Nba Point Spread Formula

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Hopefully if you’re reading this, you’ve had a chance to explore our new interactive graphic, “The Complete History Of The NBA,” which tracks each NBA and ABA franchise’s performance through every game of its history.
So now for the exciting part: 2,000 words about autocorrelation and the Akron Firestone Non-Skids.
Actually, this won’t be too bad because Elo is a pretty simple formula. The guts of the system are the same as we used for the NFL and which other researchers have applied to competitions ranging from chess to soccer. For those new to Elo, here are its essential features:
The long-term average Elo rating is 1500, although it can vary slightly in any particular year based on how recently the league has expanded (more about that below). More than 90 percent of team ratings are between 1300 (pretty awful) and 1700 (really good), but historically great or truly execrable teams can fall outside that range:
There are just a few NBA-specific parameters to set, which we’ll describe below.
Elo’s K-factor determines how quickly the rating reacts to new game results. It should be set so as to efficiently account for new data but not overreact to it. (In a more technical sense, the goal is to minimize autocorrelation.) If K is set too high, the ratings will jump around too much; if it’s set too low, Elo will take too long to recognize important changes in team quality.
We found the optimal K for the NBA to be 20. This is higher than we expected; it’s in the same range as the K used for NFL and international soccer Elo ratings even though the NBA plays far more games than those sports. It’s much higher than the optimal K for baseball. It implies that you ought to give relatively high weight to an NBA team’s recent performance.
One way to interpret this is that NBA data is subject to relatively little randomness. This makes it different from sports like baseball and hockey, whose game-by-game results are pretty noisy; in those sports, your default assumption should be that a winning or losing streak is mostly luck. That isn’t so true for basketball. Streaks may reflect true, if perhaps temporary, changes in team quality. When the Atlanta Hawks went on a 19-game winning streak this season, for instance, they were undoubtedly getting a little lucky, but they were probably tougher to beat than at other points in the season.
There are still some cases in which Elo seems too slow to catch up to reality, like when Michael Jordan left the Bulls or LeBron James left the Cavs. But remember: Elo is only looking at game scores and not the composition of the roster. If that’s all the information you have, setting Elo to react more quickly to these cases would make it overreact to others. The Oklahoma City Thunder’s Elo rating never dipped below 1508 this year despite its 3-12 start, for instance, and that proved to be prudent since the team went 42-25 the rest of the way and ended the year with an Elo rating of 1583.
As for our NFL Elo ratings, it’s possible to translate NBA Elo ratings into point spreads. Here’s the formula: Take the difference of the two teams’ Elo ratings, add 100 points for the home team and then divide by 28. That gives you a projected margin of victory for the game. For instance, in Game 1 of the 2013-14 NBA Finals, the San Antonio Spurs had a 92-point Elo advantage over the Miami Heat, as well as home court, for an overall advantage of 192 Elo points. Dividing that by 28 would make San Antonio roughly 7-point favorites in the game.
In practice, the magnitude of home-court advantage has waxed and waned over the NBA’s history. Home teams won by an average of 5.8 points in the 1987-88 regular season, for instance, but by just 2.4 points in the past season. And some teams (especially those like Denver and Utah that play at high altitudes) have historically had slightly larger home-court advantages.
Still, the spirit of the Elo system is to keep things simple. We experimented with a dynamic home-court advantage rating that changes over time, but we found that it made almost no difference to the overall ratings, partly because each NBA team plays about half its games at home and half on the road. So we’re using the constant 100-point home-court advantage instead.
Elo strikes a nice balance between ratings systems that account for margin of victory and those that don’t. While teams always gain Elo points after wins and lose Elo points after losses, they gain or lose more with larger margins of victory.
The margin of victory multiplier is calculated as follows.
For instance, in Game 1 of the Warriors-Rockets series, the Warriors entered the game with a an Elo rating 118 points higher than the Rockets’ and had home-court advantage, for an elo_diff of +218. They wound up winning the game by 4 points. Thus, their margin of victory multiplier is calculated as follows:
What if the Rockets had won by 4 points instead? Since they were underdogs, they’d get a larger multiplier:
While this formula may seem clunky, it accounts for the fact that favorites tend to win games by larger margins than they lose them. Failing to correct for this will introduce autocorrelation into the system and make the ratings less stable. See here for further discussion.
Instead of resetting each team’s rating when a new season begins, Elo carries over a portion of a team’s rating from one season to the next. In our NFL Elo ratings, teams retain two-thirds of their rating from the end of the previous season. In our NBA ratings, by contrast, they keep three-quarters of it. The higher fraction reflects the fact that NBA teams are more consistent from year to year than NFL squads.
For example, the Miami Heat ended the 2012-13 NBA season with an Elo rating of 1754. The team’s Elo rating for the start of the 2013-14 season is calculated as follows:
Detail-oriented readers may see something that seems amiss here. Each team’s Elo rating is reverted to the mean, and — as we’ve said — the long-term mean Elo rating is 1500. So why does a slightly different number, 1505, appear in the formula?
The reason has to do with the way we handle expansion teams. In principle, the implementation of this is pretty simple. Each franchise begins with an Elo rating of 1300 in its inaugural professional season. The reason we revert to a mean of 1505 rather than 1500 is that there are liable to be a couple of relatively recent expansion teams in the league at any given time. Giving established teams a rating very slightly higher than 1500 counteracts the expansion teams and keeps the league average Elo close to 1500 over the long run.
But the league average Elo rating will be slightly different from 1500 in any given season, depending on how recently the league has expanded. It was 1504.5 during the 2014-15 NBA season, for instance, slightly higher than the long-term average because the NBA hasn’t expanded much recently.
The league average tended to fluctuate more in the early years of the NBA because of constant expansion, contraction and mergers with other leagues. (We’ve learned way more than we wanted to know about the early history of American professional basketball, like that you could have once watched a game between teams named the Indianapolis Kautskys and the Akron Firestone Non-Skids.) The league average reached a peak of 1534.5 in 1954-55 after a number of losing teams had disbanded. By contrast, it was just 1440.5 in the 1970-71 season after the NBA expanded rapidly.
There’s one other tricky part. We said a team begins with a rating of 1300 in its first professional season. That doesn’t mean its first NBA season. Instead, teams get credit for their performance in predecessor leagues that merged with the NBA:
Since data on the ABL is very hard to come by, the Bullets’ initial rating is simply calculated by starting them with a rating of 1300 and then reverting them toward the mean of 1505 for each season they played in that league.
Teams retain their prior Elo ratings when they change cities or nicknames. This includes the teams now known as the New Orleans Pelicans and Charlotte Hornets. The NBA, in a bit of revisionist history, considers the current Charlotte Hornets (who were known as the Charlotte Bobcats until this season) to “own” the statistics of the team that played as the Charlotte Hornets from 1988-89 through 2001-02, before they moved to New Orleans. We instead link those Hornets seasons with the New Orleans Hornets, who are now the New Orleans Pelicans.
As for our NFL Elo ratings, it’s possible to translate NBA Elo ratings into point spreads. Here’s the formula: Take the difference of the two teams’ Elo ratings, add 100 points for the home team and then divide by 28. That gives you a projected margin of victory for the game. For instance, in Game 1 of the 2013-14 NBA Finals, the San Antonio Spurs had a 92-point Elo advantage over the Miami Heat, as well as home court, for an overall advantage of 192 Elo points. Dividing that by 28 would make San Antonio roughly 7-point favorites in the game.
The margin of victory multiplier is calculated as follows.
For instance, in Game 1 of the Warriors-Rockets series, the Warriors entered the game with a an Elo rating 118 points higher than the Rockets’ and had home-court advantage, for an elo_diff of +218. They wound up winning the game by 4 points. Thus, their margin of victory multiplier is calculated as follows:
What if the Rockets had won by 4 points instead? Since they were underdogs, they’d get a larger multiplier:
While this formula may seem clunky, it accounts for the fact that favorites tend to win games by larger margins than they lose them. Failing to correct for this will introduce autocorrelation into the system and make the ratings less stable. See here for further discussion.
Since data on the ABL is very hard to come by, the Bullets’ initial rating is simply calculated by starting them with a rating of 1300 and then reverting them toward the mean of 1505 for each season they played in that league.
Nate Silver is the founder and editor in chief of FiveThirtyEight. @natesilver538
Reuben Fischer-Baum is a visual journalist for FiveThirtyEight. @reubenfb
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In wagering, the point spread is the amount of points that the inferior team is granted for the bet to be fair. The team that is giving the points is considered the favorite, while the team that is getting the points is considered the underdog. While there is no exact way to calculate the point spread between two teams, you can use many statistics and variables to determine the point spread for a specific game when making a friendly wager.
Calculate how many points, runs or goals a team typically scores. For instance, if the Dallas Cowboys have scored 350 points in 10 games, then the average is 35 points. If their rival that week has scored 300 points over that same span, the average amount is 30.
Identify who the home team is for the game. Many times a team plays better when it is at home than when it is on the road. The factors such as fan noise and knowing the field or playing surface give an advantage to the home team. If a team generally performs well at home, meaning it has a good home record, then extra points, runs or goals should be counted in its favor.
Look at the record of the two teams playing the game. The record is one of the biggest indicators in determining the point spread. A team with a good record will generally be favored over a team with a bad record, and therefore the point spread will be larger. If the teams have similar records, then the point spread will be closer since they are in theory equally matched.
Look for extraneous factors for the teams playing. For instance, if the star athlete of one team is out, then it might stand to reason that the team will score fewer runs, points or goals. This should be factored in when calculating the point spread. For instance, if the star player averages 35 points per basketball game, and his replacement averages 20 when playing a full game, the team might score fewer points. Scoring fewer points would in theory cause the point spread to be tighter if the team is favored or larger if it is the underdog.
Calculate an average margin of victory or loss. For instance, if a team has won 10 games by a combined total of 30 runs in baseball, then it wins by an average of three runs per game. If that same team lost 10 games by 12 runs, then its average margin of loss is 1.2 runs per game. So if the team is favored, it might "give" three points to the opponent and if it is the underdog it might "take" 1 run per game (because you can't take 1.2 runs.)
Combine all of your research to calculate the point spread. There is no exact science when determining this figure. However, use the research to get the figure. For instance, in basketball if the favorite averages 100 points, with a victory margin of five points, and is playing at home, then make it a five-point favorite. Conversely, if a team has an inferior record, is playing on the road, scores 95 points and loses by three points, make it a three-point underdog.
You can check your calculation with the professional sports books by searching for the line of the game in Las Vegas, where sports book betting is legal.
If a team has a plus sign in front of the point spread number, that means it is the underdog and getting that number of points. If the team has a minus sign in front of the number, that means it is the favorite and giving up those points.
You can check your calculation with the professional sports books by searching for the line of the game in Las Vegas, where sports book betting is legal.
If a team has a plus sign in front of the point spread number, that means it is the underdog and getting that number of points. If the team has a minus sign in front of the number, that means it is the favorite and giving up those points.
Scott Damon is a Web content specialist who has written for a multitude of websites dating back to 2007. Damon covers a variety of topics including personal finance, small business, sports, food and travel, among many others.
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