A different scoring system
Rivalry games are frequently judged by a separate emotional scoring system from the rest of the season. A team can lose most of its other fixtures and still consider the year salvaged by beating its oldest rival, while a strong season can be soured entirely by losing that one game. This is not irrational; it reflects the fact that rivalries are inherited across generations of fans and players and carry meaning that a single season's record cannot fully capture.
Familiarity removes surprise
Teams that play each other every year, often for decades, tend to know one another's tendencies unusually well, which removes much of the tactical surprise available in a typical matchup. Coaches on both sides have often studied the opponent for years rather than weeks, and players may have grown up watching the fixture themselves. That familiarity tends to push rivalry games toward physical, close contests decided by execution and composure rather than by scheme innovation.
Why the emotion outlasts the season
Because rivalry outcomes are remembered independently of the broader table, they carry a kind of permanence that ordinary results lack. A single dramatic rivalry win can be discussed for years after the rest of that season has been forgotten. Understanding this helps explain why coaches and players sometimes speak about one game with a gravity that seems disproportionate to its effect on the standings; in a real sense, its effect on how the season is remembered can be larger.