Chapter 30 · Worked solutions
Chapter 30 workings: Skill or Fluke? Black Cats in Coal Cellars
Chapter thirty worked: auditing a 200-bet record with a 12.7 per cent yield and negative CLV, from strike rate to confidence interval to a verdict.
The record is a fictional composite from the book: 200 level-stake bets at an average 29/20 (2.45), 92 winners, a yield of +12.7 per cent and an average closing line value of −0.6 per cent. Four questions, one verdict.
The exercises
Strike rate against break-even
Find the break-even strike rate at 2.45 and compare it with the actual one.
Break-even
1 ÷ 2.45 = 40.8 per cent.
Actual
92 ÷ 200 = 46.0 per cent, about five points clear.
The answer
Break-even 40.8 per cent, actual 46.0 per cent.
How wide is the doubt?
With a per-bet standard deviation of about 1.22, find the standard error of the yield and a 95 per cent interval.
Standard error
1.22 ÷ √200 = 8.63 per cent.
Interval
12.7 ± 1.96 × 8.63 = 12.7 ± 16.9, so from −4.2 to +29.6 per cent.
How many bets would settle it
For a 12.7 per cent yield to clear zero at that spread you need about (1.96 × 1.22 ÷ 0.127)² = 355 bets, and that is if the yield holds, which it rarely does.
The answer
Standard error about 8.6 per cent; the interval runs from about −4.2 to +29.6 per cent.
Does the yield prove anything, and does the CLV agree?
Judge the yield on its own, then set it against the closing line value.
The yield
The interval includes zero and includes losses, so a service with no edge at all could have produced this record by luck.
The CLV
Negative CLV means the bets were struck, on average, at worse prices than the fair close. A real edge usually shows up as beating the close. Here the price evidence points the other way from the profit.
The answer
No and no: the yield is within luck, and the CLV contradicts it.
The verdict
Bet with confidence, keep watching, or stand down?
Weigh it
A small sample, an interval straddling zero, and prices that lose to the close. Nothing here is evidence of skill.
The answer
Stand down: a short, lucky-looking run on worse-than-closing prices.
These are the workings. The argument for them, and the exercises themselves, are in chapter 30 of the book, Skill or Fluke? Black Cats in Coal Cellars.
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