, and the something is small. Six runs is a full form string and a typical record to rate a competitor from, and six runs of the same competitor can disagree with each other by more than a whole field does.

Open the partner account What a figure cannot say

Sample spec

Runs behind the figure: 6
Mean of the six: 80.83
Range of the six: 16.9 points
Best run is: 1 of 6

the stringThe finishing position of the last six runs, newest first. On the samples it carries 48 of 48 positions and 0 of 48 margins, distances, grounds or field sizes.

the markThe official rating, set so a field of similar marks finishes close together on paper. On the samples it moved on four of six runs, for a net change of 8 lb.

the allowanceThe correction applied to a standard time for the ground. On the samples the going allowance is worth 19.2 points at six furlongs, against 2.4 points for the whole weight spread.

Direct answerA figure is computed from a small number of runs, usually the same six that the form string holds. One invented runner's six speed figures are 82.0, 79.4, 88.1, 71.2, 84.0 and 80.3: a mean of 80.83, a range of 16.9 points, and a best run that is 1 of the 6. The mean moves 1.45 points if the best run is dropped and 1.93 if the worst one is.

Sample H is one invented runner. Six figures is not a small sample by the standards of a race card; it is the whole of what a card usually shows. The point of the sample is to put a number on how much of the figure is the runner and how much is the day.

Sample H - one runner, six runs, six figures
Run	Figure	Against the mean	What the run was
H1	82.0	+1.17	a repeat of the usual level
H2	79.4	-1.43	a slower track, same position
H3	88.1	+7.27	the best run in the record
H4	71.2	-9.63	the worst run in the record
H5	84.0	+3.17	a step up in class, held its level
H6	80.3	-0.53	an unremarkable run
Six runs	mean 80.83	range 16.9	median 81.15

Sample H - what one run out of six is worththe six figures 82.0 79.4 88.1 71.2 84.0 80.3 sum 485.0 mean 485.0 / 6 = 80.83 sorted 71.2 79.4 80.3 82.0 84.0 88.1 median (80.3 + 82.0) / 2 = 81.15 range 88.1 - 71.2 = 16.9 points sensitivity to a single run out of the six drop the best (485.0 - 88.1) / 5 = 396.9 / 5 = 79.38 -1.45 drop the worst (485.0 - 71.2) / 5 = 413.8 / 5 = 82.76 +1.93 so one run in six moves the summary by up to 1.93 points, which is 27.6% of the 7.0 points that separated first and third in one race (sample C) and the runner's own range of 16.9 points is 2.4 times that same 7.0 point winning margin

The last two lines are the whole page. Within a single race, three runners were separated by 7.0 points of figure. Within one runner's own six runs, the figures moved 16.9. A comparison between two runners on this evidence is a comparison of two summaries whose own noise is larger than the gap between them.

The mean is a choice as well

Sample H's six figures can honestly be summarised in at least four ways, and a publisher picks one. The mean is 80.83, the median 81.15, the best run 88.1 and the most recent run 80.3. The best-run summary is the one that flatters, the most-recent is the one that responds to news, and the mean is the one that hides the most. None of them is wrong, and all four are on the same card.

Count the runs before reading the figure: a figure from three runs and a figure from thirty are different claims.
Ask which summary is being used - the mean, the best or the latest - and whether the card says.
Prefer a spread to a single number whenever one is published.
Remember the range of the sample's own runner: 16.9 points, against a 7.0 point field margin.
Treat a single outstanding run as a question about the conditions of that day.

Where to go next

The sectionals inside a racewhat the figure averaged away Every figure in one placethe whole arithmetic on one page What a figure cannot saythe limits of the whole exercise