Pappus' plane - cricket stats

As the heading indicates, this post is not about cricket.

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 1-94
Dependent 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 1-94
Dependent 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.