Didn't have the time after an ill advised football trip on Saturday to get any projections up, which given how my picks on Saturday went was probably for the best. Aspinall denied us the dream GvV/DvD final, and set up the Euros field which is pretty much a wet dream for the PDC in that they have 29 of the top 32 in the FRH live rankings (Aspinall is back into the top 16 there, but will save until after the Eoros for a fuller update), missing out Edhouse (because he could never win this), Gilding (because he could never win a major) and Cullen (because he could never win a TV title) for the Euro trio of Ratajski, Barney and Springer, the latter being the only player to actually win their spot here rather than being gifted it. I'll get some numbers up for that tomorrow.
One thing I meant to mention a few posts ago was basically the most pathetic clickbaity X post I've seen in relation to darts in quite some time, which given the level of hysteria whenever Littler loses a match is saying something. I don't know the guy in question, not someone I follow and only noticed it as it appeared on an unrelated forum, but to paraphrase it basically said "van Gerwen to not play competitive darts after the Grand Slam before the worlds". Which we could paraphrase as "darts player misses one tournament he didn't qualify for". Which he might well still do, with the author of this said post apparently being ITK that van Gerwen won't play the last two Pro Tours. This might be true, but does it matter? You could write the exact same post about half the tour card holders. Doesn't make it news.
Anyway, in a more interesting thing I read on X, David Schlichting posted the theory after Greaves made it 86 unbeaten in the Women's Series that only Littler would be P > 0.5 (in layman's terms, more likely than not) to win 100 in a row on that tour if in her position. Now I don't think for one minute that David is extrapolating to imply that Beau is as such the second best player in the world, more that to even get this close should she not get to the century is probably lucky, but on reading this I summoned my inner Martin Schindler walk on music and thought this looks like a job for me.
I'll start by saying I'm clearly not going to model every permutation of possibilities, as that would just be silly. So I'm going to make some assumptions and simplifications. Firstly, how do we get to 100 wins? This is the simplest thing probably. Enter tournament. Win tournament. Repeat until streak is at 100. As such, we can reasonably say that we can replace that "win 100 matches" with "bink x tournaments in a row". How to find x? We just need to look at the entry counts and then gauge on average how many matches we'll play. Greaves, to win 86 in a row so far, has won the last 13 tournaments, That's pretty much right in between six and seven - this makes a fair bit of sense, while I could go through all the data and work out exact entry numbers, Grok's estimating that there's typically 80 to 100 runners in these things. If we call an average field size 96 for the sake of argument, then you've got a one in three chance of a first round bye - so for any given event, you'll need seven wins two thirds of the time, and six the remainder of the time. This gives us a nice even answer - if in three events, we expect 7/7/6 in terms of matches, that's twenty matches per three tournaments. So we need to win fifteen in a row.
Next, how often do we win a tournament? Now here's where we're going to need to get a bit controversial. The standard of the series is, in relation to the Pro Tour, pretty poor. Looking at the tour leaderboard on DC, there's barely a dozen players outside of Beau that were capable of an overall average that equates to winning legs in 21 darts or less. Barely half of these have a first nine over 80, so if they are wanting a six visit kill they're on average needing a three figure outshot. In the context of putting someone up against a tour card holder, that's not good. In the context of putting someone up against Littler, that's even worse. Dennie Olde Kalter would likely be an enormous favourite to win any WS event and you only need to go past best of 9 to best of 11 where he drops below 10% to win against Littler.
As such, I'm going to do a pretty brutal set of simplifications. First, I'm going to make all games best of 9, if only because I don't have best of 7 outwardly modelled in my master computer. It's only going to make a minor difference, adding or taking away one leg required doesn't change the maths that much. Second, I'm going to assume that there are at most a dozen players, other than us, that can realistically put up a challenge, and that if you draw anyone else, you get a free win. This isn't football where you can nick a goal on the break and then timewaste for the rest of the game - you can't drag someone into a scrappy opening leg, win it in 26 darts and then stall. You need to hit (at least how I'm modelling it) five winning doubles, and once you've thrown three darts there's nothing you can do to stop your opponent from throwing three better darts. Finally, I'm going to assume that in the event where we don't get a first round bye, we (and everyone competent) avoid each other, so as to be able to model things all the same - we're in the last 64 every time, and against 51 of the opponents we win, and against the other 12 we need to work for it. This may seem like an over simplification, but it only takes the PDC to say "we're seeding 16 players next year" and you get the same result.
So, that being said, how often do we win a tournament? With the simplifications we've made, this basically becomes a function of how many times we run into a good opponent, then working out how frequently we beat that good opponent. How good that good opponent is will come later, but let's cross the first bridge first. We've got 64 players - ourself, twelve players of interest, and then 51 jobbers. There's two things we need to do here - the simple one is working out how often we need to play someone good, which is a simple 12/51. or 23.5% of the time. The other thing we need to do is work out on average how often two of our good player pool run into each other. Now this is something I probably knew how to do manually 25 years ago, but we have AI now, so I'm going to trust the number it's given in saying that we get 1.24 matches on average where it's good player against good player. Now clearly we can't eliminate .24 of a dart player in a match, so I'm going to need to round up/down accordingly and hope that we don't do one or the other that often. We'll repeat this process for each round:
Round of 64 - 0.235 matches for us, 1.24 matches total - new player count 12/20
Round of 32 - 0.355 matches for us, 2.13 matches total - new player count 10/6
Round of 16 - 0.6 matches for us, 3 matches total - new player count 7/1
From here, we know that we will get the bad player 1 time in 7, or s good plsyer with 0.857 probability, the bad player will lose to whoever, the semi finals will be between all good players so we need to go through an additional two players for a total of just a fraction over needing to beat four good players on average in any given event. That doesn't sound stupidly unreasonable, we'd expect the quarter finals onwards to see us up against someone decent a large percentage of the time, but in the early rounds the field is so weak on average that we usually don't run into any landmines early on. As such, the question is simplified into "how often do we beat a good player 60 times in a row?"
Now for the time consuming part. Working out the good player. I'm going to make one more massive assumption, and create a generic "good women's player", by taking the top dozen or so that we're trying to avoid (so women averaging better than 71.57 i.e. 21 darts on average), look at the speed that they finish legs against each other (to avoid watering down the stats where we're just playing really weak opponents who are letting us finish however quickly we want - this is the exact reason why I don't put any WS data into the database), and then I can put that data line into the master computer, stick it against whoever we want, and then if our tour card holder has a win chance of better than 98.86% in a best of 9 match (this being the sixtieth root of 0.5), then we know we're good. This is the ballache number crunching part. But it's done, and the sample of players I had has less than 100 legs in fifteen darts or fewer, and over 200 in each of the six and over seven visit buckets, with the latter being larger. Considering the database has over 50% of legs in five or better, that's a bad look. Shove that against Littler, and Luke wins a best of nine 99.47% of the time. That is way more than enough - heck, give Littler no free wins and the breakeven point is 130 matches. Yikes.
But who else would be favoured? What of Greaves herself? Well Beau would only expect to win against our conglomerate player just over 96% of the time, so for her, the breakeven point is 17 matches, or just over four tournaments as we've modelled it. So to get a thirteen tournament run is definitely a bit of sun running. Who else would be good? Well, sorting by winning average, nobody. Rock falls just short at 98.50%, Bunting despite averaging lower scores about a tenth of a percent higher but still no good, Price shows the same thing but is still short, and once you drop out of the top twelve you drop below 98%. So, too long didn't read version - yes, it is just Littler.
However, because there's always a however, there is one further thing that needs to be taken into consideration before we put the topic to bed. The data model I use for projecting matches makes the assumption that the bull is a coinflip. Now, with this level of disparity between quality of players, is that realistic? The question then becomes how often do we lose a match 5-4 (you would think that this would be most of the 1.3%, 1.4% of games that someone like a Pirce is losing), how often do we actually win the bull in practice, and how many of the additional times we win the bull were we not only not breaking anyway, but having the darts makes the difference between winning and losing? It's got to be a fairly small number, but we don't need to flip that many results to become a favourite to get to the magical 100 number. Price was breaking even at 52 wins against the good players and we needed 60 - that's pretty darned close. But that's an exercise for another post maybe.
