The water is clear; the finish makes the color
Pool water is essentially clear. The color you see is the finish at the bottom and on the walls, seen through the water. That is why two pools with the same clear water can look completely different: the surface underneath is doing the work, not the water itself.
This is the single most useful thing to understand before you choose. You are not picking a water color. You are picking a finish, and the water color is the result.
Depth is the biggest factor
The deeper the water, the more of it light passes through, and the darker and more saturated the color reads. A finish that looks pale and bright at the one-foot steps will read as a deeper, richer version of the same color at the five- or eight-foot drop.
This is why a single flat swatch is misleading and why every finish page carries a depth strip from one to eight feet. The strip shows the same finish at four depths so you can see how the color carries, not just one frozen sample of it.
Light, surroundings, and sky shift the read
Daylight changes through the day, so the same pool reads cooler at noon and warmer near sunset. A clear sky pushes the water bluer; an overcast sky flattens it. Reflections from the sky and from nearby surfaces land on the water and tint it further.
Your own materials matter too. Light decking and pale coping bounce more light into the water and brighten the read. Dark tile and heavy landscaping deepen it. The finish is the starting point; your backyard is the rest of the picture.
How to judge it before you commit
Use the depth strip to understand how a finish carries with depth, then narrow to the water read you want. Compare finishes by the color they actually produce, which is how the water-color hubs on this site are organized.
Then order a physical sample and hold it against your own tile and deck, outdoors, in daylight. This pre-empts the most common complaint in the category, which is that the water did not match the swatch. The swatch was never the whole story; depth and light are.