This is one of the rarest infractions in soccer, but has a considerable impact on a game when it does occur. And because it occurs so rarely it is actually often missed by relatively inexperienced referees during youth games. And when called, it can often cause, shall we say, confusion for both coaches and parents.
Experienced professional referee Randy Vogt wrote an excellent piece on this so I’m sharing most of it below.
Also, take a look at the clip at the end that shows how I messed up during one of my recent U17G games – I only gave a yellow card to the defender because I thought the second defender was much closer and thus able to intercept the attacker.
The clip clearly shows that the second defender was too far from the attacker to have made a difference. Oddly enough it looks like she even slowed down instead of accelerating to try to intercept the attacker.
I suspect that running from behind didn’t give me the right depth perception to judge the distance accurately. It’s obvious in hindsight and with the benefit of a replay.
Denying an obvious goalscoring opportunity (DOGSO) is a red-card offense. This rule is to prevent the defense from fouling to destroy their opponents’ most dangerous scoring opportunities and takes into account handling the ball and fouling an attacker moving toward the goal by an offense punishable by a free kick or penalty kick.
Let’s take handling the ball first. This obviously does not apply to a goalkeeper within his or her own penalty area but applies to the keeper who comes out of the penalty area to deliberately handle the ball or a field player who deliberately handles the ball on a shot that was going into the goal.
Please be aware that it is not a send-off, just a direct kick foul, when a keeper makes a save inside the penalty area and his momentum takes the ball outside the area while still holding it.
Should a defender (not the goalkeeper) deliberately handle the ball that winds up going into the goal anyway, the goal stands and the defender is cautioned for unsporting behavior.
Now let me write about an attacker moving toward the opponent’s goal fouled by a defender. Four elements are required for an obvious goalscoring opportunity before the foul becomes a red card offense. They are described as the four Ds:
• Defenders: Not counting the player committing the foul, there is at most one defender between the foul and the goal. That other defender is generally the goalkeeper. The keeper committing a foul can be sent off for this offense as well.
• Distance to the ball: The attacker must be close enough to the ball to continue playing it at the time of the foul.
• Distance to the goal: The attacker must be close enough to the goal to have a legitimate chance to score. So being in or near the opponent’s penalty area is more likely to be an obvious goal-scoring opportunity than the attacker being in the team’s defensive half of the field.
• Direction: The attacker must be moving toward the opponent’s goal at the time of the foul, not toward a corner flag or away from the goal.
So there’s an element of judgment by the referee involved here. Two reasonable persons can come to reasonable yet opposite conclusions. For example, for one person the ball might be close enough to the attacker to be played, for another person the ball might just be out of reach. This is why the Laws of the Game state ‘In the opinion of the referee [officiating the specific game]…..’.
And let’s also keep in mind, as Andy points out, to use common sense when applying this rule to (younger) youth games. It would be harsh and not in the spirit of the game to send a 8, 9, or 10 year old last defender off for accidentally tripping an attacker.
NorCal Soccer Dad 
From the camera angle much more obvious. Had to watch it again to see if that was within the 18–those football fields really hide the yellow lines. DOGSO doesn’t come up that often so you don’t get that much of an opportunity to practice it.
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