Average inflation

One of the first posts, if not the first post, I made on here was relating to averages going up when you play a better player, even if you throw the exact same darts. I thought I'd try to quantify this by looking from a BDO to PDC switch perspective. Glen Durrant averaged 93.48 in his final vs Danny Noppert, Wikipedia reliably informs me. How would he have averaged had he not faced Noppert, but instead faced Michael van Gerwen? This isn't too hard to calculate, we just need a model for van Gerwen. My stats say he's killing in twelve darts on just over 30% of occasions, and in fifteen darts 80% of the time. This then becomes easy - shove 1-10 into a random number generator, if it rolls a 1-3, van Gerwen hits a twelve darter, if it rolls 4-8, it's fifteen darts, 9 or 10 gives us eighteen darts.

I then took the Darts for Windows PDF, gave van Gerwen the throw as Noppert did, then looked leg by leg, using the first leg available where the player who should be on throw in my virtual match is throwing first. Most of the time this is the next leg, some times I needed to pop ahead (for example if Durrant had made it 2-2 in the first set, I'd need the next leg in which van Gerwen throws first, which as Durrant won the first set against Noppert in four legs, wouldn't be the opening leg in set two of the BDO final, as Noppert was on throw and not Durrant). I'd also skip a leg where I don't have enough information to determine whether Durrant would win a leg - this happened once where Noppert went out in fifteen darts on throw, while in my sim van Gerwen took eighteen darts, without a reliable way to see if Durrant would have finished the 72 he had left, I'll use another leg and come back to this one later.

Firstly, van Gerwen bagelled Durrant, dropping just four legs in the entire simulation - Durrant's best chance was in virtual set 2, where with the darts he took a 2-0 lead in legs, but then couldn't finish in 18 with van Gerwen taking the same, and allowed van Gerwen to break in fifteen darts in the deciding leg.

Secondly, Durrant's average was 97.32, nearly a whole four points higher than in the actual final. Now as van Gerwen won the sim quickly enough that I didn't even need to go into the eighth set to grab data, we should have a quick look at what wasn't used to see if there's any major discrepancy. We didn't use leg three of set six, where Durrant kills in 18, or legs two and three of set seven, where Durrant kills the two legs in 29 darts - an average a shade under 96 for those legs, nor did we use any of set 8 (average 91, five legs), set 9 (average 95, four legs) or set 10 (average 94, five legs). If anything, these sets were slightly better in terms of averaging than those which were actually used in the sim, in any case we can't say that Durrant's average is higher in the sim because he played better in the early stages of the real match.