Part of the attraction of the Ryder Cup is that it's so radically different than the golf you see on a week-to-week basis.
During the PGA Tour, there's only one match-play event -- The World Matchplay Championships. And there isn't a team event until the "Silly Season", which is after the Tour comes to a close as it just did.
But the Ryder Cup asks players to combine with each other and in a matchplay format. It's really a departure from watching one guy try and birdie the last hole to claim 3rd place check instead of splitting a 4th place one.
U.S. & World
The Cup is played over three days. The first two days have a morning session and an afternoon session. These two are split up between a four four-ball matches and four foursomes matches. The four-ball involves two players from each side being paired up, but everyone plays their own ball. Whoever gets the lowest score on a hole wins the hole. This one doesn't require as much thought as who to pair together as everyone is playing their own shots. However, you wouldn't want to pair two golfers who like to take risks together, because they might both end up in the woods and provide and easy hole for the opponent. It makes sense to have one guy who consistently gets the ball in the fairway and on the green paired with a big-hitter who can make things happen but also can get into trouble. Provides a nice baseline.
The foursomes matches take a little more thought. In these, teammates will alternate shots. This is where you can out-think yourself. Do you pair two similar players together so that everyone's playing from positions they are used to? Or do you combine two different players to cancel out their weaknesses? Still, the looks teammates will shoot each other after one leaves the other in a bunker can be highly entertaining. Tiger Woods would have maimed Phil Mickelson if looks could kill when they were paired together years ago.
Because there are only four of these matches in each session, a captain also has to decide which four of his 12 players have to sit out. Most captains like to get everyone involved before the singles matches on Sunday, but the Europeans haven't always trusted their depth to do so. This led to problems the last time the Cup was on these shores, as Europe threw four guys into the deep end on Sunday without getting a feel for the competition beforehand. It didn't work out.
The tourney wraps up on Sunday with a royal rumble of 12 singles matches. When everyone's on the course, this gets out of control. Matches are being tossed on their ear left and right and the crowd is going nuts and you go from euphoria to despair in the matter of a couple shots.
It is truly a wonderful break from what we're all used to.