These are my thoughts (and my reasoning) as to why you should foul at the end of a game to preserve a three point lead.
Once the clock gets to seven seconds (so the clock will stop at 6 on a foul) and the ball is in the front court, you have to take the ball from the dribbler. A foul is probably going to be called, but if you teach your players to take the ball, then you will either have stolen the ball (not likely to be let go by the official) or you will have fouled and kept the opponent from shooting a potentially game tying three point shot. If you are not in the bonus yet, that is even better, you keep taking the ball when the opponent inbounds until they get to go to the free throw line. You must foul the dribbler at least 10 feet away from the three point arc.
There used to be some debate as to this strategy when the offense could put four rebounders on the free throw line, but now that the offense is only allowed two rebounders, the odds for an offensive rebound have dropped significantly.
Personal experience tells me that in the almost 30 years of playing/watching/coaching games since the rule was included for high school and college games, many more late three point shots go in and send games into overtime than I have seen the sequence of: making the first free throw, missing the second on purpose, getting the offensive rebound of the missed free throw, and then making a shot to tie (or win the game if the shot is a three point shot).
To me, the following statistical argument is even more convincing.
A good three point shooter, relative to the competition level, can hit 33%, even when guarded. Today, the players have incredible range and take more shots from several steps behind the arc, so there is also a bigger area to defend, not just the sector right on the arc.
Your opponent has to have five things happen successfully to tie the game under extreme pressure if you choose to foul:
#1 They have to make the first free throw. Let’s just assume you foul an 80% ft shooter.
#2 They have to miss the second free throw on purpose without accidentally making it or missing the rim entirely. Most players do not practice missing free throws. You can’t just shoot it to the right or the left, that would give a huge rebounding advantage to the defense because the ball will not come off the rim very hard. You have to shoot it hard to get a longer than normal rebound. I would say 90% success on not making the shot accidentally and not violating and missing the rim completely. That is not even taking into account the pressure factor of doing something you rarely if ever practice during the most pressure packed time of the game.
#3 The shooting team must get the offensive rebound. I would say that 40% of the time without fouling would be great success on that.
#4 The offensive rebounder has to score without traveling or committing an offensive foul. If he/she throws the rebound to a teammate, they cannot turn it over or make a pass that makes the receiver reach for the ball and throw off shooting rhythm and balance. That is tough to do under pressure. I would say 95% of the time that would happen without a turnover. That percentage is probably high, but I am estimating high to give the benefit to the offense to drive home the point that you have to foul.
#5 The player shooting has to hit the shot–let’s say 50% success on a 2 point shot to tie, 33% on a three to win (since we assume that the first free throw was made)
If you calculate the probability that all five of those things succeed on the same play (80% x 90% x 40% x 95% x 50%) it comes to a maximum of 14% of the time you would be tied by a missed free throw, an offensive rebound, and a 2 point shot. That is also with high estimates for each of the 5 parts to happen independently, so I believe that the true probability is actually less than 14%. Either way it is not close to the estimate of 33% of making a three to tie the game. Even if you believe the odds of your opponent making the three point shot to tie are as low as 1 in 6, the percentages say that you are still better off fouling the dribbler out by the 10 second line.
When a good team (and when you are playing for any championship, your opponent is usually at least a good team) is faced with a three point deficit and 10 seconds, they are going to tie you once in a while. I would just rather make it tougher on them to tie by fouling and not letting them take a shot they will make at least one out of three times.
To hit a 3 point shot after making a free throw to win the game (again, if my percentages assumptions are correct–and I have intentionally set them high) would be 80% x 90% x 40% x 95% x 33% = 9% I would add two thoughts that I believe dramatically lower that percentage. If you are throwing the ball out beyond the arc for a shot with tougher defense on the pass out and under extreme scoreboard and clock pressure, the chance of making a safe pass would diminish. Point number two, the rebounder is more than likely not going to look to throw out for a three, but is going to focus on scoring. Depending on how much time is left, there might not be time for a pass out and a three point shot. I believe the offense will go for the highest percentage shot they can get, which is a two not a three. Based on the numbers above. my estimate is that throwing out for the winning three after making the first free throw and missing the second is less than 4%.
Even if you don’t agree with my percentage estimates, put in your own percentages and do the math to make a judgment that is based on reason, not on the criticism you could receive if you do foul and then lose the game.
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