On Monday I had a hair cut. It happens every now and then, though probably not as much as many people.

But what I was actually refering to was the process of Swiss tournaments and cuts to day 2s then cuts to top 8. It came up again on the official boards in the post Lille discussions.

The math behind swiss tournaments isn't terribly hard, it's just tiresome. So I automated it. The discussion this time around was whether for 200 people 6 or 7 constructed then 3 draft, then top eight was proscriptive - did going to the extra  constructed round make any difference?

Well, here's the numbers. When looking at predicting Swiss results, there's an upper and lower bound. The upper is when every person paired down in a round wins, and the lower when every such person loses.

So here you go, for the 208 people at Lille...
6 rounds
6-0 3 or 4 people
5-1 18 to 22 people
4-2 46 to 51 people
3-3 64 people

7 rounds
7-0 1 or 2 people
6-1 8 to 14 people
5-2 28 to 40 people
4-3 54 to 61 people

Now, Lille did a 64 to next day cut. That's the top 38 to 43 4-2 or the top 8 to 27 of the 4-3.

Blinded by the math yet?

What does all that actually mean?
Well, if you were going to make the cut after six rounds and win, you'll make the cut after seven. Pretty obvious.
But how many will change places from making to not making and vice versa?

12
(You work that out from all the matchups the 4-2 could have and their overlap into the non-cut and vice versa compared to the 4-3 from seven rounds)

So, adding that extra round potentially shifted 12 people round. Probably much less than that, though try telling that to the person who lost their round seven and would have cut but then didn't.

Moving on - you then have three rounds of draft. The issue here is the top eight cut. If you'd had nine rounds in total...

9-0 0 to 1
8-1 0 to 8
7-2 2 to irrelevant
6-3 14 to irrelevant

For ten rounds
10-0 0 to 1
9-1 0 to 8
8-2 0 to irrelevant
7-3 2 to irrelevant
6-4 14 to irrelevant


So what's that saying?
Well, it's saying that prior to the tournament it doesn't matter a jot whether there's 6 or 7 constructed then 3 draft for determining the relative numbers/odds of making the top 8. 'Worst performance' scenario sees two people top the chart, then six of fourteen below them make the cut as well. One and seven for 'Best performance'. And it doesn't change with how many rounds you run in total - you're past the 'magic number' of rounds, at this point every time one person goes up, another comes down and it's all swings and roundabouts but not changing relative numbers.

So, the move from six rounds to seven at DMF Lille achieved just one thing - at most twelve people who would've made the day 2 cut didn't and vice versa. It didn't effect relative t8 cut odds at all.



Now, moving on to Worlds. Say 500 people turn up. Here's how that pans out...

R6
6-0 7 to 8
5-1 44 to 48
4-2 115 to 120
3-3 158

R7
7-0 3 to 4
6-1 24 to 28
5-2 79 to 84
4-3 138 to 140

*****

R9
9-0 0 to 1
8-1 5 to 9
7-2 31 to 36

R10
10-0 0 to 1
9-1 0 to 9
8-2 5 to 36
7-3 31 to irrelevant

Okay, so there's actually 12/13 rounds in the worlds, but I don't need to go that high (the array size in my Visual Basic program only goes to 1024 and I can't be bothered to change it). You can already see where it's going. 10 rounds is not significantly different from 9 in terms of your potential maxima and minima - you just get a better spread as before.

What is different is the day two cut crunch going from 6 to 7. It's a bit more than at most twelve shifting. Worlds will be on the 'positive record' system (you need to get equal to or more wins than losses to day two) and the difference between 6 and 7 is up to 80 people not making the day 2 cut if you go to the seventh round, and up to 50 shuffling round.

That's a pretty big difference, over one sixth the field cut just by going that extra round.

Message here is:
If you're better at constructed than draft, hope UDE stretch to seven rounds day one.
If you're better at draft, hope they stick to the six rounds constructed day one.


If anyone wants to write their own code/Excel macro to work out swiss piarings numbers, just shout. It's a simple six line thing, not that hard once you know what you're doing.