Monday, 21 September 2015

Expected Value in Rugby League


A Draft PhD Idea for Someone a Who Just Wants To Watch Footy

American sports are at the forefront of using statistics and analytical measures to enable better decisions for better outcomes.

The most famous example is baseball, with the 'Moneyball' concept, where the Oakland Athletics were able to compete with significantly less financial resources by identifying players through unique metrics, like looking at getting on base rather than runs scored.

They then had a pretty average movie made about it long after the other richer teams copied their revolutionary approach and their advantage was lost.

In basketball, the game is evolving to a point where teams basically only take two-point shots at the rim, and otherwise jack up loads of three-point shots, as any shot in between those distances has a much lower expected value.

To understand expected value in basketball, consider that if someone shoots 50.0% on two-point shots and 33.3% on three-point shots, then the outcome from 100 shots on each is identical:

100 x 2 x 0.500 = 100
100 x 3 x 0.333 = 100

But consider the shooting percentage on two-point shots is greater than 50% at the rim, and drops the further away from the basket. So a two-point shot taken just inside the three-point line is likely to be made only marginally more than the three point shot, say 35%, but with a much lower expected value:

100 x 2 x 0.350 = 70
100 x 3 x 0.333 = 100

It therefore makes sense to take close shots, and easy uncontested two-point shots, and otherwise try and hit threes.

Basketball provides the simpler example, but perhaps the greatest power for analytics is in American football, where the stoppages mean that with enough data it's possible to develop an optimal decision taking into account the game situation, score and time left on the clock in every situation.

Because rugby league doesn't have as many stoppages, the applications for similar analytics for the NRL as the NFL are limited. However, one obvious scenario where it could be useful is around penalty decisions.

At present teams will, based on "gut feel", typically only take penalties when they are behind by 2 (to tie), scores are level (to move ahead), they are ahead by four (to lead by a converted try), or multiples of six (to move ahead by more than a converted try, or tries, so the opposition must score one extra time). Even in these situations, they will still elect to tap if it's early in the game and/or they have "momentum"

You could develop a model that enables teams to make optimal penalty decisions based on evidence rather than "gut feel".

The way you would do this is to take a number of seasons of NRL games, and watch every single one of them.

While watching, every time there is a penalty within 50 metres (a generous kicking range) record where it is on the field, the decision taken, and what the "outcome" was of that decision. So if a team takes the goal, the outcome is simply two points or zero points. If the team kicks for touch or taps, the outcome is whatever points they produce before the other team touches the ball.

With enough observations, which you should get from hundreds of games, you can build a dataset that provides fairly robust expected values.

So we might learn from 20-30m out directly in front, a team taking the penalty goal always gets two. Expected value here is simply two.

Now when a team takes the tap in the same area, maybe from all the observations a team that taps in this range scores a try 30% of the time, and makes 75% of conversion goals on those tries. This assumption feels about right to me, and will be used to demonstrate the value of the analysis, although obviously the observed data is critical for the analysis to have real value.

But for our assumption, the EV is:

(4 + (2 x 0.75)) x 0.3 = 1.65

So since 1.65 is less than two, the correct decision in this field position is to kick the penalty goal. You get more points this way, in the long run.

This is in a vacuum. Obviously game situation is important. If you are 30 points behind, this makes no sense, or if you are 30 in front, it probably doesn't matter. If you are four behind with two minutes left, it also has no value, because you wouldn't have time to score again.

But if you are four behind with 60 minutes left, or two in front, or eight in front, or have "momentum", or a myriad of other situations where teams rarely kick for goal, then it does make sense.

The expected value could be adjusted for time situations with enough observations, but I think initially it would be enough to simply determine an expected value and allow coaches or captains to assess the time on the clock.

My hypothesis is that there are numerous scenarios where it could sense to kick a penalty goal, like in this hypothetical example, and teams are actually being too aggressive in their decision making and not taking enough shots at goal. Interestingly this is the opposite on what the analytics say in the NFL, but they are different games dealing with different scoring systems and situations.

Regardless of what outcome the analysis would produce, making optimal decisions based on evidence has to be preferable to the current unsophisticated approach.

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