This is the best job of clarifying it that I've seen thus far
At that point, Slater had two choices. Per NFL Rule 4, Section 3, Article 2, he could elect whether to receive the kick or kick off OR he could declare "the choice of goal his team will defend." As NFL vice president of officiating Dean Blandino noted on Twitter, he could not choose to kick off and the direction. (Obviously, the choice to defer isn't relevant in overtime.)
Having already spoken informally to Belichick, Blakeman knew what to expect. He said to Slater: "You want to kick?" And Slater said: "We want to kick, that way."
That sentiment reflected Belichick's wishes, but unfortunately the wording locked Slater into the first set of options rather than the second. The Patriots did want to kick off, but their goal in doing so was to kick off in the opposite direction than they ultimately kicked in. To do so, Slater should have told Blakeman which goal the Patriots wanted to defend and left out the part about kicking entirely.
In other words, Slater should have said, "We want to defend that goal" instead of saying, "We want to kick, that way."
You might think it's wild that such an important decision would rely on what seems to be a distinction without a difference. And it's fair to wonder if Slater was simply following Blakeman's lead in terms of the precise wording. But that's why Slater appeared confused when Blakeman asked Jets captain Antonio Cromartie to choose the goal to defend and, thus, the direction of the kickoff.
http://espn.go.com/blog/nflnation/post/_/id/193507/a-slight-wording-mistake-caused-the-patriots-overtime-confusion
They still don't have it completely right. If Slater had said, "we want to defend that goal," then the Jets would have had the choice whether to kick or to receive. Perhaps the Jets ALSO would have preferred to kick. Probably not, but you can't be sure. So, if you really want to kick -- if that is your top choice -- you must pick it if you win the toss.
Winning the toss gets you the first
choice. Then the other team gets its choice. If Belichick wanted to kick, then if Slater had picked direction, Belichick was risking not getting his first choice. If you decide you want to kick in overtime (or you decide that direction is most important), then the only way to
ensure it is to chose to kick if you win the flip. Now, this is likely an academic point. If Slater had said, 'we want to defend that goal," then the Jets probably elect to receive, because that's what everyone not named Belichick seems to choose. So, it's likely Slater did make a mistake because he could have said, "we want to defend that goal," and gambled that they would also then kick, because that likely would be what the Jets would choose.
But the "mistake" here was that in implementing his coach's desire -- that he wanted to kick -- Slater eliminated his right to choose direction. If Belichick told him "we want to kick," and "we want to defend that goal," then Belichick made a mistake by misunderstanding the rule. He might have thought that by choosing to kick you also get to choose direction, but that would have been wrong. In that case, he needs to give more explicit instructions.
You really need to go through all the options. (1) You lose the toss and your opponent elects to kick. Now you receive and you get to choose direction. (2) You lose the toss and your opponent elects to receive. Now you kick and you get to choose direction. (3) You lose the toss and your opponent chooses direction. Now you need to know if your coach wants to kick or receive. (4) You win the toss and you want to kick. You can either chose direction and hope, or you can choose to kick, and your opponent gets to choose direction. (5) You win the toss and you want to receive. You have to declare receive in this case, and your opponent will get to pick direction. (6) You win the toss and you want direction. (Say, if there is considerable weather.) Now, you must choose direction. Because if you choose kick or receive, whichever you pick your opponent chooses direction.
Numbers 2 and 5 happen 90 percent of the time. The confusion comes in because most people (like Slater today and perhaps like Belichick) equate kicking with getting to pick direction