BY DAN AND DR HERMAN

The Canberra Raiders are the unluckiest team in Rugby League.

I mean, I would say that. I’ve chronicled the ridiculous ways they’ve conspired to lose games this year. Like giving up 18 point leads on at least two occasions, coming back from a million points only to lose, or that time they gave the best player in the game three opportunities to win the game in the last minute. Last week they added ‘winning try scored on them by a player in an offside position’.

It’s been a tough year.

It’s pretty difficult to be objective when it comes to your team. I mean, we just assume the Raiders have been the most unlucky team because if a team had been more unlucky than the Raiders that city would be rioting.

But what if we could put an objective measure to how lucky teams have been this season?

Ladies and gentlemen I give you Pythagorean Expectation Theory.

Pythagorean Expectation is a method of determining luck first developed in baseball to ascertain how many games a team ‘should’ have won in a given season.

It was invented by Bill James, the secret hero of Moneyball and the father of sabermetrics. In short, it looks something like this.

Urgh. Nerds.

It rests on two assumptions. That teams win in proportion to their “quality”, and that their “quality” is measured by the ratio of their runs scored to their runs allowed.

In baseball this makes a lot of sense. Teams play 162 games over a season and don’t score a lot, so it’s easy for you to drop a couple of games because a slugger gets lucky. And indeed this theory has been tested and has empirical support.

In general, baseball teams come within .025 of their projection, which is four games over a 162-game season. It has been successfully extrapolated to American Football, most notably by Aaron Schatz at Football Outsiders and Bill Barnwell at Grantland. Freakin’ professors have weighed in on it.

Like all sports statistics it has its limits (or so our Maths experts here at the Sportress tell me). So take it with a grain of salt. But look, it’s a measurement. It’s fun to use. And it proves that our hilariously biased view might not be so ridiculous.

So with the help of our own Dr Herman Blume we’ve expanded the Pythagorean net to include our National Rugby League.[1] Now we can finally see who’s been lucky this season.[2]

Below is the ladder at the end of round 22. You can see all your usual columns there. But notice the last two.

Position	Club	Wins	Expected Wins	Wins above or below expected
1	Broncos	16	15.17	0.83
2	Roosters	15	16.81	-1.81
3	Cowboys	15	12.60	2.40
4	Rabbitohs	13	12.88	0.12
5	Storm	12	14.29	-2.29
6	Sharks	12	9.44	2.56
7	Bulldogs	11	11.13	-0.13
8	Dragons	10	11.21	-1.21
9	Sea Eagles	10	10.62	-0.62
10	Warriors	9	8.45	0.45
11	Raiders	8	10.60	-2.60
12	Panthers	8	8.12	-0.12
13	Eels	8	7.22	0.78
14	Tigers	7	8.08	-1.08
15	Knights	7	6.81	0.19
16	Titans	7	5.82	1.18

So our additional two columns are pretty self-explanatory. One is expected wins according to the Pythagorean expectation. The second is the difference between that number and their real amount of wins.

For example, the Sharks have won 12 games this season. Their Pythagorean Expectation is 9.4 wins, a difference of 2.6. This means they’ve actually won 2 more games this season than they should have. Just to show it’s not biased against low-scoring defensive oriented teams, look at the Cowboys, an attacking juggernaut that has won nearly two more games than they should have this season. If you’re a Raiders fan you can even point to which ones.

And of course, you can see that the Raiders have won 2.6 less games than they should have by the numbers. Of course Raiders fans reckon that number should be closer to six, but it reflects the small sample size that is the rugby league season. Also notice the Storm (-2.3) and the Roosters (-2.4) have both been very unlucky this season. That should be interesting to look at come finals time.

In fact, if the teams had performed according to the Pythagorean Expectation this year, this is what the table would look like.

Position	Club	Expected Wins
1	Roosters	16.81
2	Broncos	15.17
3	Storm	14.29
4	Rabbitohs	12.88
5	Cowboys	12.60
6	Dragons	11.21
7	Bulldogs	11.13
8	Sea Eagles	10.62
9	Raiders	10.60
10	Sharks	9.44
11	Warriors	8.45
12	Panthers	8.12
13	Tigers	8.08
14	Eels	7.22
15	Knights	6.81
16	Titans	5.82

And somehow the Raiders still sit 0.2 of a game outside the semis. Even when we account for luck, the Raiders are still unlucky.

[1] Basically, there was a routine error found in the theory so some intelligent folk worked out an ‘exponent’ to correct for extreme situations. We’ve used the version used in American Football because we’re lazy and you know, it’s kinda like rugby league. Smart people would need to go back through years of data (like they’ve done for baseball and NFL) to find the right exponent for NRL.

[2] We should really wait for the season to end in a month for the sake of the sample size but we’re just too damn excited about maths!