Sunday, 27 July 2014

What's The Points?

In which I talk about points for wins, losses, and draws in rugby league, and how framing of quantitative data is important.

This week saw the announcement of major changes to the way that the top levels of rugby league in the UK would operate. The sport will be moving from two, essentially separate divisions (Super League and Championship) in 2014 to have a partially combined competition in 2015, where after 23 games the two leagues split into three tiers. The top tier features the top eight from Super League, and the bottom eight from the Championship will form the bottom tier. The middle tier will involve the bottom four teams from Super League, and the top four from the Championship. The three tiers will then compete for their own rewards.

It's actually quite straightforward and, after some initial scepticism, I'm looking forward to it. But the structural change isn't what I'm bothered about, here. One of the talking points that's come up (particularly on BBC Manchester's RL Extra) is that Super League (SL) and the Championship (C) currently offer different points for winning, drawing, or losing a game:
  • Win: SL: 2pts, C: 3pts
  • Draw: SL: 1pt, C: 2pts
  • Loss: SL: 0pts, C: 1pt (if lose by <= 12 points in the game), 0pts otherwise
and in the big announcements this week, one matter that was left undecided is what points scheme will be used in the competition next season: the "old" SL points scheme, or the Championship's "bonus point" scheme. RL fans like nothing more than a good argument, and this week's RL Extra featured a number of callers  - and guests and presenters - who objected to the bonus point scheme on the grounds that it "rewards failure", because it gives teams a point if they lose - even though it's a point for losing by 12 points or fewer, in an attempt to encourage close games.

Those people are wrong.

The reason that they're wrong is that the idea that the bonus point rewards teams for losing is only an issue of framing: it's equally correct to say that the points scheme punishes teams that lose by a larger margin than 12 points.

Imagine a different scoring scheme again, where we keep the old SL scores: 2pts for a win, 1pt for a draw, 0pts for a loss. This time though, to encourage close games, we punish teams for losing by more than 12 points in the match by subtracting one league point when that happens. So we have a "penalty" scheme:
  • Win: 2pts
  • Draw: 1pt
  • Loss (<= 12 points): 0pts
  • Loss(> 12 points): -1pts
This is clearly punishing teams for not being competitive. No-one is being rewarded for losing.

But this is equivalent to the "bonus point" system. Applying either scheme will give you exactly the same ranking of sides at the end of the season. If you add one point to every outcome in this "penalty" scheme, you have the "bonus point" scheme. The only difference between the outcomes is that in the "bonus point" system, every side will have n more points at the end of the season, where n is the number of games that they played. In mathematical terms, one scoring scheme is an affine transformation of the other.

The key thing to note is that the points difference between each outcome of a single game is identical in each scheme. It doesn't matter why you get one less point for losing by more than 12 points in a match: whether you're being 'punished' for losing by lots, or another team is being 'rewarded' for losing by a small margin, the outcome is identical in terms of the table (and numerically identical but for a constant value equal to the number of matches played).

What would have happened in 2013?

Out of curiosity, I had a quick look at what would have happened in the SL table from 2013, if the "bonus" or "penalty" points schemes would have been in play, and ignoring Salford's 2 point deduction.

I grabbed the 2013 league table and results from (manually - so there may be errors…), and used a little bit of R to render a plot of the effect of changing points schemes.

League points for each team in SL 2013, under the old, "bonus point" and "penalty" points schemes.
The first thing to notice is that the overall difference in ranking would be minor. Salford and London were clearly off the pace, and there was space between the top five and the rest of the table, in all three schemes. If anything, the gap between the middle-table teams and the the top five/bottom two is accentuated.

The next thing is that all the lines connecting league points under the "Bonus" and "Penalty" schemes are parallel: this is because the final difference under the two schemes is 27 points for each club - the number of games played in 2013. Whether you "reward losing" or "punish uncompetitive teams", the result is the same.

The most significant difference between the points schemes is that with a bonus (or punishment) point difference, Warrington would have been league leaders at the end of the season. After that, Widnes, Wakefield and Catalan Dragons would have finished slightly higher, but there would have been no change to the top eight playoff contenders - though the paired teams and home advantages would have changed slightly.

Applying the bonus/penalty scheme to last year's results is a bit artificial, though. The intent is to encourage closer games, which can only work if teams are aware of the possibility during the game. Maybe a team like Castleford (4/16 close losses) would have performed more like Wakefield (8/16 close losses) if there had been an extra point at stake - whether reward or punishment? We can't know, now. But I'd like to see what happens if it's introduced, next season.

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