Your question comes down to angle of view.

It sounds like your camera is on the sidelines somewhere near the pitch, rather than in the stands. Let's use some assumptions to calculate some numbers.

1. You are setting up the camera 10 ft (3 m) from the pitch sideline, at the halfway line.
2. The pitch is standard 69m wide by 100m, try line to try line.

Then the corresponding angles of view are:

• 2 * atan(50 / 3) = 173°, from try-line to try-line on the sideline next to the camera.
• 2 * atan(50 / 37.5) = 106°, from the centers of the try-lines between the uprights, end to end.
• 2 * atan(50 / 72) = 70°, from try-line to try-line on the far sideline.

So, without adding anything, you'll be able to see all of the far half of the field, basically from the nearest uprights on each try line, to the far side. The triangle from the nearest upright, along the try line to the near side line, to somewhere between the 10m and 22m line on the sideline, will be out of your field of view (on both the left and right sides of the camera).

You can't make a wide angle of view wider without introducing some degree of fisheye-ness.

Your idea of adding an anamorphic lens is good — in theory — assuming an anamorphic lens just "squishes" anything in front of the camera by the anamorphic factor (anywhere from 1.4:1 – 2.6:1). Unfortunately, it doesn't work that way. Any lens has a maximum angle of view, irrespective of what's behind the lens. You will have to find a specific near-180°-wide AoV anamorphic lens, which I'm not sure exists, in order to achieve what you want. And even then, even assuming anamorphic, 180° wide will still produce fisheye effects.