Ted from Amherst, NY
Although I greatly enjoy your writing, I do take exception to basic facts being dismissed as "ignorance" by another reader. In your response to my previous comment, you acknowledged that having more teams to compete with made it harder to repeat, but asked if the Chiefs really had to outdo 31 other teams given the structure of the playoffs? And you ended with, "Mathematicians out there: Is it possible to come up with an algorithm to determine which scenario would be more difficult?" I took that as a rhetorical question, but having been called ignorant for understanding the math homework my 14-year-old brought home from ninth grade, I will entertain those as serious questions. Did the Chiefs have to beat 31 other teams to become champions? No. Lombardi's teams didn't have to play the whole league either. I leave it to you as our historian to check to see if Curly Lambeau's teams played every other team in each of those three years. But the odds of winning a championship are always one in however many teams are in the league. If you want the algorithm to calculate that based on the current playoff format, here it is.
The NFL has two conferences of 16 teams. In each conference, six of 16 teams play on wild-card weekend. Half of them win, half lose so the odds of one of those six making the divisional round are three out of 16. But, one in 16 teams gets a bye, so the total odds of getting to the divisional round is (1/16+3/16=4/16). Half of them win, half of them lose, so the odds of making the conference championship is two out of 16. Only one team wins the conference championship, so the odds of going to the Super Bowl are one in 16. And as we all know, only one of the two conference champions actually wins the Super Bowl. That gets us back to one in 32 teams wins the NFL championship.
Ted, thanks for the follow-up email. Nothing figures to be more topical as this NFL season unfolds than whether Kansas City can make history by becoming the first team to win three straight Super Bowls. Therefore, I'm going to devote this entire Q&A plus another one tomorrow to your one question.
Lest no one forget, I'll start by underscoring this indisputable fact and point of great pride for the Packers: If Kansas City wins it all this season, it will only share the record for consecutive NFL titles, matching the 1929-31 and 1965-67 Packers.
Now, let's review how we've gotten to this point here.
More than five months ago, I posted a question from Bruce of Saint Louis, where he asked why the Packers' record threepeats as NFL champions weren't getting any buzz with the Chiefs positioned this season to match that achievement. In my answer, I noted that a then recent Yahoo Sports AM post incorrectly stated the Chiefs would try "to become the NFL's first threepeat champs."
Not true, as I've already pointed out. All the writer would have had to do for the sake of accuracy is turn to the "Team Records" section of the 2024 edition of the NFL Record & Fact Book. On page 580, it lists Green Bay's two threepeats as the record for "Most Consecutive Seasons League Champion," no matter that four of those six titles were won in the pre-Super Bowl era.
The conclusion I eventually drew in that post was: "My point would be that debating over the era where teams had the toughest route to winning a championship is all relative."
On April 4, I posted your response: That if the Chiefs win a third straight, they'll be "the best of 32 teams," whereas Lambeau's Packers won their championships when the total number of teams ranged from 10 to 12, and Vince Lombardi's teams did it when the NFL consisted of 14 to 16 teams but with another nine AFL teams competing to reach the Super Bowl in 1966 and '67.
I, in turn, asked – not rhetorically as you assumed but to be enlightened – if there might be an algorithm to determine the degree of difficulty of winning three straight titles now as compared to the 1960s and early 1930s.
I freely admit I'm not a mathematician. I could add 2+2 in my school days but once I got to Algebra II and Geometry, I was a candidate for the dunce cap. Nevertheless, something told me that there had to be more involved here than simply the number of teams in the league.
I, too, believe it would be tougher today than in 1929-31 to threepeat because there was no postseason back then; and it might also be true most of the time today compared to 1965-67. But I'm not convinced that it would be the case every season.
That said, I can't quantify that, only play devil's advocate based on what I know about NFL history.
When the Packers won their three straight from 1929-31, the championship was determined by the final standings. But consider this. Had the Packers lost just one more game in any of those three seasons, they wouldn't have won a single outright title, only a possible shared title with Portsmouth in 1931. In other words, the Packers played a total of 41 games over the course of those three seasons and if they had lost just one more of those, they would not be recognized today for winning three straight championships or at least outright titles.
Plus, I'd point out that the 1929 Packers played their final nine games on the road; the '30 Packers, their last seven; and the '31 Packers, six of their final seven. How many recent champions could have won that many consecutive games away from home and still prevailed?
Homefield advantage – isn't that the rallying cry of every playoff contender these days?
Let's not forget, either, that while the 1929-31 Packers played 100 percent of their games in the regular season; the regular season still accounts today for 81 percent of a Super Bowl finalist's games if it doesn't draw a bye in the playoffs.
Bottom line: Winning three straight back then was no breeze. And at least some of the challenges faced by the '29-31 Packers were tougher than today.
Moving on to Lombardi's 1965-67 champs.
The '65 Packers could not have lost any of their last three games prior to the NFL Championship Game without being eliminated beforehand. In '66, they couldn't have suffered more than two additional regular-season losses without having to play an additional playoff game. And in '67, the Packers couldn't have lost more than one or two more regular-season games, depending on whether one would have been to the Chicago Bears when point differential would have broken the tie and determined the Packers' postseason fate.
Furthermore, the '67 Packers had to beat the 11-1-2 Los Angeles Rams, 9-5 Dallas Cowboys in the Ice Bowl and 13-1 Oakland Raiders to capture their third straight title. Largely due to the fact that only 24 percent of the NFL and AFL teams made the playoffs in '67 compared to 44 percent today, the Packers three postseason opponents when they won Super Bowl II had a combined .810 winning percentage based on today's formula. When the Chiefs won the same number of playoff games in 2022, their foes had a .740 winning percentage.
Next, let's compare the regular-season challenges faced by the Super Bowl champions since 2002, the first year of the NFL's eight four-team divisions with 32 teams in all, with those of yesteryear.
Without ascertaining every possible tiebreaker and the effect kickoff times on the final weekend might have had on them, only one of the last 22 Super Bowl champions couldn't have lost another regular-season game and still qualified for the postseason. That was the 2010 Packers.
Both the 2019 and 2023 Super Bowl champion Chiefs, for example, could have lost four more games – maybe five – and still made the playoffs because no other team in their division had a winning record.
The 2004 and 2016 New England Patriots could have lost four more games and still made the playoffs. Five other Super Bowl winners since 2002 could have lost three, maybe four more games; and four others could have lost two more, maybe three.
Five of the past 18 Super Bowl champs who won their divisions were the only team in their division with a winning record. In the past 22 seasons, four teams have made the playoffs with a losing record, four others with a .500 record and 11 who finished no better than 9-7.
Clearly, and especially since 2020 with the addition of a third wild-card entrant, there are teams that make the playoffs that are relatively easy prey for the top qualifiers, the 2023 Packers being a prominent exception after winning six of their last eight regular-season games and becoming one of the hottest teams in the league.
But they earned their playoff spot as did five other wild-card teams because there are second chances today. There were none when Lambeau and Lombardi led their teams to three straight titles.
When the 1929 Packers won the championship with a 12-0-1 record, the New York Giants lost to them during the regular season, finished 13-1-1 and didn't get another shot in a postseason rematch. When the 1967 Packers won the Super Bowl, their 11-1-2, Western Conference foe Baltimore Colts didn't even qualify for the postseason.
Lombardi's 1961, '62, '65 and '66 champions had to win a mostly talent-loaded seven-team conference just to qualify for the postseason. And when they finished 11-2-1 in 1963, a half-game behind the Bears, they were done. By comparison, the 9-7, 2011 Giants won a Super Bowl as have seven teams in all since 1970 without winning their division.
I'm not trying to minimize the difficulty of winning the Super Bowl today. I'm only pointing out that winning a league crown has never been easy in the NFL's first 104 seasons.
Last season, for example, the Chiefs had to beat Miami, Buffalo and Baltimore just to play for the Lombardi Trophy. That's a beast of a schedule. And for San Francisco to draw a bye enroute to the Super Bowl, they had to win a division that included the 10-7 Los Angeles Rams and 9-8 Seattle Seahawks, also a formidable task.
But how does one quantify any of this, along with any other pertinent data? The logical answer: Ask experts.
Ted, here was the response I received from someone who has worked in the field of NFL analytics when I forwarded him the text of your email.
"I generally agree with Ted's point that a threepeat is harder to accomplish today relative to the Lombardi era, but I disagree with the reasoning that led him to that conclusion. I believe that the calculation is a bit more involved.
"I think that Ted might be confusing (a) the fact that 1/32 teams will be the Super Bowl winner with (b) the chance of one given team being the Super Bowl winner. No one can reasonably dispute statement (a), but it incorrectly frames the problem as a single event (e.g., put stickers with the logos for all 32 NFL teams in a bag, pick one at random, and that team is the Super Bowl winner). Statement (b) is more difficult to quantify because multiple things with their own probabilities need to happen (make the playoffs, win all subsequent playoff matchups) and playoff structure (e.g., seeding) needs to be accounted for."
Ted, based on that feedback, can we agree that someone's ninth-grade math homework, as you painted it, doesn't provide the answer? If not, I shared your text in full with four other experts.
They included Matt Adamczyk, a Microsoft technologist at TitletownTech; Devin Bickner, associate professor of mathematics at the University of Wisconsin-Green Bay; Eric Goska, a math major at Northwestern University and arguably the leading authority on the Packers' statistical history; and Kevin Quinn, dean of the Donald J. Schneider School of Business & Economics at St. Norbert College.
First, all four agreed with the analytics expert that there's more involved here than merely the number of teams in the league.
"The reference to the 'odds of winning a championship are always one in however many teams are in the league' does seem to suggest that the reader is assuming that each year, each team has an equally likely chance of winning the championship," said Bickner. "That would be true in today's NFL schedule and playoff structure if we were to make the very big assumption that every matchup is basically a tossup.
"Of course, the bigger reason why the claim 'each team has an equally likely chance of winning the championship in a given year' is incorrect is not the math argument, it's the fact that there are clearly better teams in the league than others. I'd say that anybody with even a moderate knowledge of the sport knows that teams like the Chiefs have a much better chance of winning the Super Bowl this year than a team like the Panthers."
My next questions to Bickner were:
Would it then be nearly impossible to create an algorithm or carry out any other strictly quantitative study to determine the difficulty of winning three straight league championships today and comparing it with different periods of NFL history?
His answer: "No, it would not be impossible to create some kind of formula or model or simulation that would quantify the idea of easy or hard. Yes, it would be nearly impossible to create one that is universally accepted or where nobody would be able to find flaws in the formulation. Think of something like quarterback passer rating, QBR, and PFF player grades for measuring how well a quarterback played. If you want something that will convince everybody, then don't bother. If you just want an interesting number or scale or rating that you can use as part of an argument for why you think one feat was harder than the other, then I think you could certainly do that. And it would be up to you how involved you want to make it."
If the Chiefs repeat as champions this season would a postseason examination of whether their challenge was greater than the Packers' threepeats be more accurate than one created today?
Bickner's answer: "Yes, analyzing known data from the past is almost always easier than projected data, especially if one of the things that you're measuring for difficulty is unknown (like win percentage or something)."
While Quinn agreed with the analytics expert that there's more to consider than just the number of teams in the league, he offered his own formula in support of his belief that it would be tougher to win three straight titles today compared to yesteryear.
"Here's how I would make thinking about the relative difficulty of threepeats in different eras a bit more intuitive without losing content," he said as a preface to the following.
- Number of teams in the league
- Percentage of league making playoffs
- Overall distribution of competitive quality (i.e., talent)
- Year-to-year stickiness of win percentage (i.e., talent movement year to year)
The effects are as follows:
- More teams make it harder to threepeat
- Higher percentage of league making playoffs makes it harder to threepeat
- More competitive balance (parity) makes it harder to threepeat
- More talent movement means less win percentage stickiness from year to year (I think)
He continued: "I would rank them as follows (1 is easiest to threepeat, 3 is hardest)." His final tally was: 12 (accomplishing it today), 8 (1965-67) and 5 (1929-31). His conclusion: "I would rank the gross statistical difficulty of a threepeat as easiest in 1929-31 and hardest now."
Here was Goska's response to my inquiry:
*"I believe it is more difficult today as well. How much more, well, that I cannot quantify.*
"If it were 'easier' today, I would expect to see more examples of teams winning two or three in a row. I would expect to see more examples of teams getting to the Super Bowl two or three times in a row.
"But that is not the case. By dividing the last 91 years into three segments, I had hoped to provide evidence that in today's NFL it is not only more difficult to win the 'Ultimate Game' in consecutive years (NFL championship game from 1933-1965; Super Bowl in the years since), it is more difficult to even reach that game in back-to-back seasons."
Here was Goska's research:
1933-1965 (33 years): 17 instances of a team making it to two or more title games in a row.
1966-2001 (36 years): 14 instances of a team making it to two or more title games in a row.
2002-2023 (22 years): 5 instances of a team making it to two or more title games in a row.
"That, to me at least, is evidence that it is more difficult to repeat/threepeat today since teams are finding it more difficult to even reach the title game two or three years in a row," he concluded.
Ted, back to you. Based on the above feedback, I'm convinced that all of us who aren't math wizards, me certainly included, basically have no clue how to arrive at an answer for all of this.
Goska convinced me of that in his initial response to my inquiry.
"I majored in math at Northwestern," he wrote. "I barely passed the one probability and statistics class I took roughly 40 years ago. While I believe it is more difficult to win a championship now than years ago (more teams, more regular-season games, more playoff games, free agency) I am unable to argue that using a mathematical model. While I imagine some type of algorithm could be set up, I lack the expertise to do so."
Ted, can we agree, no way your typical blathering pundit or faceless blogger is going to know better?
That said, Adamczyk, our other expert, will weigh in tomorrow (Oct. 4) with as quantitative and thorough an answer as I was able to unearth.
