I'm not sure why you think that Adidas is somehow bigger than Nike in the US, but if you really need confirmation:Like I said, show me the figures or I call shenanigans. I'm talking about US.
"The U.S. giant had 15 percent of the $255.1 billion worldwide sportswear market last year, compared to 10.8 percent for Adidas, according to market researcher Euromonitor International. In North America, the gap is bigger: Adidas’s 2013 revenue totaled $4.3 billion, vs. $12.3 billion for Nike."
http://www.bloomberg.com/bw/articles/2014-10-02/adidass-u-dot-s-dot-sales-drop-as-hedge-funds-circle