Democrats have a 23% Chance of Having a Majority on the Supreme Court in 2028

The retirement of Justice Anthony Kennedy and nomination of conservative Brett Kavanaugh to replace him is poised to give Republicans a more reliable majority on the Supreme Court.  But a 5-4 majority is a narrow one.  A Democratic victory in the 2020 presidential election coupled with the death of a single Republican appointed justice would produce a reversal in power on the Court.  The current state begs the question: precisely how likely are Democrats to regain the majority?

Despite the complexities of the legal and political processes that produce Supreme Court candidates, this question is surprisingly approachable statistically.  The central variables involved are not from the domain of legal theory or constitutional interpretation, but rather from areas familiar to a statistician: life expectancy, behavioral preferences, and election projection.  By consulting actuarial tables, the record on judicial retirements, and the history of presidential election results, I have endeavored to construct a quantitative understanding of the likelihood of changes of control on the Supreme Court.

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Which College Statistics Are Most Correlated With NBA Success?

The NBA draft is almost upon us! For the sake of curiosity, I decided to dig into the data to determine which college statistics have been most correlated with NBA success.

I will first give a few words on my methodology. I considered all players drafted in the year 2000 to the present whose age 25 season could have happened in 2017-18 or earlier. The age 25 season criteria is included because I measured player value in terms of Win Shares (a stat provided by basketball-reference) produced in the age 25 season. I chose to measure performance at this age rather than something like prime years (age 26-29) to allow more recent draft picks into the sample.

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Introducing 3-PIGS, a New Way of Understanding Three-Point Variability in NBA Games

The rise of the three-point jump shot in the NBA has been well documented. Over the past five regular seasons the average team three-point attempt rate has spiked from 24.3% to 33.7%, per basketball-reference. The analytically driven Houston Rockets actually attempted more three-pointers than two-pointers this past season!

In this three-point happy league, analyzing an individual game after removing the effects of “hot” or “cold” three-point shooting can be very informative. It allows us to see how well the teams played in all aspects of the game except three-point accuracy. We can strip aside a particularly unusual shooting performance and observe the “fundamentals” of a game, in a certain sense.  This is what Three-Pointer Independent Game Score (abbreviated as 3-PIGS) does.


A team’s 3-PIGS score is the percentage of times the team would win the game if we replayed the game many times* with all three-point attempts randomly simulated. The probability a three-pointer is made in each simulation is equal to the the yearly three-point percentage of the player taking it**.

I conducted 1000 simulations of 2017-18 regular season games for the purpose of testing the merits of 3-PIGS.

** Players with less than 30 total three-point attempts in the season are given a 30% chance of making each attempt.

The 3-PIGS score answers this narrow question: Given all the information about a particular game except the knowledge of the success or failure of each three-point attempt, what is the probability that a given team won the game?

Computing 3-PIGS is not complicated. I simply subtract all points added from threes from the final game score and then add points back as dictated by the simulation results. I do this a bunch of times (usually 1000) and count the percentage of times each team wins.

There are a couple reasons why 3-PIGS is informative. First, defenses tend to have more influence over opponent three-point volume than opponent three-point accuracy (I examined this to an extent here). 3-PIGS is working at exactly this level. The 3-PIGS score will be influenced by the volume of three-pointers the opponent takes and which players take them, but not whether they are actually made.

Secondly, 3-PIGS tells an interesting part of the story of a game which can be lost by simply looking at the final score. As an example, take games 1 and 2 of the Cavaliers vs. Celtics Eastern Conference Finals, which the Celtics won by 25 and 13 points respectively. By conventional wisdom, the Celtics dominated game 1 even more than they dominated game 2, but 3-PIGS tells a different story. The Celtics’ 3-PIGS scores for the games were 74.2% and 87.7%, indicating that their game 2 performance was even more impressive. The Cavaliers’ game 1 shooting woes had a large effect on the final score. They made only 4 of 26 three-point attempts in game 1, while through chance alone we would expect them to actually make a bit more than 10 on average.

Finally, 3-PIGS goes beyond team three-point percentage and takes into account the actual individuals who took the shots. This is simply because each three-point attempt is simulated with a probability of being made equal to the three-point percentage of the player taking it. The 3-PIGS score gives a bit more information than simply comparing a team’s three-point percentage in a particular game with their season average because it takes into account who shot the threes.

3-PIGS gives the proportion of time each team would win a game (after simulating three pointers), so it makes sense to see how accurate it is as a predictor of the winner. The plot below shows that 3-PIGS is a fairly well-calibrated predictor, meaning that teams win about as often as the percentage given by the 3-PIGS score for the game would suggest. The data used for this plot is all 2017-18 regular season games.


There is a trend for the home team to win more often than their 3-PIGS score would suggest, as depicted by the blue line being above the red line. This is especially true when the home team is given between a 40%-80% chance of winning the game. Interestingly, this trend cannot merely be explained by teams shooting better at home. Teams actually shot 0.2 percentage points higher on threes on the road than at home over the 2017-18 regular season.

There are certainly flaws with 3-PIGS. This statistic is not taking into account the specific difficulty of each three-point attempt. Perhaps in the future I should consider whether each shot was contested vs. wide-open or off-the-dribble vs. catch-and-shoot, and build this knowledge into 3-PIGS. And there is also the fact that missed three-pointers offer the offensive team a chance for a rebound, thus blunting a little of the downside of a missed three. Even with its flaws, I believe 3-PIGS can give us valuable insight into how much three-point shooting variability contributed to the outcome of a game.

For the sake of curiosity, I provide a link to a Google Sheet with the results and 3-PIGS game scores of all 2018 playoff games through Houston vs. Golden State game 6.  The column titles ‘Home 3-PIGS’ is the 3-PIGS score of the home team in the given game (so the road team had a 3-PIGS score of 100 – Home 3-PIGS).  The columns titles ‘Home Margin’ and ‘Expected Home Margin’ are, respectively, the home score minus the road score and the expected home score minus the expected road score, if all three-pointers were random. In the future, I will probably release 3-PIGS scores for regular season games and other postseason games.

Acknowledgement: Inspiration for this post was provided by Jacob Goldstein’s article for Nylon Calculus, Nylon Calculus: Defining and calculating luck-adjusted ratings for the NBAHe came up with a method for adjusting the net-ratings of individual players to account for three-point shooting (and free throw) luck.


Are Past Games in a Playoff Series Predictive of the Next Game?

I recently was building a simple model to forecast an NBA playoffs series. As I was building the model, I realized that I was not taking into account the possibility that each team’s strength could change over the course of the series. If a team dominates games 1 and 2, we might reasonably expect them to have a higher likelihood of winning game 3 than we did at the beginning of the series.

But perhaps we should not alter out initial belief too much. After all, the 2 games in the example above is not a very large sample. Sheer randomness and recency bias may be causing us to shift our thinking too much. My initial hunch was just that; the general public overreacts too much to a few performances.

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An Analysis of the 2-for-1 Strategy in the NBA

The appropriately named “2-for-1” is a strategy utilized at the end of a quarter in which a team tries to time their shot attempts so that, as the name suggests, they get two attempts while their opponents only have one. To execute the strategy, a team usually pushes the ball up the floor to take a shot with about 30 seconds left in the quarter, thus ensuring that their opponents cannot hold for the last shot.

Intuitively, this strategy seems perfectly reasonable. Just like holding for the last shot, a team which executes the 2-for-1 is gaining one extra possession. Who would not want an extra possession? Well, we could imagine a scenario where the two possessions are so rushed that their expected value is less than the value of the one “normal” possession the opponent is allowed. For example, suppose we value a conventional NBA possession at 1.09 expected points but the two rushed possessions usually generate bad shots and are only worth 0.5 expected points each. Then it might make more sense to execute a “1-for-1” strategy and simply grant the opponent the last shot.

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Which Team Statistics are Most Stable From the 1st Half of the Season to the 2nd?

In my work on the Threes and Layups NBA Net Rating Calculator, I have focused on 14 statistics (the same 7 on offense and defense) which capture a team’s performance across all areas of the game:

  1. 2-Point %
  2. 3-Point %
  3. 3-Point Attempt Rate
  4. Free Throw Attempts Per Field Goal Attempts
  5. Free Throw %
  6. Turnover Rate
  7. Rebound Rate (Offensive and Defensive)

The NBA Net Rating Calculator allows you to see how much a team’s regular season performance would be expected to change if you changed one of these statistics. But this leads to a natural question: which of these statistics is most likely to change?

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Are the Raptors Really a Bad Playoff Team?

The Toronto Raptors are in the middle of an impressive regular season. They have outscored opponents by 8 points per 100 possessions this season, the second best mark in the league behind only the Warriors, per basketball-reference. Regular season success is nothing new for the Raptors, as Toronto has posted a net rating of at least +3.5 in each regular season since 2013-14. This Raptors team has not only built upon the successful campaigns of the previous seasons, but also added new dimensions to their game. Their upgraded shot selection on offense has them currently ranked 7th in the NBA in 3-point attempt rate.

While the Raptor’s statistical profile is once again impressive, I can’t help but get the feeling that a lot of NBA fans are probably having right now: We’ve seen this story before. A strong regular season Raptors squad goes into the postseason and helplessly fizzles out. This feeling is backed up by the performances Toronto has put up in the playoffs since the 2014 season.

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