# NHL vs NBA: Why do underdogs do better in hockey?

As a primer to this article, please take a look at this video which inspired me to create this article! Also, the code can be found on GitHub.

In the last 30 years, the NBA title has been successfully defended 12 times, while the NHL title only 3 times during the same period. Why is this the case? Why do underdogs do better in hockey than in basketball?

If you watched the youtube video that was linked above, you will know that the reason is because hockey is a sport that relies more on luck than basketball does. **But, how do we quantify the amount of luck and skill in a sport?**

To answer this question, let us first assume that basketball is a game of pure chance. That is, in any given match, either team has an equal chance of winning, a 50/50 split. If such a scenario is true, then how many games can we expect a single team to win in a series of 82 games? This question can be modeled by a binomial probability distribution such that the probability of winning a single match is 50% and the number of trails is 82 (total number of games played by a single team in both a NBA and NHL season). The histogram below shows the results of a simulation of 5 seasons worth of data (30 teams x 5 seasons = 150 data points).

Now that we have a good sense of the outcome of a purely luck-based sport. Let us do the opposite and look at the outcome of a purely skill-based sport. That is, a team that is deemed more skillful than the other will win 100% of the time. To do this we impose an artificial ranking to each team in the NBA and have them play against each other based on the official NBA schedule taken from historic data. In such a scenario, we would expect the distribution of total wins to be uniform. That is, the same number of teams would have a 72–10 records as teams with 10 - 72. Once again, we simulate the results for 5 seasons and present the histogram below.

From the histogram, we can see that our expectations are a little off. There is a clear difference in the number of teams with a record of 72–10 than those with 10–72. This difference is due to the NBA scheduling differences from season to season since every team does not play with each other the same number of times each season. However, we do see that the general result is flatter than the pure chance simulation in which there was a bell-shaped curve around the mean of 41 games.

The real question is how does the real data of NBA/NHL distribution compare to these hypothetical ones? Below we will show the resulting plot of overlapping all three scenarios: pure luck, pure skill and real data for both the NBA and NHL data. For clarity sake, I will remove the bars from the plot just to remove some clutter and will only show the probability distribution estimate.

From the two graphs presented above, we can definitely see a difference between NBA and NHL data. The NBA distribution is flatter and looks like it tends towards the pure skill distribution while the opposite is true for the NHL data. **In other words, hockey is a sport that has more luck involved because the overall distribution of the actual data is more similar to the pure chance simulation. **Meanwhile, the opposite is true for basketball.

We can take this one step further and estimate the amount of luck-skill contribution to each sport by running another simulation. For example, let us say that basketball is a sport made up of 40% luck and 60% skill, then we can say that 40% of the time, the winner of a match can be decided by a coin flip, while the other 60% of the time, the team with more skill wins. We simulate this scenario with different percentages of luck vs skill and show the results below.

Seems like the plot with luck set at 60% matches the distribution of the real data pretty well. After some more iterations, I determined the most optimal luck-to-skill breakdown for the game of basketball to be 55% luck and 45% skill. Here is the resulting graph below.

I verified this to be the best split by performing the Kolmogorov-Smirnov goodness of fit test and obtained a **p-value of 0.89**. Meaning there is an 89% chance that the two histograms come from the same underlying distribution.

The same analysis was performed on the NHL data, which resulted in an optimized luck-to-skill breakdown of 75% luck and 25% skill (with a **p-value of 0.70**). You can see the results of the simulation below.

**What changes could the NBA implement that might be most effective at leveling the playing field?**

The short answer to this question is: the NBA should change their playoff series from a best-of- 7 to a best-of-1 format.

To answer this question in more detail, I simulate a series of NBA playoff seasons. Each playoff season has 13 series and each series is decided in a best-of-x format. I consider it one upset when an underdog team is able to win a series and advances in the playoff bracket. Therefore, in a single playoff season, the maximum number of upsets is 13. Using this simulation format and our previously defined basketball luck-to-skill breakdown of 55% luck and 45% luck, I present the histogram of the number of upsets in a single playoff season below.

As you can see, as the ‘best-of’ number goes down, the mean skews more and more to the right. This indicates that the probability of more upsets increases as the number in the ‘best-of’ series goes down.

To understand which number in a ‘best-of’ series to choose such that It mimics the results of NHL, we simply compare the two histograms. The results show that an NBA best-of-1 series would most closely mimic an NHL best-of-7 series in terms of the number of underdog upsets per playoff season.

In conclusion, I demonstrated that the reason NHL underdogs do better than NBA underdogs is because hockey is a luckier sport than basketball. An in-depth statistical analysis shows that hockey has a luck-to-skill makeup of 75% to 25%, while basketball has a luck-to-skill makeup of 55% to 45%. In order to even the playing field for NBA underdogs, I suggest the NBA change their best-of-7 playoff series format to a best-of-1, similar to how the NFL does it.