## Rugby and the ELV's

Last night's rugby Test between Australia and France was won convincingly by Australia (40-10) despite the French having much more possession (I haven't seen a figure since mid-match, but it was somewhere around 65%). This got me wondering about the relation between possession, territory, and winning in rugby. I downloaded the last two seasons' worth of data for the Super 14 from Rugby Stats to see what it said. The Rugby Stats site gives all sorts of data (unfortunately not going back further than the last couple of years), but for this post I've just used taken the home team possession and territory for each game, along with the fraction of points scored by the home team. So, eg, if the home team won 20-10, they had 0.667 of the points scored.

I'll start with the 2007 season, which of course was played under the traditional rugby laws. Here's some of what gretl had to say:
`Model 1: OLS estimates using the 94 observations 1-94Dependent variable: h_score_percent      VARIABLE       COEFFICIENT        STDERROR      T STAT   P-VALUE  const                -0.379896         0.355244     -1.069   0.28772  h_poss                1.88078          0.688795      2.731   0.00759 ***  h_terr               -0.0305528        0.182781     -0.167   0.86762  Mean of dependent variable = 0.558623  Standard deviation of dep. var. = 0.194866  Sum of squared residuals = 3.26391  Standard error of residuals = 0.189386  Unadjusted R-squared = 0.0757645`

So, having the ball helps — for each extra percentage point of ball, you got almost two percentage points worth of the final score. On average, about 44 points were scored (in total) each game, and 2% of 44 is 0.88 points. Of course, when the home side gets a bigger slice of the points, the away side must lose the same amount, so it's really about a 2-point swing. (If you work with raw scores and not fractions of total points, you get a similar result.) There's a lot of scatter in the data — the R-squared is only 0.076.

So, all other things equal, if the score is 27-17 with equal possession, it'd be (on average) 28-16 with 51-49 possession.

Territory, on the other hand, doesn't make a difference.

Now let's look at 2008, played under the ELV's.
`Model 1: OLS estimates using the 94 observations 1-94Dependent variable: h_score_percent      VARIABLE       COEFFICIENT        STDERROR      T STAT   P-VALUE  const                -1.70310          0.333894     -5.101  <0.00001 ***  h_poss                4.26355          0.656012      6.499  <0.00001 ***  h_terr                0.228343         0.111618      2.046   0.04367 **  Mean of dependent variable = 0.539166  Standard deviation of dep. var. = 0.172713  Sum of squared residuals = 1.84663  Standard error of residuals = 0.142452  Unadjusted R-squared = 0.334345`

The ELV's appear to have made possession much more important — you end up with a 4-point swing in score for each percentage point of possession, rather than 2 points. Also, territory seems to be mildly important and beneficial now. The R-squared is 0.33, so possession and territory are much better at predicting the final result under the ELV's than they are under the old laws.

If any of you are rugby fans, feel free to make any requests for rugby analysis.

Dave, great work but you simply must take into account penalties. Are penalties a result of possession or visa versa?

For mine, penalties give possession and a weight of penalties should indicate a win. Those who win against the count, on countback, you will find the opposition received "make-up" penalties usually in a poor position to build upon or late in the game when the result was beyond question.

More research is needed and I am prepared to back this study with a well written reference to his Higness Kelvin Krud in your favour.

For instance, today Parra lost to the Panthers 22-16 even though Parra had a count of something like 12-4 in their favour but possession running at 50-50.

Not sure what to make of that stat but I would like to see more work on penalties in any case.

Statistical analysis into why the All Blacks lose only once every 4 years?

Nice post DB, although I do think a Wallaby / France test is always going to twist the model a bit.

I thought I was being clever by avoiding the topic of penalties, but I see I've lasted only a couple of hours before someone's mentioned them.

I suspect that your intuitions are right about rugby league, though I don't have league data to back it up. Each set of six takes roughly the same amount of time, and field position is important - get a few repeat sets and usually you'll crack the defence.

But in union it's different, because you can have really slow ball from the breakdowns and go nowhere for ten phases. In the Super 14's in 2007, teams that conceded more penalties tended get a higher share of the points.

Teams who won with less than half the ball gave away more penalties than those who lost with less than half the ball.

I'm not entirely sure why, but I'm guessing it's because slowing the play at the breakdown was always a risk/reward - you let your defence get set, but you risk giving away a penalty. The numbers suggest that slowing the ball down was worth giving away the odd penalty.

But that's only my guess.

Under the ELV's, there doesn't seem to be a trend either way between giving away penalties and winning/losing.

Eureka! "Teams who won with less than half the ball gave away more penalties than those who lost with less than half the ball."

That is the key to All Black success. Kill the ball at the ruck and run the risk (which is always 50/50) of a penalty. Oz has been too stupid, too slow, too ethical or all three to realise that this is the key to Union success. Fitzpatrick is a past master.

Kill the ball at all cost. That should be the Oz mantra.

Plus get yourself someone who can kick a goal from any angle 50 metres out. That's all it takes to win at Union.

Think the profile of the game changes over time ? ... eg....

The last quarter the winning team may well shut up shop whilst the losing team may well reject penalties and go for the tries...

Dependent on the scoreline margin entering the final stages the possession/territory may well skew dependent on the score margin etc ...