Warning: The following contains spoilers for Horimiya: The Missing Pieces, Episode 3, "Sports Day", now streaming on Crunchyroll.
More often than not, there seems to be that one episode or few episodes where competition in a Slice-of-life is focused on, but not taken to the same intensity as Shōnen anime do. Horimiya: Missing Pieces as an example just reached its third episode where the entire focus was seeing Miyamura, Hori, and others like Yoshikawa, Ishikawa, and Sengoku participate in the overall Sports Day that reinforces good sportsmanship. As one watches this episode and series, one might think that there isn't much other room for character development, and that the episode is confused because of focusing the competition in that day. However, slice-of-life anime doesn't focus entirely on the competition, but rather on the internal thoughts of the characters, whether they win or not. What does matter is seeing their growth as people, from Miyamura's initial reluctance and Hori's support, as well as the pay-off to the previous episode that set up a lot of character moments for Horimiya: Missing Pieces.
Uniquely speaking, the main duo and their friends are actively participating in Sports Day with the intent of good sportsmanship as opposed to an intense concentration on winning. This fits the pacing of the episode, as for the most part the entire Sports Day is fit into one episode, and following our characters is through a series of shenanigans and comedy, mixed with incredible character moments that are payoffs to the scenes from the previous episode. Like Sakura's cheer practice with Yoshikawa for Ishikawa, and even Miyamura's own enjoyment of a sports event without the anxiety of his old experiences in Sports Day, cementing his growth as well as the personality that has changed since the first episode in the Missing Pieces section of the anime. Of course, what exactly happens in the episode is important, but it's more important to analyze why this episode works as a payoff to the previous episode.
The Set-Up And The Payoff
One thing to note from the third episode is that it starts off straight into the Sports Day events, from beginning to end there is a sense that we are living through the one day with the characters as well as experiencing their own internal struggles and even support for one another. A lot of this is due to the fact that the show took its time to set up a lot of major character moments here that paid off with how real and relatable they felt to the audience as well as to each other. One notable example of this could be with Hori's own running event, where she briefly slips up and almost gives up the race due to the fact that she set a bad example. Because she had told Miyamura to give it his all, Miyamura in turn during that brief moment of doubt encouraged Hori to give it her all even if she was going to finish in fourth place.
This is simply one of many characters that had a pay off that related to an action they had previously done in the last episode, and it succeeds in keeping up with the pace of the third episode overall. Another great example of this would have to be with Sakura's successful movements of her cheer event, where she succeeded and manages to improve on her cheering skills that she practiced with Yoshikawa. While this might seem completely minor, It's what allows the slice-of-life aspect of this story to work well, as it doesn't forget the continuity of the day or episode before and simply remembers it when it is needed. Of course, these two characters aren't the only ones to get development and a pay-off that contributes to their character growth. Miyamura also contributes to the episodes' entertainment by providing us a look into how different he is now in this Sports Day compared to the previous Sports Day before he met Hori.
Progression
Ultimately, the episodes end pretty well as a story where despite the shenanigans and whoever wins; Miyamura and Hori both came out of this experience as different, and better people as a result of the support. Miyamura, who never had enjoyed Sports Day before, finally managed to enjoy it and give it his all in a way that felt satisfying in that he could only thank Hori for. And in many respects, that's what Horimiya: Missing Pieces helps to provide, an experience that many people never got to see in the first season, and now we get to fit in the puzzle pieces of what happens in the story. As a slice-of-life anime, it succeeds yet again in providing a lighthearted message and even more character development for Hori and Miyamura, allowing for Horimiya: Missing Pieces to stand on its own without any issues.