Chapter 6 · Worked solutions
Chapter 6 workings: Where Prices Really Come From
Worked solutions for chapter six: reading a sharp price against a soft one, valuing a price the market has left behind, the Yellow Sam blockade and beating the close.
The habit this chapter builds is treating a sharp market as a second opinion, one that has already been argued over by people with bigger stakes than yours. The arithmetic is chapter two's conversion; the judgement is about which number to trust and what is still hiding inside it.
The exercises
Sharp 5/4, soft 11/8
A sharp book has an away win at 5/4 and your app has 11/8. What does each claim, and what else do you need before calling 11/8 value?
Convert both
5/4 claims 4 ÷ 9 = 44.44 per cent. 11/8 claims 8 ÷ 19 = 42.11 per cent. Longer odds, smaller claim: that never changes.
Find the break-even
To profit at 11/8 you need the true chance above 42.11 per cent. The sharp claim is above that, which looks promising.
Notice the rent
The sharp 44.44 still contains that firm's margin. Strip it and the figure drops; how far depends on the whole market, not this one price. The table shows how the verdict turns on that number, using three illustrative margin-free figures rather than a real market.
| Sharp chance, margin removed | EV at 11/8 per £1 | Verdict |
|---|---|---|
| 44.0 per cent | +4.5p | Value |
| 43.0 per cent | +2.1p | Value |
| 42.0 per cent | −0.3p | No value |
The answer
44.4 per cent against 42.1 per cent. You still need the sharp price with its margin removed, from the full market.
The price left behind
The sharp books move a home win from 3/1 to 5/2 an hour before kick-off; your soft book still offers 3/1. Using the moved price as your probability, what is 3/1 worth per pound, and what is the caveat?
Convert the moved price
5/2 claims 2 ÷ 7 = 28.57 per cent.
Value the stale price
Your EV per pound: 3 × 0.2857 − 0.7143 = +0.1429, about +14p per pound.
Why so big
A move from 3/1 to 5/2 is a big move: the claim jumped from 25 to 28.57 per cent, and 3/1 still pays as if nothing happened.
The caveat
28.57 is a price with margin in it. Remove it and the true chance is a little lower, so the real edge is a little smaller than 14p. Chapter 8 makes it exact.
The answer
About +14p per pound, before taking the margin out of the 5/2.
Yellow Sam
£15,000 of informed money was sitting in the shops, yet Yellow Sam's starting price held at 20/1. Why, and what does it rhyme with today?
Locate where the price is made
A starting price is set by the on-course market. Money in a high-street shop only changes it if news of that money reaches the course.
Find the pipe
The news travelled by telephone, and the course had a single line. It was kept busy, so the information never arrived.
Name the modern version
Any price copied from a feed that updates slower than the news it should reflect: a thin lower-league coupon, or the few minutes after team sheets drop when some firms have not caught up.
The answer
The price could only learn through one phone line, and that line was blocked. Slow feeds are the modern version.
Beating the close
Tuesday's bet was struck at 5/2; by kick-off the price was 9/4. Read both claims, decide whether you beat the close, and value the bet with the closing claim standing in for the truth.
Convert both
5/2 claims 28.57 per cent; 9/4 claims 4 ÷ 13 = 30.77 per cent.
Compare
The market ended up rating the outcome more likely than your price did, so you held the better price: you beat the close.
Value it
EV = 0.3077 × 2.5 − 0.6923 = +0.0769, about +7.7p per pound.
A shortcut worth knowing
When the closing claim is your probability, EV is just your decimal price over the closing decimal, minus one: 3.50 ÷ 3.25 − 1 = +0.0769. Same number, one division.
The answer
28.6 against 30.8 per cent. You beat the close by about 7.7p a pound, before removing the margin from the close.
These are the workings. The argument for them, and the exercises themselves, are in chapter 6 of the book, Where Prices Really Come From.
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