Game 7 of the NBA Western Conference Finals between the Houston Rockets and Golden State Warriors was the pivotal game of the 2018 NBA playoffs. The Rockets and Warriors were widely regarded as the two best teams all season. The Warriors won the game, coming back from a double-digit deficit, and then went on to sweep the Cleveland Cavaliers in the NBA Finals.
One of the most talked about aspects of Game 7 was the Rockets’ poor 3 point shooting, especially during a stretch in the second half when the Rockets missed 27 straight 3 pointers, an NBA record.
The likelihood of the Rockets, a 36.2% three-point shooting team, missing 26 threes in a row is .00084% or a 1 in 118757 chance.
— Eric Sidewater (@SixersScience) May 29, 2018
FiveThirtyEight did a more advanced analysis and put the odds of missing 27 straight 3s at 1 in 72000.
Whether it’s 1 in 100,000 or 1 in 72,000, the implication is that a really unlikely turn of events took place, and it’s easy to conclude that the Rockets’ performance was due to other factors, such as caving to the pressure of the moment.
But selectively focusing on specific stretches of the game can lead to misleading conclusions. Let’s take a step back.
For the game, the Rockets went 7 for 44 in 3-pointers, a shooting percentage of about 16%. Make no mistake – this was bad, and in fact it was their worst 3 point shooting performance of the playoffs:
But was the Rockets’ 3-point performance in Game 7 so bad that chance alone couldn’t explain it? During the playoffs, the Rockets’ averaged about 33%, and prior to Game 7 of the Golden State series, the Rockets’ shot as high as about 52% and as low as 25% (both in the Utah series). Could the performance in Game 7 be explained by this variance alone?
A Chi-Square test can help answer this, assuming certain conditions such as the independence of games and 3 point attempts. We only focus on playoff games, under the the assumption that playoff games are a different animal from regular season games (higher caliber opposition, more pressure, bigger crowds, etc.).
library(dplyr) game <- c('MN-1', 'MN-2', 'MN-3', 'MN-4', 'MN-5', 'UT-1', 'UT-2', 'UT-3', 'UT-4', 'UT-5', 'GS-1', 'GS-2', 'GS-3', 'GS-4', 'GS-5', 'GS-6', 'GS-7') made <- c(10, 16, 15, 16, 18, 17, 10, 11, 10, 18, 13, 16, 11, 12, 13, 15, 7) attempted <- c(37, 52, 41, 43, 44, 32, 37, 36, 38, 39, 37, 42, 34, 38, 43, 39, 44) df <- data.frame(game, made, attempted) df <- df %>% mutate(missed=attempted-made) chisq.test(df[c('made', 'missed')])
Pearson's Chi-squared test data: df[c("made", "missed")] X-squared = 19.639, df = 16, p-value = 0.2369
Using the typical significance threshold of .05, we can’t dismiss the possibility that “reasonable chance” alone was the reason for the Rockets’ performance. In other words, the 3-point shot has inherent risk to it, and sometimes that risk will come back to bite you; it just happened at a bad time for the Rockets.