A team can only have 11 players on the pitch in both soccer and American football. There are very few commercial items or natural phenomena that have anything to do with the number 11.
In soccer, each team has an even number of players who are free to move about the field. The goalkeeper is the additional player on each team, and he serves as the last line of defence against scoring attempts.
Many of the rules of American football were established by Walter Camp, who established 11-player teams. He imagined a seven-man offensive line and four-man backfield, including the quarterback.
Because 11 is one more than 10 and one less than a dozen, or 12, commercial products are rarely marketed in groupings of 11. Three rows of four or two rows of six can be used to pack products sold by the dozen. The number 10 is a logical choice, as it is the most frequent arithmetic base, and things sold this manner can be packed in two rows of five. The number 11 is a prime number, hence there aren’t any easy ways to pack it.
For the same reasons, natural events have little to do with the number 11. The number 6 is seen in natural hexagonal structures, and dividing cells are found in powers of 2, however the number 11 has no relation to these patterns.