Loss Aversion Bias in Rugby

The latest weekend of November internationals saw two very interesting and debated decisions at the end of the games.

We’ll look at each decision and investigate should teams coin flip to win or lose a 50:50 decision or take a draw. Then we’ll have a look at whether or not these actually were 50:50 decisions using our BF Sports Analysis Expected Points (xP) data.

Loss aversion is the tendency for people to feel underwhelmed by positive gains and comparatively feel overwhelmed by losses of the same value. 

For example if you found a €10 note on the ground and picked it up, you would be happy, but if you were to lose €10 and couldn’t find it, for most people your sense of loss would be far greater than the happiness gained from finding the €10. The attachment to the earned €10 is psychologically defeating despite the same value in the gained €10.

So does this feeling come into rugby or other sports? Let’s investigate those 2 decisions from the November international weekend 19th of November 2022. 

We’ll start by trying to put a value on winning/drawing/losing in each circumstance. This is a tougher exercise in a November international as it isn’t part of a league so there is limited material value in the fixture and means the value is in psychological factors. 

In a league structure, where a win is worth 4 points and a bonus point loss is worth 1 point, there is a higher weighting towards winning and therefore a coin flip would be of higher value.

We measure this decision with: “value” x “% chance of that outcome”

Then we add those values together to get an average value of decision A vs decision B.

4 points win x 50% = 2 points
1 point BP loss x 50% = 0.5 points

Total value of a 50:50 decision to win/lose in a league match in rugby is 2.5 points.

Whereas a draw in this scenario is worth 2 points.

In the sense of a league points decision, it makes far more sense to flip the coin to win or lose.

One tangible but arguably not highly valued outcome is the World Rugby Ranking points at stake. This allows us to take into consideration team strengths – a weaker team is likely to value a draw more than a stronger team.

Below are the potential outcomes in regards to the rankings points for both England and Australia in their respective matches.

England lose <15: -0.83
England draw: +0.17
England win <15: +1.17

Australia lose <15: no change
Australia draw: +1
Australia win <15: +2

So in England’s context:

Coin flip:
-0.83 x 50% = -0.415
+1.17 x50% = +0.585
Coin flip = 0.17 = draw

Australia’s context is the same. 

The bookies expected England to lose by 3.5 points and Australia to lose by 12.5 indicating that the draw could have been psychologically more appealing to those 2 teams.

Another element we haven’t considerer is a financial win bonus that players/coaches may be striving for and it’s relation to the bonus they receive for a draw.

So that leaves us inconclusive as to whether either is a better decision for now. The next way we’ll try to measure the value of the win vs draw vs loss is public opinion. We asked our followers what decision they would have made in those situations and got some interesting results. 

Combined Social Media Poll
Coin Flip: 43 (61%)
Draw: 27 (39%)

So it seems our followers have a bit more propensity for risking the loss for the potential gain of a win.

So now our question gets a bit more interesting, were these decisions actually 50:50 decisions or was there a decision that would have a higher success value? We’ll look at Australia this time.

Here are the permutations:

Decision A: kick the 3
Outcome A: Successful kick at goal > Score again to win
Outcome B: Successful kick at goal > finish with draw
Outcome C: Successful kick at goal > Ireland score and win
Outcome D: Unsuccessful kick at goal > score try from 22 to win
Outcome E: Unsuccessful kick at goal > get a new penalty and draw
Outcome F: Unsuccessful kick at goal > Ireland win

Decision B: Go to the corner
Outcome A: Score + win
B: Score + draw
C: Score + lose
D: no score + win
E: no score + draw
F: no score + loss

Using the same calculation of:

“Value of outcome” x “Probability of outcome”

Weighing it out using our database of 26000 possession we are able to estimate the probability of each outcome. Australia increased their chances of winning by 38.5% going for the corner but also increased their chances of losing by 12.5% vs going for the 3 points, based on the goal kick having a 52% chance of going over based on our expected points (xP) metrics from that area at professional level. This is also based on these being 2 even teams, which they seemed to be on the night.

This metric was based on our expected points metric for scoring from lineouts 5m out, the opportunity for Australia to gain subsequent penalties and continue their pursuit for a try. It also considered the xP of scoring from both 22 and 50m restarts from our database of xP data.

So for us, you’d have to value not losing 3 times more than you value winning to not go for the corner in this instance for the shot at goal to be the right call. Therefore, Australia made a good call going to touch on this occasion. The opportunity to score from the lineout, the phases after or indeed win another penalty to have another craic at the try line by either a lineout or tap and go made sense on this occasion. 

Let us know what you think of this article and if you want a version on the England decision from receiving the kick off.

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