The Divisional Round was one of the most exciting weekends in NFL history
By: Stephan Teodosescu
After a Super Wild Card weekend that was anything but super, NFL fans were rewarded with four absolute thrillers in the divisional round this past weekend.
The games were decided by a combined total of 15 points -- an average margin of victory of 3.8 points per game -- which is the smallest in NFL playoff history in a round with at least four games, according to NFL.com. Each game ended in walk off fashion, and seemingly got better as the weekend wore on.
The first three games -- the Cincinnati Bengals vs Tennessee Titans, San Francisco 49ers vs Green Bay Packers and Los Angeles Rams vs Tampa Bay Buccaneers -- all ended with the road team prevailing on a game-winning field goal.
But they would be outdone by an instant classic in Kansas City for the Sunday nightcap. The Bills and Chiefs played a back-and-forth affair that saw 25 points scored after the two-minute warning, included two of the best quarterback performances in playoff history, and featured win probability swings resembling a heart attack EKG (more on that later).
But we don't have to rely on superlatives, discourse of whether Kansas City-Buffalo was the greatest game ever, or Twitter memes to tell us how good these games were because we have math. And data! Inspired by Gambletron2000, and work previously done by Luke Benz, Brian Burke (ESPN), as well as FiveThirtyEight, Mike Bouy (Inpredictable.com) and others, I set out to quantify how exciting this past weekend's games were.
First, a primer on win probability, which is the basis for how I measured "excitement." Win Probability (WP) is an estimate of a team's likelihood of winning the game at a point in time given the current situation at the start of that play. Win Probability Added (WPA) is the change in WP from one play to the next. If you graph these WP changes throughout the course of the game you will get a visual representation of how that game played out.
We used the nflfastR1 Win Probability model to build the charts below2. Look at those swings at the end of these games, especially Bills-Chiefs.
Knowing the change in play-by-play win probabilities gives us an opportunity to identify how exciting a given game was. Leveraging work that Benz has done for college basketball, I computed a Game Excitement Index (GEI) for every NFL regular season and postseason game so far this year.
We do that by summing the absolute value of the win probability change from each play and multiplying by a normalized time parameter3. This gives us an index by which we can rank each game's excitement factor. The way to interpret, for example, a Game Excitement Index of 4.0 is that the win probability changed by a total of 400% over the course of that game. The higher the number, the more exciting the game.
So let's look at last weekend's Divisional Round games ranked by GEI:
Bills-Chiefs: 6.93
Bengals-Titans: 5.68
49ers-Packers: 4.08
Rams-Bucs: 3.56
The Bills and Chiefs unsurprisingly ranked as the most exciting game of the postseason with a GEI of 6.93. A record three go-ahead touchdowns scored in the final two minutes of regulation will do that, hence the heart attack EKG. The others were up there in excitement as well as the top three most exciting playoff games so far this postseason were played last weekend.
To put these excitement numbers into perspective, the average NFL game this season carried a median GEI of 3.52. The Vikings played the most exciting games in the regular season averaging a GEI score of 4.92. They were followed by the Ravens (4.80), Chargers (4.38), Seahawks (4.14) and Raiders (4.06). The least exciting teams were the Patriots, Jaguars and Broncos, who all had GEIs of under 3.0.
All but two of the wild card games failed to meet the season average for excitement while all the divisional round games were more exciting than the average 2021 regular season game.
The Bills and Chiefs didn't play the most exciting game of the year when including the regular season, according to GEI. That honor belongs to a Week 10 Lions-Steelers tie (8.76). This is more a statement on the flaws of using this relatively simple metric to quantify something so subjective as excitement and cautions you to take conclusions of a one-size-fits-all number like this with a grain of salt. Even though we take steps to normalize for the length of overtime games many of the most exciting games of the year according to GEI were overtime contests; the longer the game the more win probability swings occur, especially if it's close.
GEI is not a perfect metric, and it might fail to capture important aspects of the game that fans might find exciting, but it does give us a sense of the flow of games and a way to quantify the excitement of playoff football.
Let's hope the conference championships can deliver another blockbuster weekend that will have fans calculating their own GEI.
For more NFL advanced stats content check out my NFL Analytics website.
____________________________
nflfastR is a public repository of NFL play-by-play data and set of functions to efficiently scrape that data. It expands upon the features of nflscrapR and was created by Sebastian Carl and Ben Baldwin.
Code for the above plots can be found on my GitHub page.
The formula is GEI=3600/t∑i=|pi−pi−1| where t is the length of the game (in seconds) and pi is the home team’s win probability on play i of the game. According to Benz, "One can think of GEI as a measure of the length of the win probability curve if it were to be unwound, normalized to the length of a standard regulation game." The reason he chooses to normalize the length of games is to remove the effect of overtime games that are otherwise sloppy being considered as more exciting than others simply because they lasted longer (thus had more win probability swings).