In this study, we simulate two distinct scenarios involving basketball teams: one team exclusively shoots three-pointers, while the other focuses solely on two-pointers. We then visualize the data in a graph and evaluate which team exhibits a higher win percentage. Finally, we conduct a two-sample t-test to ascertain whether the average win percentages of the two teams are statistically different from one another.

Utilizing the average NBA shooting statistics from the 2022-2023 season, the three-point shooting success rate stands at 36.1%, while the two-point shooting success rate is 47.5%. Each team is allotted 90 attempts per game.

First, we pit the two teams against each other in a simulated game. The team shooting only three-pointers wins 75% of the time.

```
After 10,000 simulations:
Team shooting only three-pointers won 7555 times
Team shooting only two-pointers won 2258 times
Tied result: 187 times
```

Next, we run a simulation of 10,000 games and determine the number of points each team scores and plot a histogram. From the histogram we can see the two teams have very different means and standard deviations.

Here is a look at the summary statistics. It should be noted that the average points per game for the 2022-2023 season is 114.7, and both of our simulation averages fall below this mark.

```
Average points per game for the team shooting three-pointers: 108.18
Standard deviation for the team shooting three-pointers: 14.56
Average points per game for the team shooting two-pointers: 94.99
Standard deviation for the team shooting two-pointers: 9.94
```

Running a two-sample t-test we can see the two-tailed P value is less that 0.0001. We reject the null hypothesis and state the two sample sets are statistically significant.

```
T-statistic: 74.80611223225225
P-value: 0.0
We reject the null hypothesis: there is a significant difference in the means of the two populations.
```

**Conclusion**

In the last two decades, three-point attempts have more than doubled, increasing from 14 to 35 attempts per game. This analysis clearly demonstrates that teams with superior three-point shooting skills have an advantage, thereby validating the strategy of prioritizing three-pointers in gameplay.

Here is the Python code I used for this analysis.

# https://www.basketball-reference.com/leagues/NBA_stats_per_game.html import matplotlib.pyplot as plt import random from scipy.stats import ttest_ind import numpy as np # Define the number of shots to take and the shooting percentages for each team num_shots = 100 three_pct = 0.361 two_pct = 0.475 # Simulate shooting 90 shots for each team 100,000 times and keep track of how many times each team wins num_games = 10000 team_three_wins = 0 team_two_wins = 0 tied_result = 0 for i in range(num_games): team_three_score = 0 team_two_score = 0 for j in range(num_shots): if random.random() <= three_pct: team_three_score += 3 if random.random() <= two_pct: team_two_score += 2 if team_three_score > team_two_score: team_three_wins += 1 elif team_two_score > team_three_score: team_two_wins += 1 elif team_two_score == team_three_score: tied_result += 1 # Print the results print("After {} simulations:".format(num_games)) print("Team shooting only three-pointers won {} times".format(team_three_wins)) print("Team shooting only two-pointers won {} times".format(team_two_wins)) print("Tied result: {} times".format(tied_result)) # Function to simulate a game with only three-point shots def simulate_game_three(): made_shots_three = 0 for _ in range(num_shots): if random.random() < three_pct: made_shots_three += 1 return made_shots_three * 3 # Function to simulate a game with only three-point shots def simulate_game_two(): made_shots_two = 0 for _ in range(num_shots): if random.random() < two_pct: made_shots_two += 1 return made_shots_two * 2 # Run the simulation and record the total points scored in each game game_scores_three = [simulate_game_three() for _ in range(num_games)] game_scores_two = [simulate_game_two() for _ in range(num_games)] # Create a histogram of the total points scored bins_three = range(min(game_scores_three), max(game_scores_three)+1, 3) bins_two = range(min(game_scores_two), max(game_scores_two)+1, 2) plt.hist(game_scores_three, bins=bins_three, color='tab:blue', alpha=0.5, label="Three-point shots", edgecolor='black') plt.hist(game_scores_two, bins=bins_two, color='tab:orange', alpha=0.5, label="Two-point shots", edgecolor='black') plt.xlabel("Total Points Scored") plt.ylabel("Frequency") plt.title("Histogram Comparison of Total Points Scored") plt.legend() plt.savefig('basketball-simulation-histogram.png', dpi=300, bbox_inches='tight') plt.show() # Perform the two-sample t-test t_statistic, p_value = ttest_ind(game_scores_three, game_scores_two) # Print the results print("T-statistic:", t_statistic) print("P-value:", p_value) mean_three = np.mean(game_scores_three) mean_two = np.mean(game_scores_two) std_dev_three = np.std(game_scores_three, ddof=1) # Using ddof=1 for sample standard deviation std_dev_two = np.std(game_scores_two, ddof=1) # Print the mean and standard deviation of each dataset print("Average points per game for the team shooting three-pointers: {:.2f}".format(mean_three)) print("Standard deviation for the team shooting three-pointers: {:.2f}".format(std_dev_three)) print("Average points per game for the team shooting two-pointers: {:.2f}".format(mean_two)) print("Standard deviation for the team shooting two-pointers: {:.2f}".format(std_dev_two)) # Determine if the null hypothesis can be rejected alpha = 0.05 # Set a significance level if p_value < alpha: print("We reject the null hypothesis: there is a significant difference in the means of the two populations.") else: print("We cannot reject the null hypothesis: there is no significant difference in the means of the two populations.")