In both soccer and American football, a team may have no more than 11 players on the field. Extremely few commercial products or natural phenomena have any relationship to the number 11.
In soccer, there is an even 10 players on each side who freely move around the field. The extra player on each team is the goalkeeper, who serves as the last line of defense against scoring attempts.
Walter Camp, who introduced many of the rules of American football, established 11-player teams. He envisioned seven players in the offensive line and four in the back, including the quarterback.
Commercial products are very seldom sold in groups of 11 because the number is one more than 10 and one less than a dozen, or 12. Products sold by the dozen can be packed in three rows of four or two rows of six. The number 10, as the most common mathematical base, is an obvious choice, and products sold this way can be packed in two rows of five. The number 11 is a prime number and does not lend itself to simple packing solutions.
Natural phenomena have little to do with the number 11 for the same general reasons. Natural hexagonal formations use the number 6, and dividing cells are found in powers of 2, but the number 11 has no relationship to these patterns.