@deadgrantaires OKAY SO. i rewatched the last episode to try to understand seeding better and you were so right. about so many things. first of all YES some teams get to sit out the first round because the bracket looks like this:
[ID: Still from episode 11 of Big Windup showing a closeup of a tournament bracket's first three rounds. For every five teams, only two play the first round; the other three don't start until the second round. Teams assigned the slots #84 (which will be assigned to Nishiura) and its first matchup #85 (which has been assigned to Tosei) don't start until the second round. /end ID]
this is called a BYE which i totally forgot was a thing. from wikipedia:
Many different scenarios are regionally described as byes, including:
The preferential advancement of a player or team to the next round of a tournament without playing an opponent in an early round, usually as a reward for higher pre-tournament ranking;
this site (which seems to be advertising something but i did find the explanation really clear so i'm using it lol) says that this is done when the pool of competitors isn't a power of 2. which 170 certainly isn't!
from the chatter in the auditorium it sounds like there are (at least) three levels of seeds in this tournament: A, B, and C. (haruna's team is a C seed.) NOT EVERY TEAM HAS A SEED. only the really good ones! unlike in march madness where everybody gets a seed.
in the episode, the seeded teams are called to the stage first to draw their lots. my guess is that the seeded teams draw from a selection of lots that has already been narrowed down - it's decided ahead of time which specific slots will have a seeded team, but not WHICH seeded team gets each of these specific slots. this is how they equally "seed" the good teams throughout the bracket while also preserving a level of randomness in their placement. (they probably also further divide this subset among the three levels of seeds so that the A seeds are as far from each other in the bracket as possible.)
all of the slots reserved for seeded teams get a bye, i'm assuming. however, there aren't enough seeded teams to occupy all the slots that get a bye. this is how nishiura gets a bye despite not being seeded: they happen to draw the lot for one of the slots with a bye not taken by a seeded team. in fact, this is what hanai hopes for ("If I can snag a spot that starts in the second round, we'll have the advantage of playing one fewer game than most of the other teams").
(sidenote i'm not sure he's correct that "most of the other teams" have to play in the first round...in the small segment of the bracket in the still above, most of the teams do get a bye (in a ratio of 3:2). in a zoomed-out shot that shows more of the bracket, i did see a section where there are four teams that play in round one with two additional teams getting a bye (a ratio of 1:2), but such sections look rarer.)
an initial matchup with an unseeded team is probably the case for all seeded teams in order to preserve even spacing of seeds - i assume they didn't include both #84 and #85 in the selection for the seeded teams, for example, to ensure that seeded teams don't face each other until later rounds of the tournament.
after the seeded teams have drawn their lots, the announcer calls the schools numbered 1-30 up to the stage and hanai says "It's about time they made it to us." they are starting the drawing of lots for the unseeded teams. (these numbers don't have anything to do with their slots in the tournament; it's the order in which the unseeded teams draw lots. nishiura's number is something over 100, and they draw the lot for slot 84.)
so: it IS the case that seeded teams get to skip a round. however, this doesn't necessarily mean they play fewer games. after all, each time you win, your prize is that you get to play again in the next round; if you lose, you play no further games. according to the zoomed-out shot of this bracket, there are 8 rounds in the tournament. the two teams who match up in the final round will have played 7 games (if they had a bye) or 8 games (if they had to play in the first round), including the final. a team without a bye who loses in the first round only plays 1 game.
in march madness, which is the only seeding i was familiar with, there used to be 64 teams, which is a power of 2, so there were six rounds and no byes (2^6=64). then in 2011 they expanded the tournament to 68, which necessitated adding an earlier round of 4 games in which 8 teams compete for 4 slots to play in what is confusingly still dubbed the "first round" (the 4 early games are called the "first four", i guess in symmetry with the final four? personally i think it should be called the "zeroth round" but i guess i can see why they didn't go for that). so in march madness, 60 of the 68 teams get a bye to skip the zeroth round. this year, the 8 teams who played in the zeroth round were all of the 11-seeds and all of the 16-seeds. some of the teams with byes (all the 12- through 15-seeds) are ranked lower than the 11-seeds who had to play in the zeroth round. but of course, all of the really good teams get byes.
sidenote to correct my earlier correction of hanai now that i have the numbers from march madness and can reverse engineer the math to use lol: 2^8=256, so if there were 256 teams competing in koushien, there would be no byes needed. or if there were 128 teams, they could do it in 7 rounds with no byes. since there are ~170 (according to earlier in the episode), they do 8 rounds with ~42 games in round one played by ~84 teams (170-128=42, which means 42 teams need to be eliminated from the pool of 170 so that the remaining teams can fit into a round with 128 open slots). this means that ~86 teams (170-84) get byes in the first round. 86>84 so actually more teams skip the first round than play in it. but i don't think they said there are exactly 170 teams. if there are 172 teams, 88 teams play in the first round and 84 teams get byes. if there are 174 teams, 92 teams play in the first round and 82 get byes...so he might be right that the number of teams who skip the first round is lower than the number who play in it. sorry for doubting u cap'n ogyny 🫡