Thursday, 16 January 2020

Jeremy Dolan v Eight Ace

I love my Viz, it's a great Northern institution which while apparently not being as funny as it used to be, at least according to my old Geordie housemate, still brings a chuckle now and then. One of my favourite strips was Eight Ace, where our titular hero continually fails in whatever he's trying to do due to regular consumption of eight cans of Ace beer.

Now let's suppose that today, he has been entrusted with £451.49 worth of TA Towers' slush fund, with the sole goal of registering for Q-School and winning just one match, leaving £1.49 for expenses. Alas, that is just enough money to purchase the regular eight cans of Ace, and our hero is completely twatted. He can see the board, he can throw just about well enough that we know he will hit the board, but we have no clue where he's going to hit. It's completely random. He's fucked, right?

Wait. His opponent is the current star of the Twittersphere, Jeremy Dolan. He's achieved some form of notoriety for achieving this great game against former world finalist Mark Dudbridge earlier today:

That's, shall we say, not the greatest standard. 32.67 per visit would definitely not get you your bus fare home, which is what it's rumoured quarter final losers at the BDO worlds won, in comparison to Jim Williams' speedboat. But is it good enough to beat Fulchester's finest?

What we need to do is, assuming Mr Ace's throws at the board are randomly distributed, is to calculate the size of each scoring segment of the board, and then go from there. Oddly enough, while the metrics for actually mounting a dartboard are fairly well known, the actual dimensions of each scoring area took more than two seconds to Google, so let's quote what some Australian site is saying (assuming their server hasn't caught fire since I looked it up earlier... oh wait, it's based in Perth so we're fine):

Bull radius: 6.35mm
25 radius: 15.9mm
Inside treble wire radius: 107mm
Outer treble wire radius: 115mm
Inside double wire radius: 162mm
Outside double wire radius: 170mm

So, using our trusty pi*r^2 area calculations, we know there's 90792 square millimetres of surface area which Ace can hit. Of which:

- 126.7 mm^2 is the bull
- 794.2 mm^2 is the bull and 25 combined, so 667.5 mm^2 is the 25 segment itself
- 35968.1 mm^2 is inside the inner treble wire - so 35173.9 mm^2 is the thin single numbers
- 41547.6 mm^2 is inside the outer treble wire - so 5579.5 mm^2 is our trebles
- 82448 mm^2 is inside the inner double wire - so 40900.4 mm^2 is the big numbers
- Which leaves 8344 mm^2 to be our double sector.

Those are our figures. Now, as Ace is throwing completely randomly, we don't need to bother calculating every single segment - we just assume he's hitting a wedge between 1 and 20 randomly, which is 10.5 on average. So, what we need to calculate is:

(126.7*50 + 667.5*25 + 35173.9*10.5 + 5579.5*31.5 + 40900.4*10.5 + 8344*21)/90792

This, to the best of my drunken calculator work, gives us an average of slightly less than 12.92 per dart, or a three dart average of 38.75. Hooray! Ace is averaging more than Dolan is!

Now of course, this doesn't take into account that Ace will have absolutely no realistic chance of hitting a double to win a leg in any reasonable time, and Dolan being able to see where the double is likely helps matters. Then again, at the same time, remember everything that I've always said about averages - they rise in comparison to what they'd normally be if you play against a better player, as you're not throwing at doubles. We have no clue whatsoever what Jeremy's checkout percentage is, as he didn't get below 230 in any leg he played, although we can probably have a guess.

Let me finish by saying this is in no way intended to take the piss - if someone wants to pony up nearly half a grand to roll up, have a laugh and maybe draw someone notable (as Jeremy's managed to do in drawing a former world finalist), then that's perfectly fine. Whether the PDC still thinks it's a good idea to just have straight knockouts and not switch to a Swiss format to trim the worst of the field after each day, that's their problem to answer.

Edit - botched some of the initial maths by using a diameter rather than radius for the double rings, now altered and the random average actually went up. Want to validate it again tomorrow, but if we think that picking a number at random between 1 and 20 is 10.5, and doing it three times gives you 31.5, then that'd be what we'd have if there were no doubles, trebles or bulls

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