Till Death Do Us Part – A Probabilistic Look at NBA Title Odds

 

Sports are about winning. Sure, your middle school soccer coach may have told you that “It’s how you play the game” or “the real prize is the friends we made along the way” but we all know that to be bullshit. When it’s all said and done, we want to be on the team with the trophy above our heads, popping champagne bottles and parading through the city in an open-top bus.

For most of us though, our dreams of becoming professional athletes have long since passed. We’ve retreated from the fields, gyms, tracks, and rinks of the world back to our couches and reserved most of our sporting interests to high-fiving in front of TV or lamenting bad losses around the water cooler. Over the years though, we start to feel a certain kinship with our hometown teams. We slowly but surely become a part of the fabric of these franchises, a small patch in the quilt of community that professional sports can knit around a city. We share a collective memory of thousands of games, scores, coaches, fouls, wins and losses. And just maybe, if we stick around for long enough, leave our lucky jerseys unwashed and pray to the proper deities, we might get to experience the joy of our team returning home from the season’s conquest as victors, with their spoils in tow.

For some fans, the thrill of victory comes frequently, and for some it has never come at all. This immense inequity raises some obvious questions: How is it that some teams win back-to-back-to-back titles, and some never even get the chance to play in a final? How do some cities seem to bring more trophies than the rest of us? And, most importantly, if you are a fan of one of the ‘Have-Not’ teams, just how long should you have to wait for your team to win? Well, let’s look at the numbers:

For the sake of discussion, let’s look at the NBA and more specifically at my hometown team, The Denver Nuggets. The NBA is not dissimilar from any of the other three sports that make up the classic “Big Four” in America. In the NFL, NBA, NHL, and MLB, each league is made up of 30 teams (32 in the NFL) who jockey for position during the regular season and playoffs for a chance to play in the final. Whether it’s the Super Bowl, the Stanley Cup, the World Series, or the NBA Finals, one single team eventually emerges victorious, leaving the rest of the league in their wake and marching home with the trophy.

Another way to put this is that, every year, 29 teams end the season with nothing at all to show for their efforts. To borrow a phrase from Jon Bois, professional sports are a loser machine. But, what if sports were totally fair? If instead of subjecting themselves to the grueling labor of a seven-month season, every NBA team collectively came together, and drew a name from a hat to decide that season’s champion. Sure, it would be boring, but would it increase your team’s chance of winning a title, or would you be better off risking it on the hardwood? That, my friend, depends on which team you are rooting for.

There are currently 30 teams in the NBA, and it’s been that way since the 2004 season when the Charlotte Bobcats (Now the Charlotte Hornets) entered the league. That means that for the last 19 seasons, each team should theoretically have had a 1/30 chance of winning it all. Based on classical probability, this means that your team should have had about a 47% chance of winning a title during those 19 seasons. This doesn’t necessarily mean, however, that we would expect 19 unique winners over the course of our 19 year name-drawing-experiment. It is, of course, possible for a team to be drawn as champion multiple times over the course of these 19 years. Your team’s odds of winning twice in 19 years is only about 11% and the odds of winning 3 times in 19 years dwindle to only 2%. It’s worth noting that these “championships” are not likely to come in consecutive years. The odds of winning 2 championships back-to-back are 0.11% or about a 1/1000 chance. Your odds of three-peating are minuscule, with odds of about 27,000 to 1.

The Denver Nuggets, however, have been in the league since the ABA merger in 1976 when the league consisted of only 22 teams. The league would slowly add teams over the next 18 years, diluting the Nuggets theoretical odds of winning with each addition. This expansion of the league over time likely explains some of the statistical anomalies amongst the winningest teams in the NBA. Between the NBA’s first season in 1950 and the 1966 season, there were between eight and eleven teams in the league in any given year. During this time, the Lakers won 4 titles and the Celtics won 9. Winning 9 titles in 17 years is definitely a statistical anomaly, but it’s made much easier by the significantly smaller number of teams in the league. The average number of teams in the league during this 17 year span was 9, and thus the probability of winning 9 times in 17 years was about 41,000 to 1 based on our ‘name-from-a-hat’ model; only slightly longer odds than three-peating in the modern NBA. The fact that 8 of these titles were consecutive, and that the Celtics would go on to win 11 championships in 13 years is a feat which defies reasonable probabilistic interpretation, and in my opinion makes a strong case to disregard the early NBA years from our probabilistic model.

In my opinion, the aforementioned 1976 merger is a reasonable place to begin looking at the probability of winning in the “modern” NBA. The winningest teams still remain atop the count, but we begin to see a bit more parity from year-to-year. The Lakers have won 11 titles since the merger, accounting for roughly 23% of all available titles during the 47 year stretch. The Celtics have won 5 titles since the merger, tying them in third place with the San Antonio Spurs. The silver medal spot on the podium belongs to Michael Jordan’s Chicago Bulls who won 6 titles in the 1990’s. 

Since the merger, 16 unique teams have won the title. This means that, in reality, 16/30 or 53% of teams that are currently in the NBA have won a title in the past 47 years. In comparison, our ‘name-from-a-hat’ model predicts that each team should have about an 80% chance of winning a title over the course of a 47 year span. Again, the reason for this discrepancy is an increased rate of repeat champions in reality compared to our random championship lottery. 

Of course, in reality, a talented team is likely to win the championship, retain the majority of their talented team, and have a higher likelihood to win additional championships as long as they are able to keep their team together over multiple seasons. The increased salary of winning players, and players tendency to decrease in ability as they age makes this an uphill battle, but of course we anticipate that repeat champions and dynasties will lower the odds for an average (or below average) to win the title.

Since the merger, there have been 8 multiple time champions. There have been 6 instances of back-to-back champions and 3 three-peat champions. As expected, these numbers vary drastically from our random lottery model which estimates only a 0.004% chance of a three-peat occurring in any three year span. In reality there have been 45 unique 3-year-stretches since the merger and 3 of them resulted in a three-peat. This works out to a likelihood of 3/45 or about a 7% chance, based on our existing dataset. This massive difference between a truly random league and the NBA in reality is what keeps fans interested; the odds of your team winning three consecutive championships are nearly 2000 times higher when we play the games rather than draw names from a hat. 

This phenomenon is not an easily quantifiable statistics problem and is much more reasonably attributed to a long list of other factors that influence a team’s likelihood of winning. Rich owners, experienced front-offices, and the geographic location of particular big-market cities that are more likely to attract talented players are certainly part of this equation, but until the Nuggets are hoisting the Larry O’Brien, I’ll have to keep playing the numbers.

 

Speaking of the numbers, let’s go back to our NBA Championship Lottery model and draw a few more names from the proverbial hat with the intention of answering the question, “will my team win a title before I kick the bucket?”

The average life expectancy in the USA has been hovering around 78 for the last few decades. Let’s assume that winning a title before you’re 10 years-old or at the very end of your golden years isn’t likely to be memorable and end up at a completely unscientific 65-year long championship window for the average American. Based on the current 30 team league and assuming equal odds of winning for every team in any given year, there is an 89% chance that you will live to see your NBA team win a championship. Sure, that leaves an 11% chance that you won’t live to see a banner raised into the rafters at your hometown arena, but let’s look on the bright side. Based on the ‘name-from-a-hat’ model there is a 20% chance that you will live to see your team win 3 championships and a 4% chance that your hometown team will lift the trophy 5 times while you’re around to see it! 

In lieu of becoming extravagantly wealthy and buying your hometown team, petitioning to eliminate income tax in your state, or carving out some new beachfront property to attract talented players, there isn’t much that can be done to improve your odds of winning. So sit back, relax, and remember what your middle school soccer coach said all those years ago, “Winning isn’t everything”.

(Photo by Jesse D. Garrabrant/NBAE via Getty Images)