We all know that
This is stuff that any amateur darts player knows already. The first piece of advice I was given when I joined my first pub darts team at the tender age of 15 was to always aim for the treble-19.
Anyone wishing to give Eric "The Crafty Cockney" Bristow a run for his money at the oche has been offered a mathematical helping hand by a crack team from Aberdeen University, the Daily Telegraph reports. The group, from the Department of Plant and Soil Science, has demonstrated that while the optimum aiming point for skilled …
As pointed out by the above poster, everybody knows tha, my father also passed that information to me before I hit my teens
The issue 20 or 19 is even more important on 'traditional' boards which omit the treble altogether. double 19 is decided easier to hit than a double 20.
Also theres a greater chance of 'collateral scoring' around the double 19 than the double 20.
If you have two independent orthogonal Gaussian distributions around the aim point (in this case left-right and up-down), then the joint probability distribution describing the distance of the dart from the aim point is a Rayleigh distribution, not a Gaussian. The angle about the aim point is a uniform distribution in [0, 2 Pi]. The probability of actually hitting the aim point is zero. The mode of the PDF is the standard deviation.
It looks from your description of bell curves, etc. that the distribution they're using is essentially 1D - and that will translate into an isotropic (circular) 2D distribution. Surely, when aiming through a beery haze, the lefty-righty bit is easier than the uppy-downy bit. The Gaussian should be taller than wider, when seen projected onto the vertical dartboard. It might even have a bit of a slant to it. I find double 11s easier to hit than double 20s, for example. I think an anisotropic scatter would change their results somewhat, and they haven't even started to factor in Monte Carlo simulations of how likely a finish is in a game of 501. Also, where's the Plant and Soil Science angle?
..I'll get me coat.
(1) Rayleigh: certainly not. Who said independent distributions horizontally and vertically? Bad idea. Easy to see your arm, body and the entire throwing movement is not split into two independent dimensions. All the little bits, joints, muscles and sinews conspire to mix up the two. (Carefully follow the path of a laser pointer in a trembling hand, for example.)
And what do you get if you mix up a lot of causes? The Gaussian, indeed mr. Kolmogorov.
(1b) Hitting the aim point zero probability: yes, duh, that holds for any point in any continuous distribution --- yet some point is hit in the end, yes? If all points have zero probability, nothing must be hit. Hm... flaw.
It's that pesky infinity thing. Ah, maybe we're not dealing with single dimensionless points in space?
(2) Any darts player knows the spread is easier to control horizontally than vertically, so squishing the bivariate `elliptic' curve into a univariate `round' Gaussian is a sin. The article sounds as if they've done just that, `measure distance' and not the vector of horizontal and vertical distance, but that's not proof this is what they did.
That said, the `Letters' submitters should have been pointed out their obvious mistakes --- one mixes `gaussian' with `uniform' distribution and misses the whole plot, the next could have been hinted that 2D gaussians give exactly the ellipses of equiprobability that he experiences.
Certainly since the `Letters' column was in the hands of the science editor!
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