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Pulling the goalie: why Australia should play eleven batsmen in every Test

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12th January, 2019

Stand up if you’re familiar with ice hockey?

Ok, a few of you. Now sit down if you can’t jive with probability theory. For the few of you still standing, you’ll know that this situation can be described by a conditional probability.

That is, the likelihood of event B happening given that event A has already occurred. In this case, it’s the remote chance that a hockey fan has some level of education. But what does this have to do with cricket? Bear with me.

An interesting paper came out late last year, and it’s caused quite a stir. It’s called “Pulling the Goalie: Hockey and Investment Implications”. Find it on Google. The long and short of it is this – you’re a coach and your hockey team is a goal down, when should you cut your losses and replace the goalie with another attacking player?

It turns out that NHL coaches tend to pull the goalie with a minute to go. Sound pretty intuitive? Well here’s the catch. As long as you don’t care how much you lose by, you should pull your goalie way before the end of the match – with about six minutes to go in the final period in fact.

What it boils down to is this – while you only increase your chances of winning by a tiny amount, you probably would have lost anyway.

Righto, how does this apply to cricket? Over the last five years, the baggy greens have been good at two things, namely, losing the toss and losing matches. In fact, they’ve managed to lose a fifty-fifty coin toss about 63 per cent of the time. And when they lose the toss, they’ve only managed to win 13 of their 32 starts. If these trends continue, we’re all but no chance of regaining the Ashes.

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Unfortunately, we can’t affect the toss, but here’s my “pull the goalie” moment. What if we could reduce the probability of losing? For example, the opposition has to take twenty wickets to win a match. So why don’t we just pick eleven specialist batsmen? They’d each, on average, only need to face about 60 balls per innings to ensure a draw.

Statistically, that’s very doable, even with the current crop. Then, as long as there would be some non-zero probability of taking twenty wickets ourselves, our relative advantage could be substantial. Granted, it’d make for a boring bat-a-thon. But trust me, the maths checks out.

Essentially, the success of this strategy depends on this – we assume that loading the team with batsmen will decrease the probability of losing proportionately more than it will decrease the probability of winning. Sure, some Tests we’d still lose, like being put in on a raging green top, but without the eleven batsmen we surely would have lost them anyway.

Win the toss, bat big, and be patient with the ball. Lose the toss and bat for time. That’s what I call pulling the goalie.