How the epicenter is calculated

Start with one point per season

1. Sole champion. Use the historically correct primary home playing-surface coordinate for that season.
2. Two split champions. Use the midpoint of the shortest WGS84 geodesic connecting the two home locations.
3. Three or more split champions. Compute their equal-weight geodesic mean and use that as the season point.
4. No champion or cancelled championship. Keep the season on the timeline but assign no geographic weight.

The key rule is that every championship season contributes a total weight of one. A split season is not allowed to overpower a sole-champion season simply because it has multiple recognized teams.

Why latitude and longitude are not averaged directly

Latitude and longitude are angular coordinates, not flat Cartesian distances. Longitude wraps at 180 degrees, the physical width of one degree of longitude changes with latitude, and the Earth is curved. A simple arithmetic average can therefore produce avoidable distortion or even a nonsensical answer near the international date line.

The objective

Here, pᵢ is a season point and d is the shortest surface distance on the WGS84 ellipsoid. The resulting point is a Fréchet mean: the curved-surface analogue of an arithmetic mean when squared distance is the quantity being minimized.

The numerical method

1. Convert each latitude and longitude to Earth-Centered, Earth-Fixed Cartesian coordinates.
2. Average those vectors to obtain a stable initial estimate.
3. Convert the estimate back to a WGS84 latitude and longitude.
4. Refine the estimate iteratively in a local tangent plane using WGS84 geodesic inverse and direct calculations.
5. Stop when the remaining movement falls below the configured convergence threshold.
6. Quantize only the published display artifact, then verify the induced error.

Altitude is intentionally excluded. Championship locations are represented on the WGS84 ellipsoid at zero height because the product is measuring surface geography, not three- dimensional elevation.

Simple cases

How the slider uses the result

The left and right handles define an inclusive contiguous season range. Each legal range has a precomputed record keyed by sport, start-season sequence, and end-season sequence. Moving the slider retrieves that stored result; it does not call a remote calculator or reverse-geocoder.

Trail lines are assembled from those same stored range points. For example, a buildup trail for 1998–2025 follows 1998, then 1998–1999, then 1998–2000, continuing until the selected endpoint.

What the result does not prove

• It does not identify the geographic center of all teams or fans.
• It does not measure conference strength, recruiting, attendance, or television audience.
• It does not mean the nearest town is itself a championship location.
• It does not show statistical certainty that future champions will come from that region.

It is a precise descriptive statistic of the championship locations included by the selected policy and timespan.

Reproducibility

The authoritative pipeline publishes algorithm and dataset versions, source hashes, test vectors, and complete range-count checks. A changed champion, venue, coordinate, locality dataset, or algorithm creates a new versioned artifact rather than silently changing an old cached file.