Cole Jaynes-Ostrom
Photo Courtesy of patriotswire.usatoday.com
Every die-hard football fan can relate to the feeling of their team losing and the announcer reading the depressingly low likelihood of a comeback on the broadcast. It feels even worse when their team had a massive lead that disappeared.
In this article, we’ll dive a little deeper into what exactly win probability is and how it is calculated. Win probability is a tool that measures the likelihood that any given team has of winning a game based on a multitude of factors - including the score, field position, and team record. Most major broadcasts have their own method of calculating win probability and display custom win probability graphics on the screen multiple times throughout the game. So how is win probability calculated?
As Wayne Winston, the founder of PFR explains,
“If we assume that the changes in margins during different parts of the game are independent and follow the same distribution [the technical term is identically distributed], then the standard deviation of the margin during n minutes of [a] game is: (game standard deviation of margin) / sqrt(fraction of game that n minutes is)”
In order to calculate win probability in games, the formula needs to account for the game time clock. To do so, it needs to account for the average margin of victory for an NFL game which is 13.45. From there, the formula is as follows for NFL games:
STDEV = (13.45 / SQRT((60 / minutes_remaining)))
So after 1 quarter, the expected standard deviation of the scoring margin drops from 13.45 to 11.65. Statisticians also have to update the Vegas line to account for the amount of time left over. That means correlating the line by the fraction of time left. For example, if the Vegas line is +3 and the game is 60 minutes long, then after one quarter (for the remaining 45 minutes) it would be 0.75 * 3 = +2.25.” From there, as games get later, the formula has to account for the likelihood of scoring on any given drive.
The equation also accounts for down and field position. In order to do so, PFR utilizes their expected points statistic, which measures the “estimated point value at the start of a given play, based on down, distance, and field position”. A given team's expected points value is then used to calculate how likely they are to score enough points to take a lead and win the game.
This equation is, for the most part, fairly standardized. ESPN, Fox Sports, and CBS all use different methods to calculate win probability and most don’t make their formulas publicly available. There is variation in the final win probability that each formula generates but all of the formulas tend to end up within 5% of each other. This means that even when the formulas disagree on the likelihood a team will win, there is still a general consensus on what to expect.
One of the most remarkable applications of the standardized formula is when it's used to analyze the Atlanta Falcons’ impressive streak of blown leads. Even casual football fans are aware of the relationship between the Atlanta Falcons and blown leads - most notably their infamous 28-3 blown lead in Super Bowl LI. Below is a line graph depicting the Falcons’ win probability throughout that game. A combination of bad defense, horrible coaching, and a history of late-game meltdowns have solidified the Falcons' reputation for being on the losing end of insane comebacks.
After the Falcons blew a 16 point lead with 6 minutes left in week 3 against the Saints, it was the first time in history a team had lost 2 games in a row with a win probability above 99%. In fact, the chance of a single team doing so in back-to-back weeks is just 1 in 990,000.
But those weren’t the only two times this past season that the Falcons lost games with a 95% chance of winning or higher. After the Falcons blew a 17-0 halftime lead during week 17, it made for the fourth time this past season that they lost a game in which they possessed a 95% win probability or higher.
This past season, the Falcons went into halftime with a lead 9 times but only won 4 of those 9 games. During the 2020 season alone, the Falcons have blown halftime leads of 14-10, 16-10, 17-10, 17-0, and 29-10. The probability of winning each of those games was greater than 60%.
In fact, over the last 20 seasons, no single team has blown multiple 15 point leads coming into the fourth quarter in a single season. In 2020 the Falcons did so in two straight weeks. Without win probability, we wouldn’t be able to appreciate just how incredibly unlikely those blown leads were.
Furthermore, win probability allows fans to appreciate the bizarre flukes that happen all the time in the NFL. Take the win probability graph above for example. New England had a 33-28 lead over the Dolphins with just sixteen seconds left. The Dolphins had the ball on their own 20-yard line and had no timeouts remaining. With time expiring, the Dolphins successfully executed a series of laterals allowing them to march down the field into the end zone. In doing so, they won a game in which they at one point had a 99.9% chance of losing.
Win probability allows football fans to appreciate the improbability of the Falcons' blown leads and to come to terms with the fact that their team isn’t coming back. The statistic provides valuable information for sports teams and announcers while also giving fans further insight into what’s going on in the game. As broadcasts continue to improve upon their formulas, fans should expect to see win probability graphics in every sport they watch.
Sources:
foxsports.com/stories/nfl/in-the-third-quarter-the-falcons-had-a-99-5-probability-to-win-the-super-bowl
https://statsbylopez.com/2017/03/08/all-win-probability-models-are-wrong-some-are-useful/
https://www.pro-football-reference.com/about/win_prob.htm
https://fivethirtyeight.com/features/are-bad-nfl-defenses-breaking-win-probability-models/
http://archive.advancedfootballanalytics.com/2009/11/two-minute-drill.html
https://www.pro-football reference.com/about/glossary.htm#:~:text=Expected%20Points%20%2D%20expected%20points%20represent,%2C%20distance%2C%20and%20field%20position.