Monday, 24 April 2017

135 out 2 - The Quickening

Follow up post - warning, more maths follows.

I searched through Burton's twitter and found a decent sized sample of doubling stats - was all ranked TV and Euro Tour for most of last year. They read as:

On a double: 73%
Single to double: 62%
61-80: 46%
81-100: 33%
101-120: 22%
121-130: 11%
131-160: 6%
161+: 2%

Have rounded to the nearest percent, and the ranges aren't exact (e.g. 65 is in the previous range, 99 in the next range), but for this purpose they're fine.

Next step is to assign a range for what is left when we don't kill. Rather than the first post where I scraped the world final, let's use a simple "we throw straight tons so hit 1/3 in treble". Let's also assume we can't go to a higher tier - if we're on tops, we won't throw three inside and be left with single to double for example. It can happen in real life, but often enough to worry about. We'll also make the same assumption from the previous time that we don't miss big numbers or get bounceouts. This gives us the following:

Anything under 80: always on a double next throw.

81-100: on a double unless we leave bull and miss, this'll only happen in the 81-90 range with two misses at treble, then miss bull hitting 25 or anything that isn't both high and even. This should be about one in eighteen of all trials, including those we kill, so 33% kill, 61% on a double, 6% on single to double.

101-120: no bull faffing around here makes things easier. If we get a treble any visit, we're on a double next time up if we're not out, and staying straight leaves us with 60 left maximum, so it's all either on double or single to double. Three misses at treble is around a 30% shot, so the remaining 48% we're on a double.

121-130: some bull complications here. 30% of the time we miss three times as above and are on 61-80 next up. 15% we miss twice then hit a treble third dart to leave a double. 45% of the time we hit one treble in the first two darts, leaving a shot at bull, and the remaining 10% we hit two trebles, to leave a shot at double. We know 11% of the total is checkouts, so let's grab 4% of that from the two treble visits and the remaining 7% from the one treble visits. These all go to leaving a double apart from the bull shots. This gives us 11% kill, 24% on a double, 35% on single to double, and 30% on 61-80.

131-160: Need to split this up into two, as 141 or more leaves different outs. Basically, we have 6% outs, 34% on a double, 30% on a single to double, 10% on 61-80 and 20% on 81-100.

161+: Fairly straightforward. Three misses is 101-120 (30%), two misses is 61-80 (45%), the remainder is a double, unless we go out, or miss the bull trying and leave a single to double. This is about 8% of trials, so taking off the 2% of outs, 15% of the time we leave a double.

Following that? No? Excellent. Now let's run the figures we have from the previous 135 post and run them against each other until we can see which route wins more legs. Out of 1000 legs, how often should we win?

Opponent on a double: 276 going bull first, 271 going treble first
Opponent on single to double: 344 either way
Opponent on 61-80: 445 bull first, 453 treble first
Opponent on 81-100: 527 bull first, 544 treble first
Opponent on 101-120: 602 bull first, 626 treble first
Opponent on 121-130: 701 bull first, 723 treble first
Opponent on 131-160: 731 bull first, 760 treble first
Opponent on 161+: 795 bull first, 823 treble first

I thought it'd be a bit more in favour of going treble first, even at lower levels. Having less than a 1% difference on anything below 80 is close enough that it doesn't matter, but it quickly escalates to a 2-3% edge going treble first once the opponent is needing more than 100. I guess that only needing single for double checks out quicker than I expected compared to just being on a double accounts for a chunk of this.

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