If your sister has a husband, he is your brother-in-law. If two or more of your sisters have husbands, they are your brothers-in-law. This is an unusual example in English in which the adjective goes after the noun it modifies. We make the first word of the phrase plural since it is the noun.
Similarly, a state or the federal government has an Attorney General. When they all get together for their annual picnic and sack race, we have a group of Attorneys General. The word “general” tells us what type of attorney he or she is.
I’m going a bit off topic here, but bear with me. My two children had the dubious honor of having parents, uncles, and older cousins who were teachers. Saddest of all, I was an English teacher. While other mothers and daughters were discussing fashion or reality TV or complex political issues, my daughter and I debated questions of English usage.
I contend that the correct phrase in the title is “times out,” since it refers to the instances of a game when the players are “out,” or not playing. Hence, “out” describes “time,” and the plural should be “times out.” My daughter, however, insists that the noun in the phrase is “out” and so the traditional way of saying it is correct.
We had many contentious discussions of this issue before Katie turned my own words on me. As I have often pointed out, language only works when the people who speak it agree on the meanings of its words and their usage. Since “time outs” is in common use, it is by default the correct phrase.
I still think it’s “times out,” though.