Today’s post is a re-post from friend of the program Bryan Frye’s site, which is being republished with his permission and encouragement. As regular readers know, Bryan operates his own fantastic site, http://www.thegridfe.com. You can view all of Bryan’s guest posts here, and follow him on twitter @LaverneusDingle. What follows are Bryan’s words, with minor editing from Chase.

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Over the years, I’ve given much thought to the value (Championship Leverage) of postseason games relative to regular season games. Sabermetrics guru Tom Tango invented the Leverage Index in 2008 to apply a value to the gravity of a given base-out-inning situation in baseball. Later, Neil Paine used the concept for basketball and, subsequently, football. I found his application of the concept to NFL quarterbacks to be particularly interesting, and I decided to go into more detail on Neil’s methodology and expand the findings back to 1936 (the first NFL season with a standardized schedule).

Championship Leverage: In Theory

Championship Leverage is, in effect, an attempt to quantify the importance of a given game by determining the amount by which it changes a team’s odds of winning a title. If we are taking a talent-agnostic approach, each team has a 50% chance of victory in each game. That means the league’s championship game has (quite obviously) the highest leverage. The two parties involved see a 50% change in title odds at the end of the game; their odds either move up to 100% or down to 0%. It’s a pretty straightforward concept. ^[1]It is also a concept that could become significantly more complex if we were to apply real-time win probability calculations to every play of every game and look at them from the perspective of the … Continue reading

Championship Leverage: Methodology

Four years ago, Chase, with an assist from Neil, posted a terrific article entitled Super Bowl Leverage and the Best Postseason Passers since 1966. The purpose of the article is to look at quarterback passing value over average (measured by ANY/A) and apply increasing weights to each round of the playoffs. As Chase writes, in order to find the Championship Leverage of a given playoff game, we have to know the “Expected Delta” of each game. We just saw that the Super Bowl moves a team 50% of the way toward a title, in one direction or the other. Therefore, the Expected Delta of the Super Bowl is 50%. In the Conference Championship round, teams have a 25% chance at a title. That chance moves down to 0% or up to 50%, meaning the Expected Delta is 25%. That figure is 12.5% in the Divisional Round and 6.25% in the Wild Card round.

Neil then provided the following equation to determine the Super Bowl Leverage of each playoff game relative to other playoff games:

(4 *0.0625 + 4 *0.125 + 2 *0.25 + 1 *0.50)/11 = 0.1591. ^[2]That’s four games at the 6.25% level, four at the 12.5% level, two games at 25%, and one game at 50%.

Because the Super Bowl has an Expected Delta of 0.5000, it is worth 3.14 times as much as an average playoff game (that’s 0.5000/0.1591). On the other end of the spectrum, a Wild Card game is worth 0.39 times as much as an average postseason bout (0.625/0.1591). For all intents and purposes, this is just a more complicated way of saying that each round of the playoffs is worth twice as much as the previous round.

What about the value of a regular season game? Well, in 2015 Neil wrote an article about Tom Brady but really about Championship Leverage. In it, he provides the generic value of a regular season game, as well as a somewhat vague explanation of the math:

Here’s how the math works out: The average regular-season game moves a team’s chances of winning the Super Bowl by about 0.24 percentage points. That’s because every team starts out with a 1 in 32 chance of winning it all, which inevitably moves to either zero (for the 20 teams who miss the playoffs) or 1 in 12 ( for playoff teams) once all 16 games are played. Meanwhile, the Super Bowl swings each team’s chances by 50 percent — either up from 50-50 to 100 percent, or down to zero.

According to Neil, his calculations also mean that Wild Card games are worth roughly 26 times as much as regular season games. That makes Divisional Round games about 51 times as valuable, Conference Championship games 102 times as valuable, and Super Bowls 205 times as valuable.

Given that he was writing for a major publication with hard editorial guidelines, he had limited space to detail his process. As such, I found the explanations a bit confusing and asked him to go into detail on the methodology he used for the NFL. He explained to me what he did, and I’m going to use a very similar methodology today and explain it below.

My numbers differ slightly from his, as he originally based his findings off of twelve teams making the playoffs, whereas I based mine off of eight teams making the Wild Card round and four teams getting guaranteed byes. In other words, instead of every team starting the playoffs with a 8.33% chance of a title, eight teams get that opportunity, while four teams skip straight to having a 12.5% shot at a title.

My findings are also different because, while Paine used the modern league and playoff format (32 teams, 16 game seasons, 12 playoff spots, 11 playoff games) and applied the results retroactively, I used each league year’s unique situation. Thus, every season since 2002 has been the same, while 1999-2001 is slightly different due to having 31 teams in the league, and 1995-1998 is different still because there were just 30 teams. From 1976 until 1994, the NFL comprised 28 teams. However, teams played 14 regular seasons games in 1976-77, before moving to the current 16-game schedule, except when they played nine in 1982 and 15 in 1987.

I’ll explain why that matters. Currently, there are 32 teams in the league. That means each team begins the season with a 3.125% (1/32) chance of winning the championship. ^[3]This is talent agnostic. Obviously teams like the Patriots realistically have a higher chance of winning than do teams like the Bills. However, when speaking in the aggregate, the average team is … Continue reading By the end of the regular season, 20 teams miss the playoffs and have a zero percent chance of bringing home a title. Twelve teams make the playoffs, and eight of them have to play in the first round. Four of the teams get a free pass to the second round and never have a 1 in 12 (8.33%) chance at the title but, instead, begin the postseason with a 1 in 8 (12.50%) chance for a ring.

For the 20 teams that miss the playoffs, their championship odds move from 3.125% to 0.00% over the course of the season. That’s a -3.125% change in 16 games, or a -0.195% change per game.

For the eight Wild Card teams, their title odds move from 3.125% to 8.33% over the course for the season, which is a 5.208% change (0.326% per game).

For the four teams with byes, their odds of winning it all move from 3.125% to 12.50% over the course of the season. That’s a total change of 9.375%, or 0.590% change per game.

That means that, under the current league setup, we have:

• 20 teams with an absolute change of 0.195% per game
• 8 teams with an absolute change of 0.326% per game
• 4 teams with an absolute change of 0.586% per game

Here’s how we use that information to find how much an average regular season game changes a team’s odds of winning the Super Bowl. Multiply 20 teams by 0.195%, multiply 8 teams by 0.326%, and multiply 4 teams by 0.586%. Now add that together to arrive at 8.854%. Last, divide by 32 teams to land on 0.277%. ^[4]This isn’t too far from Paine’s 0.24% finding. That means the Super Bowl is about 181 times more valuable than an average regular season game in today’s league (0.50/0.00277).

How about in 1970? In the first year of the NFL-AFL merger, the league had 26 teams, a 14-game schedule, eight playoff spots, and seven playoff games. There were no byes, so every team began the postseason with a 12.5% chance of winning it all. They began the regular season with a 1 in 26 (3.85%) chance of earning a title.

Thus, the league had:

• 18 teams with an absolute change of 0.275% per game
• 8 teams with an absolute change of 0.618% per game

We multiply 18 by 0.275% and add that to 8 times 0.618%, then divide by 26 teams, and we get a Championship Leverage value of 0.380% for the average regular season game in 1970, and that Super Bowl V was about 132 times more valuable than the average regular season game in 1970 (0.50/0.00380).

The table below shows Championship Leverage values for the three major leagues since 1936. Read it thus: The 1946 AAFC had one postseason game. The league featured a 14-game schedule and contained 8 teams. An average regular season game was worth 1.339% as much as the league championship game. The first round of the playoffs was worth 37.33 times as much as a generic regular season game. There were no games, and thus no values, for Wild Card, Divisional, or Conference Championship rounds. The league title game was worth 37.33 times as much as the average regular season game. ^[5]Note: I still am not entirely convinced my approach is the right way to treat the pre-merger Super Bowl era (1966-69). We’re talking about two completely separate leagues who don’t have … Continue reading

As you can see from the table, and probably already gleaned by the explanation of the methodology, the more league teams, playoff teams, league games, and playoff rounds there are, the less important each individual regular season game becomes. In 1944-45, there were ten teams in the NFL, and they played just ten games apiece for the right to play in the championship game — the only postseason game. That meant regular season games had much higher stakes back then; in terms of Championship Leverage, a regular season game in 1944 was worth 5.78 times as much as a regular season game today.

If we want to flip the perspective, we can also say that a modern championship is far more valuable than those of decades past. Relative to a regular season game, the 1945 championship game was 31.25 times as important. Super Bowls since 2002 are 180.71 times as critical as the regular season counterparts.

Does this mean that we shouldn’t give full credit to teams and players for what they did in the playoffs prior to 2002, or that we should give less credit to modern players for what they do in the regular season? I don’t know. This is just math, and I’m not here to make philosophical arguments like that. ^[6]But if you’re asking, I lean toward soft yes to the first and hard no to the second. I will probably use this in the future as a resource when updating my QBGOAT series, and when looking at the statistical impact runners and receivers made. Just keep in mind that this is a measure of value and not necessarily of skill.