You are the HJ of a sealed PTQ. 127 players sign up and are seated for deck construction. Just before seating for round 1, 4 players approach you and want to be added to the event with a round 1 loss.

If you were to add these players to the event do you need to add an additional round to compensate for the extra players?

At what number of additional (late) players would you add a round?

From a logical perspective I would increase the number of rounds to the
appropriate number so that the math works properly. As they are going to
be a part of the tournament just like any other player, so they would have
the same effect on the tournament as anyone else. (Note that this is what
I would choose to do - I'm not sure what anyone else has to say on the
matter.)

We have the current number of rounds calculated based on the assumption that making X-1 should guarantee a Top 8 spot. Adding 4 players with a first round Loss will not change the math, so no need to add a round. When starting a 7 round PTQ with 127 players and an additional 99 show up (to play from round 2 with a first round Loss), I'm fine with that.
When more than 100 players show up, bringing the number over 226 and thus requiring a 9th round… I would have to do some math, but probably you need 8 rounds then to guarantee Top 8 to all palyers at X-1 or better.

Originally posted by Dustin De Leeuw:

We have the current number of rounds calculated based on the assumption that making X-1 should guarantee a Top 8 spot. Adding 4 players with a first round Loss will not change the math, so no need to add a round. When starting a 7 round PTQ with 127 players and an additional 99 show up (to play from round 2 with a first round Loss), I'm fine with that.
When more than 100 players show up, bringing the number over 226 and thus requiring a 9th round… I would have to do some math, but probably you need 8 rounds then to guarantee Top 8 to all palyers at X-1 or better.

I'm not sure this parses properly - at 131 players you end up with 2 X-0 and 8 X-1 at the end of Round 7 (which is how many swiss rounds you'd have at 127); someone gets cut on breakers if I'm not mistaken?


Unrelated to the above, but relevant to the topic: Do PTQs have explicit rules for their round configuration like GPTs do?

Edited Rebecca Lawrence (April 8, 2014 03:48:14 PM)

Originally posted by Nathaniel Lawrence:

Unrelated to the above, but relevant to the topic: Do PTQs have explicit rules for their round configuration like GPTs do?

Yes they do. For instance, this is the info page for PTQs feeding into Pro Tour Magic 2015: https://www.wizards.com/Magic/TCG/Events.aspx?x=mtg/protour/qualifiers/portland14

You'll see a chart halfways down the page that tells you how many rounds you need to run for X many players.

Each player you add does affect the math, even though they're receiving a round one loss.

With 127 players, you should have - at most - 63 players at X-1 after one round. Instead, you now have 67 players at X-1; that changes how many of them can finish the 7 rounds at X-1. (Simple math says adding 4 players means 2 more can finish at X-1, but I suspect it's nowhere near that simple…)

There's a customer service aspect to this question, however. At the end of the deck construction, you have 127 players expecting to play 7 rounds. While that rarely affects deck building choices, some of those players will believe it did affect theirs, or it otherwise inconveniences them, if you add another round.

If I only have a handful of late entrants, I won't change the already announced number of rounds. If I have more than a handful, I'm not sure I should add them all, because of the negative impact for those who were on time.

But, that's just my thoughts on it. I'm pretty sure there's no (need for) Official Policy on this. :)

d:^D

Originally posted by Nathaniel Lawrence:

I'm not sure this parses properly - at 131 players you end up with 2 X-0 and 8 X-1 at the end of Round 7 (which is how many swiss rounds you'd have at 127); someone gets cut on breakers if I'm not mistaken?

This is only true if all 131 players start round 1; because in this scenario, 4 players start with a round 1 loss, it's impossible to end up with that many players at X-1 or better. But, to be honest, I didn't run the math on it… I recall a discussion with another mathematician and we reached this conclusion ^^

Because I am a very nice person vith a lot of spare time, I took the
liberty to do the math using the most tedious (but also most obvious) way:

1-0 64
0-1 67

2-0 32
1-1 32 + 34 = 66
1-1 33

3-0 16
2-1 16 + 33 = 49
1-2 33 + 17 = 50
0-0 16

4-0 8
3-1 8 + 25 = 33
2-2 24 + 25 = 49
1-3 25 + 8 = 33
0-4 8

5-0 4
4-1 4 + 17 = 21
3-2 16 + 25 = 41
2-3 24 + 17 = 41
1-4 16 + 4 = 20
0-5 4

6-0 2
5-1 2 + 11 = 13
4-2 10 + 21 = 31
3-3 20 + 21 = 41
2-4 20 + 10 = 30
1-5 10 + 2 = 12
0-6 2

7-0 1
6-1 1 + 7 = 8
5-2 6 + 16 = 22
4-3 15 + 21 = 36
3-4 20 + 15 = 35
2-5 15 + 6 = 21
1-6 6 + 1 = 7
0-7 1

As you can see, adding 3 players more than a maximum number can result in 1
player with 6-1 not reaching the TOP 8.


2014-04-08 20:58 GMT+02:00 Dustin De Leeuw <

It will make a difference even when they start 0-1 as you can see in the following charts:
First for the original 127 without draws being accounted for)
Start:
127
Round 1:
64 63
Round 2:
32 64 31
Round 3:
16 48 48 15
Round 4:
8 32 48 32 7
Round 5:
4 20 40 40 20 3
Round 6:
2 12 30 40 30 12 1
Round 7:
1 7 21 35 35 21 7 0

and now when we add 4 players in round 1 with a loss:
Start:
127
Round 1 (+4):
64 67
Round 2:
32 66 33
Round 3:
16 49 50 16
Round 4:
8 33 49 33 8
Round 5:
4 21 41 41 20 4
Round 6:
2 13 31 41 30 12 2
Round 7:
1 8 22 36 35 21 7 1

so we see when we keep the 7 rounds and assume no draws or DQs that we will have 1 with 7-0 and 8 with 6-1 resulting in one poor guy not making the T8 due to tiebreakers…

Doing some quick math on this (for speed this doesn't factor the values of draws, just straight X-Y records).

Your expected values with 127 players are:
Round 7
X-0 0.9921875
X-1 6.9453125
X-2 20.8359375

Meaning 7.9375 players at X-1 or better

With 127 players in round 1 + 4 added with a R1 loss:
Round 7
X-0 0.9921875
X-1 7.0078125
X-2 21.2109375

Meaning exactly 8 players at X-1 or better.

Here's a full chart of how many X-1s or better would be expected based on number of players added with a R1 loss:
Added X-1 or Better
0 7.9375
1 7.953125
2 7.96875
3 7.984375
4 8
5 8.015625
6 8.03125
7 8.046875
8 8.0625
9 8.078125
10 8.09375

Joe there must be something wrong with your calculation, most probably due to 0.9453… players being hard to achieve… ;) see the scheme above

Ok. I can do this math, and I can do it fast enough to figure out my
numbers starting a PTQ.

Should we have this expectation of any TO running a PTQ? We have the round
number cutoffs specifically so people don't have to do this math, right?


~Rob McKenzie
Magic Judge Level III
Minnesota

My approach to this situation is this: if I start an event with a number of players close to the number for another round, I (try to remember to) make an initial announcement that says something along the lines of “we currently have x players, so it looks like we'll play y rounds; however, if we have any late entries, we might jump to y+1 rounds; I'll let you know the final number at the start of round 1 (for limited events) or round 2 (for constructed events)”. I haven't heard complaints from players yet.

Thanks everyone for running the math properly! I don't remember why we thought that R1 Losses would not be a problem… *shame*