How do I manage time for a round robin pool? (TOing)

Juggleguy

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#1
In the second half of this two-part article, I'll discuss how to manage time specifically with round-robin pools. This is a very popular starting format at Smash tournaments because of the seeding foundation it builds transitioning into a final bracket, the extra competitive playing time it provides to all players, and the creative control it offers to organizers (we'll talk more about the advantages and disadvantages of round robin pools in a future article dedicated to tournament formats). Round-robin pools are a staple of Smash tournaments, but time management of the format is often butchered.

As usual, think about some of the expected values for your event before proceeding. The answers to these questions will serve as the parameters for your time estimate.

Entrants: How many entrants do I expect per pool?
Setups: How many full setups do I expect to be available per pool?
Time: How many minutes do I expect the average set to require?

Let’s jump right into it. Due to the number of parameters involved with estimating time for round robin pools, I'll present the solution first and then explain it later.

The time required to run a round robin pool is:
kt(n(n-1))/2s

where
k = efficiency factor
t = average time per set
n = number of players in the pool
s = number of setups available in the pool


For those of you who are interested in how this formula is derived, see below for an explanation. For those of you who trust that the formula works and want to go straight to some examples, skip ahead.


Formula Explanation

n(n-1)/2 is an expression that represents the number of total sets that have to be played in a round robin given n players in the pool. Consider the classic handshake problem: if you're in a room with n people and everyone has to shake hands once with everyone else, how many handshakes occur overall? This is pretty much the exact same question as: if you're in a pool with n players and everyone has to play each other in one set, how many sets occur overall? Plenty of documentation exists on how this formula is derived, and you can read up on it [1][2][3] if you're curious.

n(n-1)/2 is multiplied by the variable t, which represents the average time per set. We are essentially taking the number of total sets and multiplying it by the time per set to obtain an expected value for the time required overall, or the time required to play out every set in the pool one after the other.

tn(n-1)/2 is multiplied again by the efficiency factor k, which represents the multiplier coefficient that accounts for downtime between sets. If the average set takes 10 minutes but players experience an average downtime of 5 minutes per set, then the efficiency factor k would be 1.5 to account for the extra time between sets. Well-run tournaments often achieve an efficiency factor close to 1, while poorly-run tournaments often have an efficiency factor that exceeds 2. Use your TOing experience to come up with a reliable empirical value for k to use at your tournaments.

ktn(n-1)/2 is then divided by the variable s, which represents the number of setups available in the pool. Since more setups means more sets can be played concurrently instead of one after the other, we can divide the overall expected time by s to account for the decrease in consecutive sets that have to be played until pool completion. Keep in mind there is an upper limit to s represented by s' = min(s,floor(n/2)) which accounts for the fact that after a certain point, additional setups do not help decrease time required (for example, 3+ setups for a pool with 4 players).


The Handshake Problem illustrated in grid format (left) and geometric format (right).


Example #1

You're at a small Melee tourney with the standard ruleset and you see a round robin that contains 6 players in it, with 2 available setups to use for the pool.

Let
k = 1
t = 10 minutes per set
n = 6 players in the pool
s = 2 setups available in the pool

Time required to run this round robin pool:

= kt(n(n-1))/2s
= (1)(10 mins)(6(6-1) players) / (2(2 setups))
= (1)(10)(6(6-1))/(2)(2)
= 75 minutes
= 1 hour 15 minutes

A six-person round robin pool.


Example #2

You're at a large Brawl tourney with the standard ruleset and you see a round robin that contains 8 players in it, with 2 available setups to use for the pool.

Let
k = 1.5
t = 10 minutes per set
n = 8 players in the pool
s = 2 setups available in the pool

Time required to run this round robin pool:

= kt(n(n-1))/2s
= (1.5)(10 mins)(8(8-1) players) / (2(2 setups))
= (1.5)(10)(8(8-1))/(2)(2)
= 210 minutes
= 3 hours 30 minutes

An eight-person round robin pool.


Example #3

You're at a large Project M tourney with the standard ruleset and you see a round robin that contains 10 players in it, with 6 available setups to use for the pool.

Let
k = 1.2
t = 10 minutes per set
n = 10 players in the pool
s = 6 setups available in the pool => 5 setups *

* Be careful here! Even though 6 setups are available, only 5 setups can be used concurrently since there are 10 players in the pool and each set requires 2 of them at once. The sixth setup does not help reduce time. Because of this, s = 5 in this example.

Time required to run this round robin pool:

= kt(n(n-1))/2s
= (1.2)(10 mins)(10(10-1) players) / (2(5 setups))
= (1.2)(10)(10(10-1))/(2)(5)
= 108 minutes
= 1 hour 48 minutes


A ten-person round robin pool.


Food for Thought

* This article’s scope is limited to that of time management within one round robin pool. We'll talk more about round robin pools -- advantages and disadvantages, how to determine the number of pools to run and number of players to advance, and more -- in a future article dedicated to tournament formats. In any case, if you’re a new TO, you’re advised to evaluate the setups situation at a tournament and calculate the time required manually before looking too far ahead.

* Be careful scaling up the number of players per pool. While the number of players grows linearly, the time required grows at a more unforgiving rate. In Example #1, an increase from 6 players to 7 players results in an increase in time required from 75 minutes to 105 minutes. In the same example, an increase from 7 players to 8 players results in an increase in time required from 105 minutes to 140 minutes.

* Waves are extremely useful. For TOing purposes, assume the definition of a wave to be a period of time in which only a subset of your entrants have tourney obligations. Multiple waves allow events to be broken down into chunks that contain a subset of the entrants, such that TOs have to manage a smaller number of entrants at any given time and players have to be present for a smaller period of time while still playing the same number of matches.

* Pay attention to setup utilization. To calculate a round robin pool's setup utilization, divide the number of setups by the number of available sets. If a pool of 8 players has 2 setups to work with, the setup utilization is (2 setups) / (4 available sets) = 0.5 = 50% setup utilization. You want this number to be as close to 1 (or 100%) as possible. Splitting your pools into multiple waves allows you to accomplish this. Number of setups remains constant throughout, but you control the number of pools happening at any given time.

--

Juggleguy is a national tournament organizer, Melee It On Me team member, and Smashboards contributor. You can follow him on Twitter: @JuggleRob
 
Last edited:
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#5
This is really useful; I've been considering in TOing in the UK once SSB3D comes out, and round robin seems like perfect for the format; no need to over-organise, just tell people who they need to fight.

As a side note, what would be the best way to set up a round robin with 4-player matches?
 

CTL17

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#9
I'm gonna have to go all math-technical on you and say s should be replaced with s' = min(s,floor(n/2)) to continue with your "critical value" statement from part one.
 

LydianAlchemist

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#11
I'm actually writing a program for this for my C class. earlier in the program I ask how many setups. this is for 8 setups. my math might be wrong its a WIP EDIT: also is assumes each game will go the full 8 minutes and there is no time between games. assumptions are fun.

(To seed a bracket of 16 players from 24 initial players in the given amount of time, there needs to be:

FORMAT: A

1 pools

24 amount of players each

With the top 16 players of each pool advancing to bracket

Which would be 300 max sets that must be played in each pool and take max 25.00 hrs. to complete per pool

Which would be 300 max sets that must be played for all pools, which would take 25.00 hrs. to complete before bracket is seeded

With 31 sets in bracket, the entire tournament would take 26.55 hrs.

FORMAT: B

2 pools

12 amount of players each

With the top 8 players of each pool advancing to bracket

Which would be 78 max sets that must be played in each pool and take max 6.50 hrs. to complete per pool

Which would be 156 max sets that must be played for all pools, which would take 13.00 hrs. to complete before bracket is seeded

With 31 sets in bracket, the entire tournament would take 14.55 hrs.

FORMAT: C

3 pools

8 amount of players each

With the top 5 players of each pool advancing to bracket

Which would be 36 max sets that must be played in each pool and take max 3.00 hrs. to complete per pool

Which would be 108 max sets that must be played for all pools, which would take 9.00 hrs. to complete before bracket is seeded

With 31 sets in bracket, the entire tournament would take 10.55 hrs.

FORMAT: D

4 pools

6 amount of players each

With the top 4 players of each pool advancing to bracket

Which would be 21 max sets that must be played in each pool and take max 1.75 hrs. to complete per pool

Which would be 84 max sets that must be played for all pools, which would take 7.00 hrs. to complete before bracket is seeded

With 31 sets in bracket, the entire tournament would take 8.55 hrs.

FORMAT: E

5 pools

4 amount of players each

With the top 3 players of each pool advancing to bracket

Which would be 10 max sets that must be played in each pool and take max 0.83 hrs. to complete per pool

Which would be 50 max sets that must be played for all pools, which would take 4.17 hrs. to complete before bracket is seeded

With 31 sets in bracket, the entire tournament would take 5.72 hrs.

FORMAT: F

6 pools

4 amount of players each

With the top 2 players of each pool advancing to bracket

Which would be 10 max sets that must be played in each pool and take max 0.83 hrs. to complete per pool

Which would be 60 max sets that must be played for all pools, which would take 5.00 hrs. to complete before bracket is seeded

With 31 sets in bracket, the entire tournament would take 6.55 hrs.

FORMAT: G

7 pools

3 amount of players each

With the top 2 players of each pool advancing to bracket

Which would be 6 max sets that must be played in each pool and take max 0.50 hrs. to complete per pool

Which would be 42 max sets that must be played for all pools, which would take 3.50 hrs. to complete before bracket is seeded

With 31 sets in bracket, the entire tournament would take 5.05 hrs.

FORMAT: H

8 pools

3 amount of players each

With the top 2 players of each pool advancing to bracket

Which would be 6 max sets that must be played in each pool and take max 0.50 hrs. to complete per pool

Which would be 48 max sets that must be played for all pools, which would take 4.00 hrs. to complete before bracket is seeded

With 31 sets in bracket, the entire tournament would take 5.55 hrs.

Choices of:

FORMAT A would take 26.55 hours

FORMAT B would take 14.55 hours

FORMAT C would take 10.55 hours

FORMAT D would take 8.55 hours

FORMAT E would take 5.72 hours

FORMAT F would take 6.55 hours

FORMAT G would take 5.05 hours

FORMAT H would take 5.55 hours

DISCLAIMER:

ALL CALCULATIONS ARE ESITMATES AND DO NOT FACTOR IN -

TIME TAKEN BETWEEN GAMES/SETS/MATCHES. EX: TIME TAKEN TO FIND PLAYERS.)
 
Last edited:

Juggleguy

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#12
I'm actually writing a program for this for my C class. earlier in the program I ask how many setups. this is for 8 setups. my math might be wrong its a WIP EDIT: also is assumes each game will go the full 8 minutes and there is no time between games. assumptions are fun.

...
Good start. One thing I would get rid of is all pool numbers that aren't a power of 2. For example, 3 pools, or 5 pools, or 6 pools, or 7 pools. Those numbers of pools aren't legitimate options for transitioning into bracket, so might as well disregard.
 

Monkley6

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Messages
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#13
These always look like good informative posts. Are they archived anywhere? While I have no interest in TOing now, they may prove helpful in the future. Especially if 2 years from now, there are newer TOs trying to get a hold of things.
A directory linking these types of posts in Tournament Discussions seems like a good idea, for example.
 
Last edited:

Juggleguy

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#14
These always look like good informative posts. Are they archived anywhere? While I have no interest in TOing now, they may prove helpful in the future. Especially if 2 years from now, there are newer TOs trying to get a hold of things.
A directory linking these types of posts in Tournament Discussions seems like a good idea, for example.
http://smashboards.com/articles/smash-to-guide/
 

Depster

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#15
Calculus? Nah, you learn it all in a discrete math class, graph theory and everything. Unless you've only seen n(n-1)/2 with summations. I really like seeing math applied like this though, it's quite interesting.
 

LydianAlchemist

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#16
Good start. One thing I would get rid of is all pool numbers that aren't a power of 2. For example, 3 pools, or 5 pools, or 6 pools, or 7 pools. Those numbers of pools aren't legitimate options for transitioning into bracket, so might as well disregard.
you're totally right! haha derp. thanks.

here is new output
(
~POOLS~

Please enter number of initial players:

140

Please enter number of setups:

57

Please enter desired "Best of" number for pools:

3

You have chosen best of 3 for pools

Please enter desired "Best of" number for bracket:

3

You have chosen best of 3 for bracket

Please enter the time limit (or average match time) for each match in minutes

5

Please choose amount of players you would like to seed into the bracket:

4 8

16 32

64 128

128
To seed a bracket of 128 players from 140 initial players in the given amount of time, there needs to be:


FORMAT: A
1 pool
140 amount of players each
With the top 128 players of each pool advancing to bracket
Which would be 9870 max sets that must be played in each pool
and take max 43.29 hrs. to complete per pool
Which would be 9870 max sets that must be played for all pools, which would take 43.29 hrs. to complete before bracket is seeded
With 255 sets in bracket, the entire tournament would take 44.41 hrs.

FORMAT: B
2 pools
70 amount of players each
With the top 64 players of each pool advancing to bracket
Which would be 2485 max sets that must be played in each pool
and take max 10.90 hrs. to complete per pool
Which would be 4970 max sets that must be played for all pools, which would take 21.80 hrs. to complete before bracket is seeded
With 255 sets in bracket, the entire tournament would take 22.92 hrs.


FORMAT: C
4 pools
35 amount of players each
With the top 32 players of each pool advancing to bracket
Which would be 630 max sets that must be played in each pool
and take max 2.76 hrs. to complete per pool
Which would be 2520 max sets that must be played for all pools, which would take 11.05 hrs. to complete before bracket is seeded
With 255 sets in bracket, the entire tournament would take 12.17 hrs.
FORMAT: D
8 pools
18 amount of players each
With the top 16 players of each pool advancing to bracket
Which would be 171 max sets that must be played in each pool
and take max 0.75 hrs. to complete per pool
Which would be 1368 max sets that must be played for all pools, which would take 6.00 hrs. to complete before bracket is seeded
With 255 sets in bracket, the entire tournament would take 7.12 hrs.


FORMAT: E
16 pools
9 amount of players each
With the top 8 players of each pool advancing to bracket
Which would be 45 max sets that must be played in each pool
and take max 0.20 hrs. to complete per pool
Which would be 720 max sets that must be played for all pools, which would take 3.16 hrs. to complete before bracket is seeded
With 255 sets in bracket, the entire tournament would take 4.28 hrs.

FORMAT: F
32 pools
5 amount of players each
With the top 4 players of each pool advancing to bracket
Which would be 15 max sets that must be played in each pool
and take max 0.07 hrs. to complete per pool
Which would be 480 max sets that must be played for all pools, which would take 2.11 hrs. to complete before bracket is seeded
With 255 sets in bracket, the entire tournament would take 3.22 hrs.


FORMAT: G
64 pools
3 amount of players each
With the top 2 players of each pool advancing to bracket
Which would be 6 max sets that must be played in each pool
and take max 0.03 hrs. to complete per pool
Which would be 384 max sets that must be played for all pools, which would take 1.68 hrs. to complete before bracket is seeded
With 255 sets in bracket, the entire tournament would take 2.80 hrs.


Choices of:
FORMAT A would take 44.41 hours
FORMAT B would take 22.92 hours
FORMAT C would take 12.17 hours
FORMAT D would take 7.12 hours
FORMAT E would take 4.28 hours
FORMAT F would take 3.22 hours
FORMAT G would take 2.80 hours

DISCLAIMER:
ALL CALCULATIONS ARE ESITMATES AND DO NOT FACTOR IN -
TIME TAKEN BETWEEN GAMES/SETS/MATCHES. EX: TIME TAKEN TO FIND PLAYERS.
)

BTDUBS to everyone.
I realized the other day the semi primes only have 2 factors right? (other than 1 and itself)
which are prime numbers.

if you give each player a jersey number in a round robin/pools. and the jersey number is prime. you can keep track of matches using the product of 2 players jerseys.

example:

Fly Amanita is player #7
HBOX is player #11

I can't remember who won, so I go to my notebook and look up match 77. idk how practical it is.

but it'd be cool to implement for the sake of number theory

also easier to keep track of on paper? or maybe more complicated...
 
Last edited:

KinGly

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#17
Can someone explain how round robin pools work, for instance:

-How many games can you lose before your out
-does seeding take any role in round robins
-it seems to take longer than double elimination, considering that with 8 players it takes around 3 and a half hours. so what advantages does it possess

I'm not a to, I'm just a player, but all my tourneys have been double elimination, so I don't understand pools at all. I'd be happy if someone could explain it.
 

Zach777

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#18
KinGly said:
Can someone explain how round robin pools work, for instance:
-How many games can you lose before your out

You don't get eliminated in a round robin pool. If you don't win enough matches you won't be put into the next pool or put into the bracket.

-does seeding take any role in round robins

Kind of, sometimes. There is multiple pools and top level players will be seeded so as not to have another top player in their pool.

-it seems to take longer than double elimination, considering that with 8 players it takes around 3 and a half hours. so what advantages does it possess

Everyone fights everyone. It is much more accurate than in a doub elim. In a doub elim, say there is a player who is the best of them all and will beat everyone except two guys. But those two guys lose to more people than our best player does. The best player might face both of his achilles heels and finish very poorly in a doub elim, whereas a round robin pool will let our best guy fight 5 more matches and move to the bracket or next pool.

Well, I'm done. Hope this helps and doesn't make you more confused.
 
Last edited:

KinGly

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#19
-How many games can you lose before your out

You don't get eliminated in a round robin pool. If you don't win enough matches you won't be put into the next pool or put into the bracket.

-does seeding take any role in round robins

Kind of, sometimes. There is multiple pools and top level players will be seeded so as not to have another top player in their pool.

-it seems to take longer than double elimination, considering that with 8 players it takes around 3 and a half hours. so what advantages does it possess

Everyone fights everyone. It is much more accurate than in a doub elim. In a doub elim, say there is a player who is the best of them all and will beat everyone except two guys. But those two guys lose to more people than our best player does. The best player might face both of his achilles heels and finish very poorly in a doub elim, whereas a round robin pool will let our best guy fight 5 more matches and move to the bracket or next pool.

Well, I'm done. Hope this helps and doesn't make you more confused.
Thanks, I've got my first tourney running pools this weekend so it's nice to know what I'm getting into.
 

shuall

Smash Apprentice
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#21
nitpick: kt(n(n-1))/2s == (kt(n(n-1))/2) * s != kt(n(n-1))/(2s)

But you explained it, so not really a problem.
 

M32

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#23
Hi, I need an opinion.
We have 64 players, divided in 8 pools. Obviously Round Robin.
We own 8 setups.
Would it be more efficient to have 2 pools at each time, dividing the schedule into 4, or having 4 pools at each time, dividing the schedule into 2?
Notice I'm talking about efficiency especially.
It has been a long debate between me and another TO and I just can't seem to get through him with my ideas, hopefully I can get some input from someone experienced so I can just show him I'm right.
I'm obviously not stating my side to avoid making you biased.
Good job on the article
 

Juggleguy

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#24
Hi, I need an opinion.
We have 64 players, divided in 8 pools. Obviously Round Robin.
We own 8 setups.
Would it be more efficient to have 2 pools at each time, dividing the schedule into 4, or having 4 pools at each time, dividing the schedule into 2?
Notice I'm talking about efficiency especially.
It has been a long debate between me and another TO and I just can't seem to get through him with my ideas, hopefully I can get some input from someone experienced so I can just show him I'm right.
I'm obviously not stating my side to avoid making you biased.
Good job on the article
Run 4 pools at a time and divide the schedule into 2 waves. It's definitely more efficient. The players will enjoy the schedule more, the organizers will enjoy the schedule more, win win.
 

M32

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#25
Run 4 pools at a time and divide the schedule into 2 waves. It's definitely more efficient. The players will enjoy the schedule more, the organizers will enjoy the schedule more, win win.
Thank you very much for reply, I'm also pretty glad your opinion is the same of mine.
Have a good day!
 

NEX-GEX

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#26
M32 M32 : Correct me if I'm wrong, but if you have 8 pools and 8 setups, wouldn't it be the easiest solution to play out each pool on an individual Setup? As a player, I don't have to check after every Match where to go next, I just stay at the setup and check out my next opponent's play. That way everything I need is in one place.
What do you actually achieve by dividing the pools into waves?
 
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