The thing about having one game never really matter that much is that you get all of the upside of a victory, really, without any of the downside of the loss.
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Understanding that just one game is a tiny cog in a larger machine doesn't take away the fun of winning, because that's going to be there no matter what; it just eases the sting of losing. Understanding that no one game makes that much of a difference allows you to just bask in the enjoyment of the thing. It lets you have fun.
This is something unique to baseball. Every NFL loss is like losing 10 baseball games in a row; every NBA and NHL loss is like losing two. The length of the season -- whether it's 162 games or, maybe one day (again), 154 games -- bakes in both disappointment and euphoria. The Arizona Diamondbacks lost 98 games last year, an absolutely miserable season, but if you were at Chase Field on April 30, when the D-Backs were behind 4-1 but scored one in the eighth, two in the ninth and won on a Miguel Montero walkoff in the 10th … you had a terrific time. You jumped and hollered and hugged whoever was next to you, even though your team was 9-22 and had just lost four in a row.
Look at them:
They're so happy! They're spraying Montero with water as he slides into home plate! The Diamondbacks were 9-22!
That's what baseball does. It is capable of providing you with pure, mainlined mirth, regardless of context, on any given day. Collectively, it can mean more, and all moments are, yes, just data points, but that doesn't mean those little moments and those data points matter any less while they're happening.