Chapter 20 · Worked solutions
Chapter 20 workings: Luck, PDO and the Regression Monster
Chapter twenty worked: PDO for six teams ten matches in, and which two are the clearest candidates to regress, one down and one up.
PDO adds a team's shooting percentage (goals over shots on target) to its save percentage (saves over shots on target faced). Over a long run almost every side drifts back towards 100, written here as 1.00, because the luck in finishing and goalkeeping evens out.
The exercises
Six PDOs and two regression candidates
Given each side's shooting and save percentages after ten matches, compute PDO and pick the most likely faller and the most likely riser.
Add the two percentages
Team A: 38 + 70 = 108, so PDO 1.08. The table does the rest, sorted from luckiest to unluckiest.
Measure the distance from 1.00
A sits 0.08 above par. C sits 0.15 below, the furthest from 1.00 in either direction.
Pick the faller
A. Scoring with 38 per cent of shots on target and saving 70 per cent is a pairing that rarely lasts; its points total is ahead of its play.
Pick the riser
C. Converting under a quarter of its shots on target while letting in nearly four in ten faced is a run of bad luck at both ends, and both ends tend to recover.
And the one to leave alone
F is the trap. A poor 22 per cent conversion is balanced by a superb 79 per cent save rate, so its PDO is almost exactly par. The total says nothing unusual is going on, even if the parts look extreme.
| Team | Shooting | Saves | PDO | From par | Reading |
|---|---|---|---|---|---|
| A | 38% | 70% | 1.08 | +0.08 | likely to cool |
| D | 31% | 73% | 1.04 | +0.04 | slightly lucky |
| F | 22% | 79% | 1.01 | +0.01 | about par |
| B | 30% | 68% | 0.98 | −0.02 | about par |
| E | 29% | 66% | 0.95 | −0.05 | slightly unlucky |
| C | 24% | 61% | 0.85 | −0.15 | likely to improve |
The answer
A (1.08) is the clearest candidate to fall back; C (0.85) is the clearest candidate to improve. F, at 1.01, is a mid-table side playing like one.
Related on this site
These are the workings. The argument for them, and the exercises themselves, are in chapter 20 of the book, Luck, PDO and the Regression Monster.
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