Here's how to visualize a golf scramble tournament. Imagine a sped up version of a Charlie Chaplin movie where a group of golfers all tee off, chase their respective balls down and then gather in one location for their respective second shot. They all take their second shot and again trot off after their own ball only to again gather together in one spot for their third shot. The group continues this behavior until one of them finishes the hole.
In a scramble format golf tournament, the competition is usually between groups of two-, three- or foursomes. In each case all tee off. The team then selects the best drive and each team member hits their second shot from the location of what they determine is their most advantageous drive location. They go through the same process for their third shot. Which of their second shots gives them the best chance for a good third shot? Each hits from there. This process continues until one of the team members holes out.
There are many variations to golf scrambles. In some formats a team handicap is used. The handicap could be a percentage of the member handicaps averaged. Another wrinkle is to divide all players into flights determined by handicaps and make sure each foursome has a member from each of the four flights. You could further have different flights tee off from different tees. Making sure that four drives from each of the foursome members gets used is another way to add interest. Another permutation is that the player whose shot is chosen sits out the next shot while all other team members hit from the location. See the various types of golf scrambles tournament formats.
In the scramble format, you need only put one score on the card for the team.