⚾ From my daughter's question, 'How do you set up a tournament for 49 schools?', I tried making Koshien 64 schools
I have a daughter who has almost no interest in baseball.
One day, we were talking about high school baseball.
"They say there are 49 schools in the summer Koshien tournament."
Then my daughter said, out of the blue.
"How do you set up a tournament for 49 schools?"
...That's true.
That is a curious point.
🔢 Tournaments like 'powers of 2'
Tournaments have such clean numbers.
64 → 32 → 16 → 8 → 4 → 2 → 1
All schools play in the first round.
Half the winners move on to the second round.
Then half again.
Finally, one school remains.
It's incredibly simple.
However, Koshien has 49 schools.
The number 49 is actually quite tricky for a tournament.
🎫 How do you turn 49 schools into 32?
If it were 64 schools, you wouldn't have to think about anything.
But it's 49 schools.
If all schools play in the first round, 25 schools will remain.
From there on, it doesn't connect cleanly.
So, the goal is a 'clean 32 schools' for the second round.
To narrow it down from 49 schools to 32, we need 17 schools to be eliminated in the first round.
To make 17 schools lose, 17 matches are required.
Since 2 schools participate in one match, 17 matches × 2 schools = 34 schools will play in the first round.
Out of all 49 schools, 34 schools will play in the first round.
The remaining 15 schools will be exempt from the first round and enter from the second round (seeded).
With this,
First round survivors (17 schools) + Seeds (15 schools) = 32 schools
and from here, a clean tournament begins.
This way,
49 → 32 → 16 → 8 → 4 → 2 → 1
it connects.
Mathematically, it works out perfectly.
But, this makes me wonder again.
🤔 Isn't it quite an advantage not to play in the first round?
Of course, the 15 schools exempt from the first round are decided by lottery.
It's not that strong schools are chosen.
Therefore, the system appears fair.
However, the schools that play in the first round
play one more game at Koshien.
The pitchers throw one more game.
The fielders also run for one more game.
They wear themselves out for one more game in the heat.
If they advance, they move on to the next game while carrying that fatigue.
On the other hand, the schools exempt from the first round
start directly in the second round.
Of course, the outcome isn't decided by just a one-game difference.
But,
only 15 schools hold the card of 'playing one fewer game.'
When you think about it that way, it's a bit concerning.
🎲 Then why not just make it 64 schools from the start?
At this point, I suddenly thought,
'If you're going to exempt 15 schools, wouldn't it be better to just add 15 schools?'
49 schools.
Add 15 schools to that.
64 schools.
If we do this,
64 → 32 → 16 → 8 → 4 → 2 → 1
It becomes.
There are no first-round byes either.
Every school can start from the same place.
The tournament bracket is also incredibly clean.
So, what do we do about those 15 schools?
🗾 First, keep 'one representative per prefecture'
I don't want to change this.
Tottori gets one school.
Kochi gets one school.
Saitama gets one school.
Tokyo gets at least one school.
Hokkaido gets at least one school.
No matter where you are in the country,
'our local representative is at Koshien'
we will preserve that charm of high school baseball.
First, we use the current framework of 49 representatives as the foundation.
On top of that, we add 15 slots.
📊 Where do we distribute the 15 additional slots?
So, what should we do with the 15 additional slots?
Simple prefectural population would be fine too.
It could also be based on the high school student population.
But since we're talking about high school baseball,
“High school student population × Number of baseball clubs”
is the approach I'll take.
There are many high school students.
And there are many high school students playing baseball.
Regions like that should be able to send additional representatives more easily.
In other words,
“Regional fairness” + “Fairness in the number of participants”
is the concept.
Let's try distributing 15 spots as a test.
🗼 Tokyo: +3
🏯 Aichi: +2
🐙 Osaka: +2
🌊 Kanagawa: +2
🦀 Hokkaido: +1
🍘 Saitama: +1
🥜 Chiba: +1
🐄 Hyogo: +1
🍜 Fukuoka: +1
🗻 Shizuoka: +1
With this,
3+2+2+2+1+1+1+1+1+1=15.
I will add these 15 schools to the current 49 representatives.
49+15=64.
🗼 Tokyo, an unbelievable 5 representatives
Looking at this, the place that will be most surprised is definitely Tokyo.
Currently, there are 2 representatives: East Tokyo and West Tokyo.
And now,
5 representatives.
Tokyo A.
Tokyo B.
Tokyo C.
Tokyo D.
Tokyo E.
...It is quite possible that a 'Tokyo vs. Tokyo' matchup could happen at Koshien.
But when you think about it,
The number of high schools is large.
The number of high school students is large.
The number of baseball clubs is also large.
In that case,
rather than the current rule of '2 schools because it's Tokyo',
one could also consider
a concept of '5 schools based on the size of the high school student population and baseball clubs'.
This is also a possible way of thinking.
🏯 Aichi, Osaka, and Kanagawa also get 3 representatives
Aichi, Osaka, and Kanagawa get 3 representatives.
This also feels somewhat convincing.
They have many high school students.
They have many baseball clubs.
They also have many powerhouse teams that appear in national tournaments.
In that case,
3 representatives per prefecture.
Such a system is also possible.
🦀 Hokkaido is a bit difficult
Hokkaido also gets 3 representatives.
However, Hokkaido cannot be discussed based on population alone.
Currently, Hokkaido has 2 representatives, North Hokkaido and South Hokkaido, but
it is just so vast.
The distance between schools is also great.
Just the travel for the qualifiers is a huge task.
So, in the case of Hokkaido,
population
is not the only factor; we might need to consider
geographical conditions
as well.
System design is a deep subject once you start thinking about it.
⚖️ What does 'fairness' actually mean?
I think this is the most interesting part.
One school for each of the 47 prefectures.
This is
regional fairness.
Increasing the number of representatives based on the number of high school students.
This is
population fairness.
Increasing the number of representatives based on the number of baseball clubs.
This is
fairness in terms of the number of participants.
The answer changes depending on which one you prioritize.
'Five schools from Tokyo is just too many'
There is, of course, that opinion as well.
Conversely,
There is also the opinion,
'Isn't it stranger that there are only two schools when there are hundreds of high schools in Tokyo?'
In other words,
there are many different kinds of fairness when it comes to the word fairness.
🏟️ But with 64 schools, the tournament is beautiful.
This part is clear.
64 → 32 → 16 → 8 → 4 → 2 → 1
Every school enters from the first round.
There are no first-round byes.
No school has to play an extra game just because they played in the first round.
Everyone starts from the same line.
And in the end, only one school remains.
The story that began with my daughter's,
'How do you set up a tournament with 49 schools?'
simple question,
before I knew it,
'Is there even a need for it to be 49 schools in the first place?'
had turned into that kind of discussion.
Instead of fitting the tournament to 49 schools,
fit the 64 schools to the tournament.
Perhaps that kind of reverse thinking is also a possibility.
🔍 However, I want to properly investigate where those 15 spots would go.
Of course, if the number of games increases,
another issue arises where the tournament period would be extended, but...
This allocation by prefecture is,
a calculation based on the question, 'What would happen if we used this line of reasoning?'
as it were.
If we were to actually consider this as a system,
we should look at the high school student population,
the number of high schools,
the number of hardball baseball clubs,
the number of baseball club members,
the distribution of schools by region,
and furthermore, geographical conditions like those in Hokkaido.
Using such accurate data,
we should verify 'where it is truly appropriate to distribute the 15 additional spots.'
that would be better.
Perhaps it won't be 5 schools from Tokyo.
Maybe Saitama will get 3 schools.
An unexpected prefecture might get an additional slot.
It all started with a casual remark from my daughter,
the 'Koshien 64-Representative Plan'.
If we really were to make it 64 schools,
where would it be most fair to distribute the 15 extra slots?
I wonder what the results would be if I calculated it using accurate data.
I've started to get a little curious.