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.