# Introduction

In the 2023 NBA playoffs, Jimmy Butler had an incredible performance in Game 4 of the Heat's first round series against the Bucks. The Heat were up 2-1 in the series, largely because Giannis Antetokounmpo had missed the previous game with a minor injury. With Giannis returning and Tyler Herro out for Miami, Game 4 was expected to be a Bucks blowout win. However, against all odds, Butler scored a career-high 56 points and led the Heat to a huge 4th quarter comeback victory. This gave the Heat a commanding 3-1 series lead, which would eventually lead them to winning the series. This historic playoff game was a one of a kind, but truly how unlikely was his performance?

# Method

For this project I decided to use my code from the "NBA Home-Away" as the base so I am still scraping from StatMuse. Instead of just using surface level statistics I decided to use Player Efficiency Rating. Unfortunately, on statMuse, you can only view 25 individual regular season game statistics, so I got the PER from each of those games. Then, I calculated the PER all of Butler's playoff games excluding the Bucks series and stored all of those values in a list as well.

After I got all of those values used R's data visualization tool to display a histogram of the PER values. Here's the graph:

This data looks about normally distributed so I used R to run a test of normality. As you can see the p-value is much greater than .05 so there is strong evidence to suggest that this data is normally distributed.

# Findings

Now that we know the data is normally distributed, I decided to use Z-score to rate analyze Butler's performance. In game 4, Butler had a dominating 55.0 PER which compared to his distribution, revealed he played 3.49 standard above his average that game against the Bucks. This Z-score translates to 0.0242% probability of Butler dropping that historic stat line.

# Conclusion

This game is proof that no matter how hard you crunch the numbers, you can never truly predict the outcome of sports games. 0.0242% doesn't even account for Butler's opponent's, the number 1 seed Bucks, or the 4th quarter comeback. Taking those into factor the probability could be even less. Never the less, this staggering win ended up leading to a Heat win to the series knocking out championship contenders in the first round of the playoffs.