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ILLUMINATION

# Have the Super Bowls gotten closer? (And is Tom Brady the reason?)

If you follow the NFL, and if you’re familiar with its history, you may have noticed something strange about the Super Bowls: they seem to be so much closer than they used to be. In the 21st Century so far, most of the Super Bowl games have been back-and-forth thrillers which don’t get decided until the very end of the game. In stark contrast, in the 20th Century, most of the Super Bowl games were blowouts which were basically over after three quarters (some of them were over as soon as they started). It seems that we, in the 21st Century, have been spoiled, because we get to expect a thrilling Super Bowl every year, while our parents’ generation lacked this luxury.

But is this difference real? Is there statistical evidence to prove it? After all, statisticians love to remind us that our intuitions aren’t always right. Statisticians always tell us that we humans tend to observe patterns where they don’t exist and that we tend to jump to conclusions based on insufficient evidence.

I decided to work a little math problem to test whether or not it’s really true. It was a great chance for me to review the statistics I learned in college. I used the standard normal test statistic for comparing two population proportions. My goal is to prove that p2, the fraction of the “population” of 21st Century Super Bowls that were close, is greater than p1, the fraction of the “population” of 20th Century Super Bowls that were close. (The “populations” would contain an infinite number of possible Super Bowls, of which the real ones would be considered a small sample. But that’s not relevant to the calculation itself.) Statistically speaking, my goal is to find enough evidence to reject the null hypothesis, that p1 — p2 = 0, in favor of my alternative hypothesis that p1 — p2 < 0. As is standard practice, I used a level of significance of α = 0.05.

When testing a statistical hypothesis, one computes a “p-value”, which is calculated under the assumption that the null hypothesis is true. The p-value is the probability that the test statistic could land on [whatever it landed on], or even farther out, just by chance. The verdict of the test is found by comparing the p-value and the level of significance.

If the p-value is less than the level of significance (0.05), that means I win. That means I have enough evidence to reject the null hypothesis in favor of my alternative hypothesis. That means I have proven that the 21st Century Super Bowls have been substantially closer than the 20th Century Super Bowls, to the point that it can’t have been mere coincidence. And that means I can conclude that there must have been some inherent change in the Super Bowl games that made them become closer, sometime around the year 2000.

On the other hand, if the p-value is larger than the level of significance (0.05), that means I lose. That means I have failed to reject the null hypothesis. That means that there is not enough evidence to conclude that the 21st Century Super Bowls have been closer than the 20th Century Super Bowls, and that the perceived difference might just be a coincidence.

So let me gather the data and see what happens:

There were 34 Super Bowls that took place in the 20th Century, from Super Bowl I in January 1967 to Super Bowl XXXIV (34) in January 2000. Meanwhile, there have been 20 Super Bowls in the 21st Century so far, from Super Bowl XXXV (35) in January 2001 to Super Bowl LIV (54) in February 2020. In statistical terms, we would say that n1 = 34 and n2 = 20.

Now, before I continue, I have to add a disclaimer: the sample sizes are a little too small. My own statistics professor advised us that in order to be safe in using the standard normal test, both sample sizes should be at least 40. Meanwhile, I have n1 = 34 and n2 = 20. Well, this is the point in the argument in which I just wave my hands and pretend that I didn’t hear that. After all, no true mathematician has ever gotten through an argument without waving his hands at least once. Anyway, while n1 = 34 and n2 = 20 are a little too small, I think they are large enough that the standard normal test has at least degree of reliability. So let me continue.

In order to calculate the sample values of p1 and p2 (the proportions of the Super Bowls that were close games), I had to use a little bit of subjectivity. Unlike FiveThirtyEight, I don’t have any clearly-defined index to measure the closeness of a game. However, I do have some knowledge of all 54 Super Bowls, and because of this, I was able to categorize them into three levels: close, somewhat close, and blowout. Again, there’s a little subjectivity here, but it’s the best I could do.

I awarded one point for each close game, half a point for each somewhat-close game, and zero points for the blowouts.

For the 34 Super Bowls in the 20th Century, I got that twenty of them were blowouts, seven of them were somewhat close, and seven of them were very close. 7 + 7*0.5 = 10.5. 10.5/34 = 0.309. Thus, p1 = 0.309.

For the 20 Super Bowls in the 21st Century (so far), I got that twelve of them were very close, five of them were somewhat close, and three of them were blowouts. 12 + 5*0.5 = 14.5. 14.5/20 = 0.725. Thus, p2 = 0.725.

Now, I have all the variables I need to compute the test statistic, Z, which is given by

We use the letter Z because we intend it to be the standard normal distribution, which is almost always denoted by the letter Z. I plugged in my values: p1 = 0.309, p2 = 0.725, n1 = 34, and n2 = 20. This yields Z = -3.26.

The next step in hypothesis testing is to calculate the probability that such a number (-3.26, in this case), or a number even farther out, could arise by chance, under the assumption that the null hypothesis is true. For a standard normal variable Z, what’s the probability that Z < -3.26? Using an online calculator for the standard normal distribution, I found that the probability is 0.000557 — not even one tenth of one percent.

And that’s the p-value. I got a p-value of 0.000557. Meanwhile, the level of significance was α = 0.05. That’s more than 80 times larger than the p-value ………… and that means I win!

My calculated p-value is much smaller than the level of significance, which means I have found sufficient evidence to reject the null hypothesis, in favor of my alternative hypothesis. Therefore, I have proven that the 21st Century Super Bowls have indeed been closer than the 20th Century Super Bowls and that it was not mere coincidence.

Furthermore, because the p-value turned out to be so tiny, I think I can also conclude that it doesn’t matter that the sample sizes were a little too small. I think I have enough evidence as it is.

Anyway, since I have proven that the 21st Century Super Bowls were significantly closer than those of the 20th Century, that means something must have changed in the nature of the Super Bowl itself sometime around 2000. Hmmmmm …………… what might that have been?

Different commentators have put forth different ideas, including more offensive dominance over defense and the development of free agency. However, I am convinced that the primary cause of the increased closeness of the Super Bowls has been one single person: Tom Brady.

Yeah, that guy. The man who thinks he’s the embodiment of the American Dream. But while I dislike Brady as a person, I have no choice but to respect his success as an athlete. Over the course of his 20 seasons with the New England Patriots, he turned the franchise into a relentless winning machine and made them a regular fixture in the postseason, and often in the Super Bowl.

The Patriots’ dominance over the NFL during the Brady-Belichick era has been historic. Between 2001 and 2019 (a span of 19 years), the Patriots won their division 17 of 19 years, compiled an overall winning percentage of 0.727, appeared in 41 playoff games, and won six Super Bowls. All of these are NFL records. In particular, Brady’s record of 41 playoff appearances is off the charts. In second place is Joe Montana, who had only 23. It’s not even close.

But all these records, by themselves, do not answer my original question. We have no doubt that Tom Brady is great, but I have not yet explained how this is relevant to the increased closeness of the Super Bowls. I would need to somehow illustrate that Tom Brady, who is only one person, is the primary reason why the Super Bowls started to become closer right around 2000. That seems like a tough challenge, but as I will explain, I have four reasons for holding this belief. They are: 1. You can’t discuss the 21st Century Super Bowls without mentioning Brady, 2. He was drafted in the year 2000, 3. There is something in his DNA that results in the Super Bowl being a close game every time he plays in it, and 4. He may have raised the standard for others to follow. Let me elaborate on each of these in turn.

1. You can’t discuss the 21st Century Super Bowls without mentioning Tom Brady

There have been twenty Super Bowls in the 21st Century so far. The New England Patriots, led by quarterback Tom Brady, have appeared in nine of them, of which they won six and lost three. Nine out of twenty is 45%. That means a single quarterback appeared in 45% of all the Super Bowl games over the span of the last two decades. As such, you could hardly mention the Super Bowl games of the 21st Century so far without immediately mentioning Brady. If we aim to compare the Super Bowls of the 20th and 21st Centuries, our discussion would have to involve Mr. Brady in one way or another.

2. Brady was drafted in the year 2000.

Given that the Super Bowls of the last two decades have been noticeably closer than the ones in the preceding decades, it makes perfect sense to use the famous year of 2000 — the dawn of the new millennium — as the dividing line. And now I want to determine what might have changed in the NFL around 2000, and I have proposed Tom Brady as a possible answer. Well, let’s see then, when did Brady enter the NFL? Say, wasn’t it ……… in the year 2000?!! Indeed, Tom Brady was drafted into the NFL on April 16, 2000. That works out very nicely for my argument.

To be fair, Brady didn’t become the Patriots’ starting quarterback until 2001. But it’s okay, it didn’t have to be perfect.

3. There is something in Brady’s DNA that results in the Super Bowl being a close game every time he plays in it.

As stated above, Brady has played in nine Super Bowls. Eight of those nine games have been nail-biters. They didn’t get decided until the very end of the game. The sole exception was his most recent Super Bowl, Super Bowl LIII (53), and even that one was still somewhat close. (The game was tied going into the fourth quarter and was still competitive in the waning minutes.)

That is a remarkable consistency on Brady’s part: every time he plays in a Super Bowl, it ends up being a very close game. In fact, all of the Brady Super Bowls except the last one have been among the greatest sports games I have ever watched. If you want to watch a thrilling sports game, watch an old Super Bowl game involving Tom Brady and the Patriots. Whether they won or lost, they never failed to provide us with an exciting game.

We are immediately led to wonder why this might be. Some might call it coincidence, but I find that hard to believe. I think the root cause is in Brady’s DNA. I think that because he is who he is, it is very likely that whenever he’s playing in a Super Bowl, the game will end up being very close. I suspect that Brady is just the sort of athlete who would play slowly, carefully, and methodically, especially during a championship game, and who would reserve his best heroics for the game’s final minutes. And that would result in a close game almost every time.

Brady’s critics often charge that he is overrated because his numbers are not the highest. They have a point: if you look at the normalized* NFL quarterback records, you will find that Brady is usually not #1. For example, in career passer rating, Brady only comes in 7th place, while in career passing yards per game, he is only in 9th place. However, when combined with his record-setting successes, this criticism of Brady could be flipped on its head and turned into a compliment: it probably means that Brady tends to play best when it matters most. In other words, he’s clutch. Brady is not the strongest or most athletic passer, but he managed to win six Super Bowls anyway, because he always plays best when it matters most, while other quarterbacks don’t.

*(“normalized”, meaning they take the average of something over a player’s career; as a result, these statistics are not directly affected by the longevity of any player’s career)

Brady’s “clutch” performances can be observed both within an individual game and over the course of a season. Within a single game, he often plays his best in the fourth quarter. And throughout his tenure with the Patriots, the team usually had a higher winning percentage in the second half of the season than in the first. Most importantly, Brady has almost always performed well in the playoffs. This is how he’s managed to appear in 41 playoff games and win 30 of them, which is far more than any other quarterback in history. Brady became the winningest quarterback of all time because he tends to play best when it matters most, even though he is neither the strongest nor the most accurate passer.

Having followed Brady’s career over the last two decades, I get the sense that he is a quarterback who plays the game of football very slowly and methodically. He plays cautiously at first, but over time, he masters his strategy and technique, while he figures out how to exploit the weaknesses of his opposition. As a result, he plays best near the end of a game and near the end of a season — especially in the playoffs.

Given that this is how Brady plays the game of football, his effect on the Super Bowls makes perfect sense: it makes sense that he would appear in nine different Super Bowls (he always plays his best in the playoffs), and it makes sense that eight out of the nine would be thrilling nail-biters (he plays slowly and carefully and saves his best performances for last, resulting in a lot of close games).

And given that a whopping 45% of the Super Bowls of the 21st Century so far have involved Brady, I hypothesize that this is the primary reason why the 21st Century Super Bowls have been closer than those of the 20th Century. Specifically, my hypothesis is:

I do not claim to be certain of this hypothesis. It’s only a guess. After all, nine games is still a pretty small sample size. But as you can see, I had good reasons for reaching my conclusion.

There is one further aspect of Brady’s gameplay that ought to be mentioned here, and that is that he is absolutely obsessed with winning. As stated above, I dislike Tom Brady as a person, regardless of how much or how little success he might be having on the field. One thing that I really dislike about him is his obsession with winning. Obviously, every professional athlete wants to win, but Tom Brady is above and beyond the rest. Those who knew Brady in his youth testify that he was fiercely competitive and was visibly upset whenever he lost. This has not changed: he has lost his temper on the field several times. I get the sense that Brady’s self-esteem is almost completely dependent on the outcomes of his games. He seems to be exuberant after every win and heartbroken after every loss, more so than most athletes are. I think he is with winning. I think he covets winning, in the same way that Ebenezer Scrooge covets money.

In fact, I think that Brady’s obsession with winning is probably the reason why he is still playing football at the age of 43, well above the age when most quarterbacks retire. But Brady is actually a rather immature person: even at the age of 43, it seems to have never dawned on him that there is more to life than winning.

But anyway, Brady’s obsession with winning helps to explain his effect on the Super Bowls. When a quarterback is so committed to winning as much as possible, it makes sense that he would succeed in the playoffs and would reach nine different Super Bowls. And when a quarterback is so deeply invested in winning the game, especially when it’s a championship game, it makes sense that he would play the game slowly and carefully, saving his best performances for the end of the game, and resulting in a close game almost every time.

And over the course of the last two decades, I think is the primary reason why the Super Bowl games have become closer.

4. Brady may have raised the standard for others to follow.

Again, Brady and his Patriots played in nine out of the twenty Super Bowls that have taken place in the 21st Century so far. Out of those nine, they won six and lost three. Eight out of the nine were close, thrilling games (and the ninth one wasn’t bad, either).

However, when you subtract those nine games, that still leaves the other eleven Super Bowls of the 21st Century so far. What do we see in those games?

Well, we see some games that were less close, including some blowouts. Specifically, Super Bowls XXV (35), XXVII (37), and XLVIII (48) were complete blowouts. At first glance, that might seem like more evidence for my hypothesis.

However, out of the eleven remaining games, we still observe a relatively high concentration of close games. I can think of three 21st Century Super Bowls that did not involve Brady that ended up being very close and exciting games: Super Bowls XLIII (43), XLVII (47), and LIV (54 — the most recent one).

But perhaps this only means that Brady’s influence on the Super Bowl has extended beyond the Super Bowl games in which he himself was playing. After all, everyone knows that there is a psychological aspect of sports. For example, athletes are more likely to succeed when they are confident, when they believe in themselves, and when they know how to keep a calm and focused temperament throughout the game.

As such, it’s quite possible that the closeness of the Brady Super Bowls has carried over to the other Super Bowls of this century. It’s quite possible that over the course of the last two decades, all the teams that have played in the Super Bowl have felt more motivated to persevere through the whole game and not to lose hope when they start to fall behind. This would result in closer Super Bowls throughout this century so far, and not just when the Patriots are playing.

Given that Brady and his Patriots had set the standard of the close, thrilling Super Bowl, I think it’s quite possible that most of the other teams that have played in the Super Bowl in this century have come to expect that same sort of result every time. This would motivate the losing team to be more resilient and to fight back with determination whenever they start to fall behind. This would result in closer games, on average. The players’ expectations may have created a reality.

At this point, I should admit that I am only guessing. But I do think it’s possible. I think that Brady may have permanently changed the Super Bowl, because he set the standard of the close Super Bowl game that doesn’t get decided until the very end. And all the other Super Bowl teams in this century may have been attempting to follow his lead.

Afterword

On March 17, 2020, Tom Brady announced that he was leaving the New England Patriots. The next day, he signed with the Tampa Bay Buccaneers. I was saddened by that news, and not because I particularly care about the Patriots or the Buccaneers. I’m not a fan of either of those teams. But I was saddened by the news because I thought it was morally wrong.

I think that Tom Brady his fans in New England. After all, most people in New England have adored Tom Brady for the last two decades. By leaving the team, I think he abandoned his many loyal fans in New England. And I think that’s wrong.

But I am not surprised, either, since I have the impression that Brady’s only goal in life is to win as much as possible. I don’t think he cares if he’s betraying people; he just wants more wins.

Brady and his Buccaneers went 11–5 this season. Given that Brady is 43 years old, that is quite an accomplishment. The Buccaneers will play their first playoff game tomorrow (January 9, 2021) against the mediocre Washington Football Team (yes, that is their actual name). It will be Brady’s 42nd playoff appearance, but it will be his first playing for any team other than the Patriots.

Given that Brady’s Buccaneers went 11–5 this season, and given that Brady has such a reputation for success in the postseason, it is possible that he might reach another Super Bowl. I think it is somewhat unlikely, and I that it doesn’t happen, because I wish he would just retire, already. But it’s not out of the question, either. It is possible that we might see Tom Brady playing in yet another Super Bowl within the next two or three years. Considering everything I’ve written in this article, I would expect it to be another thriller of a game that doesn’t get decided until the very end. And knowing Brady, he would probably pull through in the clutch and win the game, which would be his seventh Super Bowl championship (ugh!).

After all, no matter how much he might irritate me, it seems like the man just never stops winning.

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