Ok – I dropped the ball a bit and didn’t finish off the full explanation of the expected return methodology. The idea is really simple though. If we imagine that each surfers opportunity to win a given round is the same, then we can look at how much risk/reward is offered in each round. This view of ratings shows that in general, the WSL doesn’t reward enough for winning the final, in that every other round rewards you with the opportunity to earn more. After writing the first two parts of the series, the WSL updated their system to give a little bit more to the winner. I thought it looked good before I actually calculated the effect.

Long story short: they didn’t change much about the effect of conservative surfing in the later rounds. But I like how they’ve added the elimination and seeding rounds. It’s a great way to give the surfers a little warm up.

The charts below are generated from the top down. I start by knowing the points at elimination and for winning the final (in bold). Then I work my way down, filling in the intermediate round effective points for a win then how much can be expected from winning or losing a round. And then I repeat down round by round.

They are easiest to read these charts, though, is from the bottom up. For the 2019 rankings, each surfer starts with about 2718 points. Let’s follow a surfer who loses the first two rounds. In the seeding round, you have a 2/3 chance at a win, so only win 307, but lose -613. (It’s like betting on the favorite). So if you lose, you then have 2105 effective points. In the elimination round, the stakes are raised by a factor of 3. If you lose, you lose 1840 points, all the way down to 265 – as given by the WSL ratings. So far so good. From there on the elimination rounds are 1 on 1 and easier to follow. And almost every round the **stakes go down**. This is the problem – and it still leads to safe strategy.

If you look at the 2017 ratings, they are are actually pretty similar, except for Round 4, where the stakes drop really low. But there is still the general problem that later rounds have lower stakes. And the new rankings hardly did anything to improve things. Darn!

### 2019 Rankings

Win Points | Loss Points | Return from win | Return from loss | |

Final | 10000 | 7800 | 1100 | -1100 |

Semi | 8900 | 6085 | 1408 | -1408 |

Quarterfinal | 7493 | 4745 | 1374 | -1374 |

Round of 16 | 6119 | 3320 | 1399 | -1399 |

Round of 32 | 4719 | 1330 | 1695 | -1695 |

Elimination | 3025 | 265 | 920 | -1840 |

Seeding | 3025 | 2105 | 307 | -613 |

Entering | 2718 |

### 2017 Ranking

Win Points | Loss Points | Return from win | Return from loss | |

Final | 10000 | 8000 | 1000 | -1000 |

Semi | 9000 | 6500 | 1250 | -1250 |

Quarterfinal | 7750 | 5200 | 1275 | -1275 |

Round 5 | 6475 | 4000 | 1238 | -1238 |

Round 4 | 6475 | 5238 | 825 | -413 |

Round 3 | 5650 | 1750 | 1950 | -1950 |

Round 2 | 3700 | 500 | 1600 | -1600 |

Round 1 | 3700 | 2100 | 1067 | -533 |

Entering | 2633 |

## How to improve rankings?

Well, it’s pretty easy to create a ranking system with constant expected return each one on one round. Here is an example where each round the surfers “bet” 2 points. Note that in most rounds, the points awarded for losing in that round just jump by 2 points. But you get double incremental points for winning final. This is really the minimum sensible approach, and means that winning the final is at least as well rewarded as winning any other round.

Win Points | Lose Points | Return from win | Return from loss | |

Final | 15 | 11 | 2 | -2 |

Semi | 13 | 9 | 2 | -2 |

Quarterfinal | 11 | 7 | 2 | -2 |

Round of 16 | 9 | 5 | 2 | -2 |

Round of 32 | 7 | 3 | 2 | -2 |

Elimination | 5 | 0 | 3 | -2 |

Seeding | 5 | 2 | 1 | -2 |

Entering | 4 |

This begs the question, should we go further? It’s also easy to create a more aggressive ratings approach, where a little more is “bet” each round. This certainly increases the stakes, which is exciting for fans. On average, the competitors are more equally matched for later rounds, so I suspect a small increase in stakes makes sense. On the other hand, underdogs tend to win in earlier rounds and I’d like to see them rewarded for their efforts too.

My approach is inspired by the Elo ratings in chess. In the chess rating system, the winning player “takes” points from the loser. If the winner is more highly rated, the point exchange is low. But if the underdog wins, there is a large exchange points. The system is self correcting so that, with time, players reach their “true” ratings. Also this means to get your rating to climb you have to actively seak out other highly rated players. With the WSL method, higher seeded surfers get an advantage by generally facing lower seeded competitors. This means that, though the system is self correcting, it happens relatively slowly. I think the best fix would be to lose seeding all together and randomize the draw. I’d say that they should adopt something like Elo, but then we wouldn’t be able to say exactly what each surfer needed to win the title at the end the year.

So that’s that – We should we go to a constant expected return model of ratings and randomize seeding to get more accurate ratings at the end of the year for all surfers.

## Comments