Division Winners Now Face Small, But Not Infinitesimal, Possibility of Not Making Playoffs

The NBA formally announced this past week that it will be eliminating the rule that guarantees a division winner a top-four playoff seed. This is the first change to the NBA playoff rules since a small change prior to the 2008-09 season (if you are a hardcore fan, it is worth a read as to why that change was instituted). Divisions are not entirely made irrelevant, as the second tiebreaker after head-to-head is whether a team was a division champion.

Given this, I was curious to calculate the odds that a division winner would NOT make the playoffs. This is meant to be a purely objective exercise - whether the event that a division winner not making the playoffs should be considered "good" or "bad" is not the purpose of this article.

I started off by constructing a Monte Carlo model that performed 1,000 simulations of the NBA season using the 2014-15 season schedule. In this 1,000 season simulation, among 6,000 division winners (three in each conference times two conferences for 1,000 seasons) there were 27 division winners (0.45%) that did not make the playoffs, which means that 5973 (99.55%) did make the playoffs.* This also means that in a given season, the odds of at least one division winner not making the playoffs is approximately 2.67%.** This is small but not infinitesimal.

I then calculated the odds that this event (that at least one division winner does not make the playoffs in a given season) occurs at least once over the course of X number of seasons.*** 

As you can see from the table below, over the next 15 years there is approximately a 1/3 chance that we will have at least one season in which at least one division winner does not make the playoffs.

Season	Odds
Odds of having at least one season where at least one division winner does not make playoffs, over 1 season	2.67%
Odds of having at least one season where at least one division winner does not make playoffs, over 2 seasons	5.27%
Odds of having at least one season where at least one division winner does not make playoffs, over 3 seasons	7.80%
Odds of having at least one season where at least one division winner does not make playoffs, over 4 seasons	10.26%
Odds of having at least one season where at least one division winner does not make playoffs, over 5 seasons	12.66%
Odds of having at least one season where at least one division winner does not make playoffs, over 6 seasons	14.99%
Odds of having at least one season where at least one division winner does not make playoffs, over 7 seasons	17.26%
Odds of having at least one season where at least one division winner does not make playoffs, over 8 seasons	19.47%
Odds of having at least one season where at least one division winner does not make playoffs, over 9 seasons	21.62%
Odds of having at least one season where at least one division winner does not make playoffs, over 10 seasons	23.71%
Odds of having at least one season where at least one division winner does not make playoffs, over 11 seasons	25.75%
Odds of having at least one season where at least one division winner does not make playoffs, over 12 seasons	27.73%
Odds of having at least one season where at least one division winner does not make playoffs, over 13 seasons	29.66%
Odds of having at least one season where at least one division winner does not make playoffs, over 14 seasons	31.54%
Odds of having at least one season where at least one division winner does not make playoffs, over 15 seasons	33.36%

* While it is tempting to believe that at least two division winners MUST make the playoffs, there are a (very, very) small number of situations in which this may not occur – hence I treat a division winner not making the playoffs as an independent event by division (with 6 independent events per season – one for each division) rather than by conference (with 2 independent events – one for each conference). For example, in the Western Conference, say two divisions have four teams with the same record (say 50-32, last teams record is irrelevant), and the remaining division has three teams at 50-32 (last two teams records are irrelevant). There could be a situation where out of those 11 teams with a 50-32 record, in their head to head records (now the first tiebreaker) the three worst performing teams could actually be the best team in their respective divisions based on head to head records within their own divisions as a divisional tiebreaker. Either way, the probabilities in the chart above differ by just fractions of a percent if you treat winning a division as an independent event by division (as I did) versus independent events by conference. Here’s an analogy - if there’s a 5% chance of something happening during an event and you want to calculate the odds of it happening at least once in 5 events, the probability is nearly identical to if there’s a 2.5% chance of something happening during an event and you want to calculate the odds of it happening at least once in 10 events.

** Taken by calculating the inverse of the probability of an event (in this case, the event is all six division winners making the playoffs). The probability of all six division winners making the playoffs is (.9955^6) = .9733, so 1-.9733 = .026698 = 2.67%.

*** Taken by calculating the inverse of the probability of an event (in this case, the event is that there are no seasons over X number of seasons in which all six division winners make the playoffs). The probability of having this type of a season is .9733 as calculated earlier, the inverse is 1-(.9733^x) where "x" is the number of seasons completed.