▣The Form Line Open the partner account
paid
Affiliate disclosure. The partner link in the masthead and in the band beside the copy on this page is a sponsored link to a partner operator, and this site may be paid if you open an account through it, at no extra cost to you. It carries rel="sponsored noopener" and opens in a new tab. The subject of this desk is the figure printed next to a competitor, so its own interest is stated here rather than left for a footer: one link funds the site, and no operator, race, track, rating service or product is named, rated or recommended anywhere on it.
The Form Line / The rating system
The figure ยท part nine

The same arithmetic in a rating system

The mark and the rating service are the same idea in two sports: keep a number, compare it with the opponent, move both by a share of the surprise. The share is a choice, and it decides how fast the number moves.

Open the partner accountWhat a figure cannot say
Sample spec
Sample system
a points rating
Update weight
24
Prior gap
100 points
Move in one match
15.4 each
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 rating system keeps a number per competitor, turns the gap between two numbers into an expected result, and then moves both numbers by a fixed share of how wrong that expectation was. The share is called the update weight. Two systems can hold identical results and publish different numbers, because they use different shares, different rating periods or a home advantage adjustment.

Sample R is one invented match. Team one is rated 1500 and team two 1600. The gap is turned into an expectation, the underdog wins, and both ratings move by the same amount in opposite directions.

Sample R - one match, two ratings, two rows of arithmeticrating one 1500, rating two 1600, update weight 24 expected score for team one gap = 1600 - 1500 = 100 expectation = 1 / (1 + 10^(100/400)) 100 / 400 = 0.25 10^0.25 = 1.7783 1 / (1 + 1.7783) = 1 / 2.7783 = 0.36 so team one was given a 36% chance and team two 64% team one wins, so the result is 1 for team one and 0 for team two team one 1500 + 24 x (1 - 0.36) = 1500 + 15.4 = 1515.4 team two 1600 + 24 x (0 - 0.64) = 1600 - 15.4 = 1584.6 one match moved the gap from 100 points to 69.2 points and moved each rating by 15.4 against sample B, one run moved a mark by 2.33 lb on average, and the largest single move in six runs was 6 of a net 8 so the two systems move at different speeds on the same idea

Fifteen point four points from one match is a large move, and it is a direct consequence of the update weight of 24. Halve the weight and the same result moves each rating by 7.7, so a season of results changes the ranking half as quickly. The weight is not a detail of the system; in any practical sense, it is the system.

Why two systems disagree

Four decisions separate two rating systems that both work. The share of the surprise that is applied (the update weight), the period over which older results count (some systems decay results, some reset at the start of a season, some count everything ever played), whether a home or venue advantage is folded into the expectation before the update, and the population the number is calibrated against. Two systems can agree on the method and disagree on every number, which is exactly the position a reader of a speed figure is in when the standard time and the allowance are not published.

What the two systems share

Both are iterative: the published number is the previous number plus the last result's effect. Both are relative: they order a population rather than measure an absolute quantity. Both are stable by construction: the update weight is what prevents a single result from rewriting the number, and it is also what makes the number slow to notice a real change. And in both cases the numbers on the inside - the update weight for a rating, the standard time and the allowance for a figure - are the ones a reader cannot see.

Where to go next

The mark and how it movesthe same idea, one sport, a published scale The runs behind the figurehow few results a number usually rests on Every figure in one placesample R beside the other seven