Every figure on this site, in one place

This page is the desk reduced to its arithmetic. Ten invented samples, every figure derived from them, and no figure on the site that is not on this page.

Desk spec

samples: 10 invented
pages: 17
figures: all derived
real operators named: 0

the composed priceThe number returned for a set of outcomes the customer named. It is not the product of the legs: on the samples 5.60 multiplies and 4.80 is offered, because the legs happen together more often than independence implies.

the requestA customer asking an operator to invent a market. 500 arrived in the sample month, 218 produced a price, 131 could not be priced at all, and the median answer took 3 hours 40 minutes.

the void legA leg that never happens, repaired by re-pricing the combination from its remaining legs. Dividing the price by the void leg gives 4.50 where the real three-leg price is 4.80 - a 6.7% error.

Direct answer

Every figure on this site derives from ten invented samples: a three-leg combination (5.60 multiplied, 4.80 composed), 500 requests for a market, 40 combination rules, a four-leg combination with one void leg, three limits, a model whose answer is a band, four refusal reasons, 40 terms pages, and one month of money at 170,400.00 of turnover.

Sample A - the combination

Three legs from one match, priced 1.60, 1.75 and 2.00. The product of the three is 5.60 and the joint chance independence would imply is 17.86%. The model measures 20.83%, so the composed price is 4.80 - a difference of 0.80 of price, 14.3% of the product, and 8.00 on a 10.00 stake. Priced at the product, the leg-set would lose 16.6% of every stake placed on it.

Sample B - the requests

500 requests in one month: 218 accepted (43.6%), 96 refused on price (19.2%), 131 with no market (26.2%), 37 never answered (7.4%) and 18 withdrawn (3.6%). A request arrives every 29 minutes of an eight-hour day, the median answer takes 3 h 40 m and 12.0% are answered inside an hour. Of the 218 accepted, 194 were published (89.0%) and 24 kept private (11.0%).

Sample C - what may be combined

Of 40 documented rules, 22 permit a combination automatically (55.0%), 11 require a person to price it (27.5%) and 7 refuse it (17.5%): two opposing outcomes inside one market, three mutually exclusive statistics, one settlement dependency and one leg the model cannot price.

Sample D - the void leg

A four-leg combination multiplying to 13.44 and composed at 10.80. One leg of 2.40 is void. Dividing gives 4.50; re-pricing the remaining three gives 4.80. The difference is 0.30, or 6.7%, and 3.00 on a 10.00 stake.

Sample E - the limits

2 to 12 legs. Twelve legs means 66 pairwise relationships and 4,096 joint states. Twelve legs at 1.50 each is 129.7; at 1.70 each it is 582.6, above the 500.0 the operator will accept. The maximum stake is 250.00, behind a payout ceiling of 25,000.00, so above a price of 100.0 the stake is capped by the ceiling: 192.75 at 129.7 and 50.00 at 500.0.

Sample F - the record

Of 40 terms pages: 26 state that a model prices the combination (65.0%), 4 state that the price is not the product of the legs (10.0%), 9 state the void-leg re-pricing rule (22.5%), 0 state that a combination may settle in part, 18 state the leg limits (45.0%), 7 state that a request may be refused (17.5%), 7 state the payable price limit, 4 state the maximum stake, 11 state the payout ceiling, and 1 states all six rules together (2.5%).

Sample G - the money

12,000 combination bets in a month at a mean stake of 14.20 is 170,400.00 of turnover. Priced at the product of the legs rather than the composed price, the same bets would cost the operator 16.6% of that turnover - 28,286.40 in the month and 339,436.80 in a year.

Sample H - the queue in money

One request costs 41.07 of trader time at 112.00 an hour and 22 minutes. The month's 500 requests therefore cost 20,535.00 to answer, or 246,420.00 a year, and 94.20 for each of the 218 markets that were accepted. The 186 requests that produced nothing cost 7,639.02, of which 5,380.17 was spent on the 131 requests no model could price - 64,562.04 over a year.

Sample I - the refusals

The 96 priced-then-refused requests: 38 with no model (39.6%), 27 below the minimum accepted price (28.1%), 19 on an unverifiable statistic (19.8%) and 12 beyond the correlation limit (12.5%). 84 of the 96 could have been re-asked in a different form.

Sample J - the model's band

A joint chance of 20.83% with an uncertainty of +/-1.50 points prices between 4.48 and 5.17 - a band 0.69 wide, or 14.4% of the composed price.

The figures in one line each

Ten samples, one line each - the figures every page in this desk is built from
Sample	Subject	Central figure	Derived figure
A	The combination	5.60 product	4.80 composed
B	The requests	500 requests	218 accepted
C	What may be combined	40 rules	7 refusals
D	The void leg	2.40 void	4.80 re-priced
E	The limits	12 legs	500.0 payable
F	The record	40 pages	1 states all six
G	The money	170,400.00	16.6% avoided
H	The queue	41.07 a request	5,380.17 wasted
I	The refusals	96 refused	84 re-askable
J	The model	20.83% joint	0.69 band
Every sample	Illustrative only	10 samples	0 real operators

sample A - the whole desk in one subtraction product of the legs when they are treated as independent = 1.60 x 1.75 x 2.00 = 5.60 the chance that multiplication implies = 1 / 5.60 = 17.86% the chance the legs actually have together = 20.83% the price that chance produces = 1 / 0.2083 = 4.80 the difference in price = 5.60 - 4.80 = 0.80 = 14.3% the difference in money on a 10.00 stake = 56.00 - 48.00 = 8.00

sample G - the same subtraction across a month bets in the month = 12,000 mean stake = 14.20 turnover = 12,000 x 14.20 = 170,400.00 priced at the product, the expected cost = 0.166 x 170,400.00 = 28,286.40 over a year = 28,286.40 x 12 = 339,436.80 the composed price is the whole of that difference, and it is charged to nobody: it is a price at which the market can be run at all.

sample H - the queue, priced cost of one request = 112.00 x (22 / 60) = 41.07 requests in the month = 500 cost of the queue = 500 x 41.07 = 20,535.00 accepted markets = 218 cost per accepted market = 20,535.00 / 218 = 94.20 requests that produced nothing = 131 + 37 + 18 = 186 cost of those = 186 x 41.07 = 7,639.02 of which no model existed = 131 x 41.07 = 5,380.17

sample J - one probability read at its edges central joint chance = 0.2083 -> price = 4.80 edge low 0.1933 -> price = 1 / 0.1933 = 5.17 edge high 0.2233 -> price = 1 / 0.2233 = 4.48 band width 5.17 - 4.48 = 0.69 = 0.69 / 4.80 = 14.4%

sample E - three limits at once legs = 2 to 12 pairs at twelve legs = C(12,2) = 66 joint states = 2^12 = 4,096 twelve legs at 1.50 = 129.7 twelve legs at 1.70 = 582.6 -> above the 500.0 payable payout ceiling = 25,000.00 maximum stake at 4.80 = 250.00 -> returns 1,200.00 maximum stake at 129.7 = 25,000.00 / 129.7 = 192.75 maximum stake at 500.0 = 25,000.00 / 500.0 = 50.00

Every figure on this page is illustrative and derives from the ten invented samples defined here. No real operator, sport, player, match, market or terms page is described by any of them.