In the previous post, we have established the expected probabilities of the winning margins in the NBA playoffs. This time we compare them with the past data and test our hypothesis.
The null hypothesis (H0) was that the games-outcomes occur with equal probabilities, irrespective of the rank in the regular season. The alternative hypothesis (H1) says that the game outcomes are not at equal chances but based on the team’s strength.
Matches including round 1
We gather all the playoff outcomes until 2021, from the starting point of 2003, the beginning year of the best-of-seven series for round one. The summary of the observed results and expectations is in the following table.
| Observed (O) | Expected (E) | (O-E)2/E | |
| 4-game series | 52 | 0.125 x 285 = 35.63 | 7.52 |
| 5-game series | 74 | 0.25 x 285 = 71.25 | 0.106 |
| 6-game series | 99 | 0.3125 x 285 = 89.06 | 1.109 |
| 7-game series | 60 | 0.3125 x 285 = 89.06 | 9.48 |
| Total | 285 | 285 | 18.21 |
obsfreq <- c(52,74, 99, 60)
nullprobs <- c(0.125,0.25, 0.313, 0.312)
chisq.test(obsfreq,p=nullprobs)Not among equals
With a chi2 of 18.2 (> the critical value of 7.81 for the 5% significance level) and a p-value of 0.00042, we reject the null hypothesis that the playoff games were coin-tosses. The results are hardly surprising because of the presence of first-round playoffs in the data. Most of the matches in the first round are not played among equals. In the first round, the number one (of the regular season) plays against the number 8, 2 against 7, 3 against 6, and 4 against 5. With a closer review of the table, you can see far more 4-0 results (52) than expected (35) and fewer 4-3s (60) than coin-tosses (89).
After the first round
Once the screener of the first round is completed, it is the start of the conference semi-finals. We now anticipate that the matches are between equals or teams of comparable strength. We repeat the test by taking data from 2003 to 2021, excluding the first round. The analysis is below.
| Observed (O) | Expected (E) | (O-E)2/E | |
| 4-game series | 19 | 0.125 x 132 = 16.5 | 0.38 |
| 5-game series | 30 | 0.25 x 132 = 33 | 0.27 |
| 6-game series | 52 | 0.3125 x 132 = 41.316 | 2.76 |
| 7-game series | 31 | 0.3125 x 132 = 41.316 | 2.52 |
| Total | 132 | 132 | 5.93 |
The chi2 is below the critical value (7.81), corresponding to a 5% significance level. Yes, the null hypothesis stays.
The final
We will now take it to the next level. Let’s cover only the NBA finals of the last 75 years. We expect the outcome to match that of matching probability events. And the expected chi2 value could be the lowest we have seen so far. Keep your fingers crossed.
| Observed (O) | Expected (E) | (O-E)2/E | |
| 4-game series | 9 | 0.125 x 75 = 9.37 | 0.015 |
| 5-game series | 18 | 0.25 x 75 = 18.75 | 0.03 |
| 6-game series | 29 | 0.3125 x 75 = 23.44 | 1.3 |
| 7-game series | 19 | 0.3125 x 75 = 23.44 | 0.83 |
| Total | 75 | 75 | 2.17 |
Yes, it is – chi2 of 2.17 with a p-value of 0.54.
