NBA

No hold market in Jazz vs Clippers series

Sportsbooks impose a cost when you bet a spread. -110 means you wager $1.10 for every $1 in winnings. This extra ten cents is a hold that lets sportsbooks make money.

But what if you only had to wager $1 for every $1 won? This price of +100 on both sides of a spread is an example of a no hold market. If you picked games at random, you would not lose money in the long run.

No sportsbook has these odds on a spread or total. However, as suggested in The Logic of Sports Betting book by Ed Miller and Matthew Davidow, you can find these no hold markets by looking at related markets.

For example, let’s look at the Jazz vs Clippers series which tips off on Tuesday night. At FanDuel, the Jazz are -4 in game 1.

With 3 points in playoff home court advantage, this implies that the Jazz are a point better than the Clippers on a neutral court. Given this difference, my code works out the series win probability by careful multiplication of the win probabilities in individual games.

If Utah is 1 point better than Los Angeles, this calculation gives Utah a 60.8% series win probability. The market price for the series is -130 for Utah, which implies a break even percentage of 56%.

There are two possibilities.

You like the Jazz, believing in their NBA best regular season record. You would bet Utah -130 for the series at DraftKings.
You like the Clippers, believing in the talent of Kawhi Leonard and Paul George. You would bet Los Angeles +4 at FanDuel.

Personally, I have no idea which side to like. I have neither run numbers or watched much NBA this season. Listening to my advice would be like making Nathan Peterman your franchise QB.

But you’re a lot smarter than me, and you can use this no hold market to bet this game/series.

Of course, there are uncertainties in my calculation of the series probability. FanDuel has a higher juice to bet the Clippers side (-114 instead of -110). In addition, maybe home court isn’t quite 3 points for Utah in this series.

To account for this, I ran the calculation again assuming Utah is 0.5 points better than Los Angeles. I also assumed a home court of 2.5 points, which hurts the home team Utah. Utah has a 56.6% series win probability, still higher than the break even price -130.

I doubt this no hold market will last until tip at 10:05pm Eastern time on Tuesday night.

The Logic of Sports Betting is a fantastic read which I highly recommend. Check it out here.

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Lakers series win probability down 3-2 to the Suns

By Dr. Ed Feng Leave a Comment

The Suns vs Lakers series was fascinating from the beginning. With LeBron James and Anthony Davis, the Lakers were the pre-playoff favorite out of the Western conference as the 7 seed.

When Suns veteran Chris Paul got hurt and couldn’t play in game 2, it seemed all but assured the Lakers would advance. Now, Paul has returned, and Anthony Davis didn’t play in game 5 due to a groin injury.

In an NBA playoff series with no injuries, the spread usually swings back and forth based on home court. For example, the Knicks have been about a 1.5 point favorite at home but a 4.5 point underdog at Atlanta.

There is no regularity in this series. Let’s go through the games.

Game 1. Suns -2.5. Both teams were healthy, so this might be the best pure estimate of team strength given the Suns home court. (Suns win by 9)
Game 2. Lakers -2. Suns didn’t have Chris Paul and were down 1-0 heading into this game. (Lakers win by 7)
Game 3. Lakers -6.5. The Lakers had home court in game 3, but Chris Paul came back. (Lakers win by 14)
Game 4. Lakers -6.5. Anthony Davis gets hurt during the game. (Suns win by 8)
Game 5. Suns -4.5. Lakers didn’t have Anthony Davis on Suns home court (Suns win by 30)
Game 6. Lakers -2. Morning of the game on Thursday.

The spread has stumbled around more than Ernest Hemingway after hitting the bars in Cuba.

In my last correspondence, I argued that home court should be 3 points. While the markets have confirmed this in the Denver vs Portland and Atlanta vs New York series, it has been more complicated in the Suns vs Lakers series.

The difference in the markets between Game 1 versus Game 3 was 9 points, which should be twice home advantage. This implies a whopping 4.5 points for home advantage. Note that the injury to Chris Paul might have impacted the spread in Game 3; Paul played but not at full strength.

Based on the spread in Game 1 and 3, the Lakers are 2 points better than the Suns on a neutral court. I have code that translates this edge into a series win probability. With a 3-2 lead, the Suns have a 69% series win probability. This is a good estimate with a healthy Anthony Davis.

If Anthony Davis can’t play, we can estimate team strength by taking the difference in spreads between Game 5 and 6. This implies the Suns are better by 1 point. Anthony Davis is worth 3 points, and his absence raises the series win probability of the Suns to 79%.

FanDuel has the Suns at -290 to win the series, which implies a break even probability of 74%. This seems reasonable given the uncertainty around the health of Davis.

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NBA home court advantage in the 2021 playoffs

By Dr. Ed Feng Leave a Comment

There’s nothing like home cookin’.

With a home playoff game, a player sleeps in his own bed instead of a hotel and finds local sex workers instead of prowling the clubs. (Joking… but kind of serious. Looking at you, James Harden.)

No wonder home teams win a higher percentage of games than their road opponents.

What should home court advantage be in the 2021 NBA playoffs? There are two competing factors that affect home advantage:

an increase due to the playoffs
a decrease due to smaller crowds because of the pandemic

Due to small sample size, getting an exact value is harder than getting warm water to spontaneously separate into hot and cold. However, we’ll make a best estimate based on the data.

First, let’s look at the increase in home court in the playoffs. In the regular season from 2016 through 2019 (3 seasons), NBA teams had a home court advantage of 2.66 points. In the playoffs during those 3 seasons, the home court jumped to 4.11 points, a 55% increase.

Second, let’s look at the effect of reduced crowd size due to the pandemic. The book Scorecasting looked at the reasons behind home court advantage. The authors found that the impact of crowds on referees is a factor. Reduced crowds during the 2020-21 season should imply a smaller home advantage.

Overall, home teams have scored 0.94 points more than road teams, a figure that includes Toronto’s home games in Tampa Bay. However, it’s important to break this down into games with and without fans.

According to data from Basketball Reference, home court has been 2.18 points in the 503 games with some fans this season. In games with no fans during the 2020-21 season, road teams have scored more points than the home team (-0.13 home court advantage).

Let’s suppose NBA home court is 2 points with limited fans during the regular season. During the playoffs, all teams will allow a limited number of fans. Assuming a 50% increase for the playoffs, this gives 3 points for home court during the playoffs.

We can check this 3 point assumption against the markets. With no major injuries in a series, the difference in the spread between home and road games provides an estimate of home court.

For example, Milwaukee was a 5 point favorite against Miami at home in game 2. The markets have Milwaukee +1 as an underdog for game 3 in Miami. Since the Bucks have swung from a home court advantage to not having it, this shift in point spread should be twice a uniform home court. Hence, this 6 point swing implies a 3 point home court.

Denver was a 2 point favorite over Portland at home in game 2. The shift to a 4 point underdog at Portland in game 3 also implies a 3 point home court.

3 points seems roughly correct for home court in the 2021 NBA playoff.

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Predictability vs skill in sports analytics: 3 point shooting

By Dr. Ed Feng 1 Comment

To listen to the audio version, click on the triangle or grab it on Apple Podcasts. The text version is below.

You’re interested in making sports predictions. The more accurate, the better.

To do this, we typically take a statistic and look at its correlation from season to season. This is especially relevant in preseason football as we look to predict the upcoming season.

If there is a high correlation from season to season, we say the statistic is predictive and include it in our models. If the statistic has a weak correlation, then it’s not predictive. Analytics 101.

However, this exercise can be confusing. For example, consider 3 point shooting percentage in the NBA. There’s a weak correlation from season to season, as a player’s 3 point shooting percentage from last season explains 14.5% of the variance during the current season.

I think there’s a problem with this analysis; more on that later.

In addition, the analysis doesn’t make sense. There is clear skill in shooting a basketball. Who would pick Russell Westbrook over Steph Curry in a three point shooting contest? No one.

In discussing the lack of correlation in 3 point shooting percentage, data scientists like myself usually say something like “randomness plays a big role in 3 point shooting percentage.” This is true, but not the entire picture.

In this article, I’ll discuss predictability versus skill and how they are related but different concepts.

Skill in shooting 3 pointers

Why is there skill in three point shooting?

To get some intuition, let’s take the following approach: assume 3 point shooting is random, and compare the actual data on players with this assumption.

I looked at NBA data from 2014 through 2020 before the lockdown. During this period, the average 3 point shooting percentage was 35.6%. If 3 point shooting is random, each player makes shots at this rate.

Based on this random assumption, a player’s 3 point shooting percentage won’t land exactly on the mean value of 35.6%. Some players will end up above this value, some below. But as a player takes more shots, his shooting percentage approaches the mean value of 35.6%.

When you look at many players based on this random assumption, you get a distribution of 3 point shooting percentages spread around the mean. If each player takes 2000 shots, the width of this distribution is about 1%. This implies that two out of three players will have a percentage between 34.6% and 36.6%.

Let’s compare this random assumption with actual players like Steph Curry. Steph has made 43.2% of his 3 point shots over the past six seasons. If each of Steph’s shots had a 35.6% chance to go in at random, Steph’s shooting percentage would be 9.6 standard deviations from the NBA average (based on 3,681 attempts). This is extremely unlikely.

This confirms what we all know: Steph Curry is a great shooter, probably the best to have ever played the game.

In contrast, Russell Westbrook has made 30.4% of his 2,150 attempts from 3. His percentage is five standard deviations below the NBA average. That’s the kind of ineptitude you expect if you made Dave Gettleman the CTO of your sports analytics startup.

Westbrook is not the worst in the NBA over this period by the standard deviation analysis. More on that later.

These outliers seem to confirm the skill in three point shooting. Let’s put some numbers behind this.

Skill vs luck

To distinguish skill from luck, I’ll use an idea from Michael Maubossian’s book The Success Equation. He defined a model in which outcomes are a combination of skill and luck.

outcome = skill + luck

For 3 point shooting percentage, some of a player’s results comes from skill while the remainder comes from luck. There’s always some randomness. A shot is not always going in, even if Steph Curry is wide open.

Consider the variance in outcomes. Based on this simple model, we get:

Var(outcome) = Var(skill) + Var(luck)

In taking the variance of the previous equation, there is usually a term that considers the correlation between skill and luck. However, by definition, I’m assuming that there’s no correlation between skill and luck. Every player has an equal chance to get lucky.

Let’s go back to our random assumption in which every player makes shots at the same rate. By taking the standard deviation of each player from NBA average, we get a normal distribution with variance of 1. There is no skill in this model.

Let’s compare this assumption with the actual data on NBA players over the past 6 seasons. The wider this distribution in 3 point shooting percentage, the more skill in 3 point shooting.

To measure skill, I consider the fraction of variance in 3 point shooting percentage, Var(outcome), explained by skill, Var(skill). This is similar to the previous idea of predictability. A player’s 3 point shooting percentage from last season explained 14.5% of the variance in a player’s 3 point shooting percentage this season. To get a visual explanation of this concept, click here.

For both predictability and skill, we ask how much of the variance in outcome can be explained by another quantity.

For predictability, how does last season’s data explain the variance in this season’s 3 point shooting percentage.
For skill, how much bigger is the variance in player 3 point shooting percentage than the variance based on the random assumption.

In the NBA, 78% of the variance in 3 point shooting percentage is explained by skill.

To put this into perspective, let’s look at Maubossian’s results on teams. If winning NFL games were all luck, each game would be a 50-50 coin flip. The distribution of win percentage for teams would have a certain width based on a 16 game season.

The actual distribution of win percentages is wider than the random assumption, and Maubossian calculated the following:

NFL: 62% of variance in win percentage is explained by skill
NBA: 88% of variance in win percentage is explained by skill

There is more skill in shooting 3 pointers than winning NFL games, as skill explains 78% of the variance in outcomes. However, there is less skill in shooting 3’s than winning NBA games.

For another perspective, let’s look at free throw shooting. Based on the same 6 season NBA data set, skill explains 98% of the variance in free throw shooting percentage.

On the good side, Damian Lillard is 16.8 standard deviations higher than average. On the bad side, Andre Drummond is more than 33 standard deviations worse than NBA average. That is some massive Dave Gettleman ineptitude.

This analysis supports the idea of skill in shooting a basketball. Almost all of the outcome in free throw percentage is skill. It’s the player and the basket. The analysis reveals less skill in 3 point shooting, presumably because of increased randomness due to factors such as defense.

Unlike 3 pointers, free throws are also highly predictable. A player’s free throw shooting percentage from last season explains 70% of the variance in free throw shooting percentage in the current season. We expect that high degree of predictability when a statistic is 98% skill.

3 point shooting percentage is not a strong predictor. From before, a player’s data from last season explains 14.5% of the variance in 3 point shooting percentage this season. This is despite the analysis that 3 point shooting is 78% skill.

3 point shooting is a skill but not predictable. Let’s look at an example.

Unpredictability of 3 point shooting

In performing this analysis, Duncan Robinson of the Miami Heat showed up as one of the best shooters in the NBA. In the 2019-20 season before the lockdown, he made 45% of his 3 point shots.

Robinson played his college basketball at Michigan. He was a senior in the spring of 2018 when Michigan made a run to the NCAA tournament title game against Villanova.

Robinson was a great shooter in college. This was obvious either from looking at his shooting motion or his numbers from his first two seasons at Michigan. But as a senior, he only shot 38% from 3.

However, those 203 eight attempts his senior year didn’t provide a sufficient sample to predict future performance. In his second NBA season, Robinson has shown his skill as a three point shooter.

In contrast, Giannis Antetokounmpo does not have skill in shooting 3 pointers. Over the past 6 seasons, the Greek Freak was the one player worse than Russell Westbrook. Only an MVP caliber player can make 28% of his 3 pointers and still take almost a thousand attempts.

Better 3 point shooting predictions

There’s another problem with looking at year to year correlations in making statements about predictability, especially in pro sports. We have multiple seasons of data on pro players. This is not college.

To see how an increased sample helps predictability, I took the six season NBA sample and asked how five seasons of data could predict the remaining season. To do this, I took a player and picked one of the six seasons at random. To include this player in the analysis, he needed 100 attempts in the target season and 300 in the remaining seasons.

A five year sample was able to explain about 24% of the variance in 3 point shooting percentage in the target season. This doesn’t make me run to put this statistic in a predictive model. However, five seasons gives about a 60% improvement over one season.

For free throw shooting, a five season sample explains 72% of the variance in free throw shooting in the target season. Based on the 70% value from one season, four addition seasons result in about a 3% improvement.

There’s a lot of randomness in three pointers, and a larger sample gives a significant boost in predicting the future. There is less randomness in free throw, and one season is a decent sample to predict the future.

Predictability vs skill in the NFL

Here’s the take home message: predictability and skill are related distinct ideas.

In this analysis, predictability is the correlation of a statistic from an earlier to a later time period. I’m defining skill in terms of the distribution of player statistics over a six year period in the NBA. The variance of this distribution in excess of a random assumption is defined as skill.

Usually, predictability and skill are related. We saw this with free throw shooting. However, skill does not imply predictability. 3 point shooting is a skill, an intuitive results confirmed by the analysis in this article. However, a player’s three point shooting percentage in the past struggles to predict the future.

Next month, we’ll see how these ideas apply to the NFL. In particular, we’ll look at the 32 most important men in sports: NFL quarterbacks.

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Early season NBA rankings for 2018-19

By Dr. Ed Feng 1 Comment

I like to look at NBA rankings about this time of the season as we reach a crossover point with football. NBA, college football and NFL have all played about 10 games.

Here are my NBA team rankings through games on Monday, November 5th, 2018. The rating gives an expected margin of victory against an average NBA team.

1. Milwaukee, (7-1), 11.57
2. Golden State, (9-1), 9.21
3. Toronto, (9-1), 8.39
4. Denver, (9-1), 7.26
5. Boston, (6-4), 5.45
6. Portland, (7-3), 5.39
7. Charlotte, (4-5), 2.52
8. Indiana, (7-4), 2.30
9. Oklahoma City, (5-4), 1.94
10. Utah, (4-6), 1.25
11. Memphis, (5-4), 1.14
12. New Orleans, (3-6), 1.12
13. Los Angeles Clippers, (5-4), 0.90
14. Los Angeles Lakers, (4-6), 0.63
15. Sacramento, (5-4), -0.09
16. Miami, (4-5), -0.11
17. San Antonio, (6-3), -1.15
18. Minnesota, (4-6), -1.38
19. Houston, (4-4), -1.43
20. Philadelphia, (6-5), -1.52
21. New York, (3-7), -1.64
22. Washington, (2-6), -3.23
23. Orlando, (4-6), -3.48
24. Chicago, (3-7), -4.24
25. Brooklyn, (4-5), -4.58
26. Detroit, (4-5), -5.12
27. Dallas, (2-6), -6.50
28. Phoenix, (2-7), -7.75
29. Cleveland, (1-9), -9.28
30. Atlanta, (3-6), -9.66

From only early season results, we would conclude that top ranked Milwaukee is better than Golden State, the dynasty that has won 3 of the last 4 NBA titles.

We might give up on LeBron, as the Lakers aren’t even the best team in Los Angeles. The Lakers are ranked 14th, right behind the Clippers.

Of course, these results reflect small sample size. Remember this when you look only at football numbers from this season.

Follow along with my NBA rankings, which get updated daily, to see how the season plays out.