So, as Mervyn King's re-established his status as the greatest of all time following his victory over Michael van Gerwen at the UK Open, let's take a look at one of his largest quirks, namely to go sixteens when requiring 80.

Now if the opponent is not on a finish, or is on a finish but one he's not likely to get very often, I've got zero problem with this - set up the shot on a favourite double if you don't kill it. Here we're going to consider the case where the opponent is in range and we want to maximise our chances of going out.

Conventional logic says to go 20's on 80, because you can still leave yourself a dart at a double if you hit two singles. There is, of course, an argument to go tops-tops straight off the bat, but we'll leave that another day, this is about Mervyn and if he's not wanting to go tops once, he sure as hell isn't going to want to do it twice. One would think that you're more likely to go out this way as a result, but that's assuming that you're equally good at all sections of the board. Looking back at Carl Fletcher's stats from before the worlds, Mervyn was hitting tops 35% of the time and D16 39% of the time, but is that going to be enough to justify a different route?

Let's make some assumptions - let's assume Mervyn hits T20 40% of the time - that's probably a bit more than he actually hits it (ochepedia's stat bundle from before the worlds reckoned he was hitting 37% on stage), but let's make it a nice round number that's in the ballpark of being right, Mervyn does tend to hit a lot of maximums, at least it feels like he does, so I'll give him the benefit of the doubt. Let's also assume that he hits T16 the same percentage of the time - now clearly people don't go for this target anywhere near as often as T20, but it seems fair to do so, again from ochepedia's stats, Mervyn hits T19 within 1% as often as T20 and that's in the same area, and the whole premise is that King likes the bottom left quarter of the board.

Now we've got two more issues that we need to resolve. Firstly, the route we take is not necessarily going to have us going for tops or D16 exclusively - if we go the 20's route then we end up on D10 if we hit first dart and can end up on D5 if we shank inside, and if we go the 16's route, hit, then miss inside, we end up on D8. I think it's fair to group these as "good" doubles and "bad" doubles - after all, 16's and 8's are next door, 20's and 5's are the same, 10's is a bit different and is the same height as the double we like, but let's play along with it.

Secondly, what the hell do we do if we miss the first dart going 16's? There's two main choices - either we go for 14 to leave the option of the bull (let's assume King hits the bull 1 in 4, more or less what ochepedia's stats say), or we go double double on 16. I think we need to treat these as different cases when comparing, and treat double 11 as a "good" double if we hit T14, as it's the same quadrant of the board. Let's not even consider just going for the big number to be sure of a shot at bull, or even going close to the double to have an outside shot of setting up D18 instead.

We'll also assume that we don't miss big numbers. If we go 20s, our chances are:

P(20out) = 0.4*(b+(b*(1-b))) + 0.6*b

i.e. the 40% of the time we hit the treble, we need to multiply that by the times we hit first dart plus the times we miss first dart multiplied by hitting second dart, and then for the 60% of the times we miss the treble, we assume we hit fat 20 all the time, and just multiply that by the times we hit a double.

Next, if we go 16s and bail out to the bull, we have this scenario:

P(16bullout) = 0.4*(g+(g*(1-g))) + 0.6*0.4*g + 0.6*0.6*0.25

The first part of the equation is the same, i.e. we hit and then either hit the double, or miss and hit, then it's a little different - the second part of the equation is the 16-T14-D11 out, the final part is the 16-14-bull route.

Finally, if we go 16s and try to double-double:

P(16doubledoubleout) = 0.4*(g+(g*(1-g))) + 0.6*g*g

First part is logically exactly the same, the second part should be intuitive - we miss the treble 60% of the time, then hit the good double twice.

So which is better, and where's the break even point? Let's plot some graphs:

The x-axis is the percentage of time we hit on our chosen double group, be it D20/D10/D5 or D16/D8/D11. The y-axis is the percentage of time we check out.

The purple line is our 20's route. The black line is our 16's double-double route, the green line is our 16's bull out route.

Now note obviously the green line has a non-zero checkout chance if we can't hit a double ever, as the one in four shot of hitting the bull is hard coded into the formula - similarly if we never miss a double, we still don't check out every time, due to the chances of us ending up on the bull and missing.

As we'd expect, going 20's checks us out more often if the chances of us hitting any sort of double are any kind of reasonable figure, but it's not by that much, oddly enough - if we do hit double 16 as often as we think Mervyn does, say 40% of the time, we still need to hit tops about 36% of the time to go out for the 20's route to be more profitable, if we go the bull route - which is looks like we should do up until the point where we're inhumanly good on D16. If you think about it, it somewhat makes sense to go the bull route - 40% of the time we hit T14 and end up on a good double anyway, the rest of the time we still have a 25% shot of hitting the bull, so we need to have quite a large percentage of hits to justify going for it twice given the additional downside of having no shot if we miss the first time. So, if our simplifications aren't throwing things off, and the figures on Mervyn's D16 and D20 shooting are accurate, it's no more than a one or two legs out of 100 difference by going that route. Less than you thought I guess.

I've updated the second and third division darts tables - there's not been many games played but the second division's still real tight with only de Zwaan off to a bad start with a couple of 6-4 losses, while Schindler and Dobey are down early in division three with Dimitri opening up a big early lead - Aspinall's played the most, but as it's mostly been against Lennon it's not going to count for many points at all.

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