The shape of a stadium bowl is determined almost entirely by sightlines. Every other decision about the seating follows from a single geometric requirement.
The measurement that controls everything
Designers work with the vertical distance between a spectator's eye and the sightline of the person directly in front, taken over the same viewing point.
A larger value means a clearer view over the head in front, and a smaller one means spectators must lean or stand to see the near touchline.
Achieving a generous value requires each row to sit higher above the one in front, which is why good sightlines produce steep stands.
Why the focus point matters
Sightlines are calculated to a chosen point, typically the nearest edge of the playing surface, since that is the hardest thing to see from a low seat.
Designing to the far side of the pitch instead would allow a much shallower stand, but spectators would lose the action closest to them.
Different sports use different focus points, which is one reason a stadium built for one sport rarely suits another without compromise.
The curve this produces
Meeting the requirement from every row produces a rising curve rather than a straight incline, with the rake increasing toward the back of the stand.
Front rows can be relatively shallow because they are close to the focus point, while upper rows must be steep to see over everyone below. The difference in rake between the bottom and top of a large stand is substantial.
The resulting profile is what gives modern stands their distinctive shape, and it is a consequence of geometry rather than an aesthetic choice.
Where the constraints bind
Building regulations limit how steep a stand may be, since evacuation and everyday movement become difficult beyond a certain angle.
Overall height may be capped by planning conditions, particularly on constrained urban sites where the building must respect its surroundings.
Designers meet these limits by moving seats closer to the pitch, since proximity reduces how much height is needed to achieve the same view. This is why the tightest bowls tend also to be the ones with the best sightlines.
Why running tracks change the answer
A track between the stands and the pitch pushes every seat further from the action, which flattens the required rake but worsens the actual view.
Athletics stadiums converted for other sports therefore feel distant, and the problem cannot be fixed without rebuilding the lower tier.
Venues designed for both purposes often use retractable lower tiers that slide forward over the track, which is expensive but preserves the geometry for each configuration.
