Question: In the bronze medal game of the 2014 FIBA Asia Cup... In the bronze me

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Question: In the bronze medal game of the 2014 FIBA Asia Cup... In the bronze medal game of the 2014 FIBA Asia Cup, and with his team down by two points, Philippines guard Paul Dalistan was fouled while attempting a three-pointer at the buzzer. He missed the shot and headed to the line for three foul shots.

1. Watch the video of Dalistan preparing to take his first shot. Before he shoots, what is the probability that Philippines will win the game? Lose the game? Send it into overtime? For the season behind the free throw line, 84.6%.

2. Watch the first shot. Based on this, what is the new probability that Philippines will win? Lose? Go into overtime?

3. Watch Dalistan’s second shot. Now, what are the probabilities that Philippines will win? Lose? Go into overtime?

4. When you are done, watch the conclusion of the video to find out what happened. Do you think it was a good decision for China to foul at the buzzer?

https://youtu.be/-gCQh83oa1Q

Explanation / Answer

1. Score before the first shot: 77-79 (Philippines-China)

For each shoot, probability of a score = 0.846 and probability of a miss = 0.154

For Philippines to win the game, Dalistan has to score in each of his 3 foul shots.

Probability of scoring in all the 3 foul shots = 0.846 X 0.846 X 0.846 = 0.6055. So the probability of Philippines winning the game is 0.6055 before the start of the foul shots.

Philippines would lose if the score is 77 or 78. So, they would lose if Dalistan doesn't score at all, or scores once out of the 3 shots.

Probability of no score in 3 shots = 0.154 X 0.154 X 0.154 = 0.00365. Probability of one score in 3 shots = 3 X 0.846 X 0.154 X 0.154 = 0.06.

So, the probability of Phiippines losing before start of the 3 foul shots = 0.00365 + 0.06 = 0.064.

To send the game into overtime, the scores have to be tied. This can happen if there are 2 scores out of the 3 foul shots. Probability of 2 scores in 3 foul shots = 3 X 0.846 X 0.846 X 0.154 = 0.3307.

2. After the first shot, score is 78-79 (Philippines-China)

Probability of a Philippines win = probability of 2 scores out of 2 shots = 0.846*0.846 = 0.7157

Philippines will lose if there is no score in the 2 shots. Probability of this happening = 0.154 X 0.154 = 0.0237

There would a draw (go into overtime) if there is one score in 2 shots. Probability of this happening = 2 X 0.846 X 0.154 = 0.2606

3. Score after the second shot: 79-79 (Philippines-China)

Probability of Philippines win = 0.846

Probability of Philippines loss = 0

Probability of overtime = 0.154

4. Assuming there was no foul at the buzzer, Dalistan could have shot or missed with probability 0.5. So, before the foul, probability of China winning or Philippines winning was 0.5 each. However, after the foul and before the start of the 3 foul shots, probability of Philippines winning was 0.605 and China winning (Philippines losing) was 0.064.

Hence, it was a bad decision to foul at the buzzer.

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