Tom Brady and the Orthogonal Pivot

The title of this post was inspired by the original series of Tom Swift novels, such as the prescient Tom Swift and His Video Telephone (1914). If that eponymous Tom was around today, we might see him as a blend of MacGyver, Indiana Jones, and Harry Potter. Half spontaneous inventor, half madcap adventurer, and half boy magician — more halves than that Tom could have stuffed into His Aerial Warship.

Now, a few weeks after Super Bowl LI, our Tom, quarterback of the New England Patriots, could easily appear to Matt Ryan and the Atlanta Falcons as precisely such a mix — half inventor, half adventurer, and half (Golden) boy magician. (And for any readers who are Patriots haters, yes, three halves is one more than allowed by the NFL bylaws, the Collective Bargaining Agreement, the Ideal Gas Law, and basic arithmetic. It’s just a metaphor, people. Besides, this post is neither paean nor attack.  I’m a Dallas fan… eagerly awaiting next year.)

The Patriots’ dramatic, unprecedented, overtime defeat of the Falcons indeed had a touch of magic about it. In fact, it was so magical that the next day Tony Kornheiser sheepishly admitted on-air to Mike Wilbon, his partner on ESPN’s Pardon the Interruption, that he had gone to bed early, thinking that Atlanta had settled the matter.

Looking at the box score for the game, a casual fan could have been forgiven at the midpoint of the third quarter for switching over to the History Channel, even a re-run of The Curse of Oak Island. Atlanta had just gotten a touchdown and extra point to make the score 28-3. Then the magic happened — the first game ended, and the second one began.

You can see this abrupt change — my titular “Orthogonal Pivot” — in the stairsteps of a simple scoring graph, terminating at the location of the final score of the game:

The blue dots show successive game scores — 7-0, 14-0, 21-0 — moving up the vertical axis as Atlanta scored touchdowns; then a minor zag to the right from New England’s field goal just before halftime; then Atlanta resumed the upward path with its mid-third quarter touchdown to 28-3. Ho hum, and Kornheiser goes to bed.

Abruptly, the red arrow turns 90° (orthogonally) to the right as New England scored the first of its three touchdowns, plus a field goal, in the final 17 minutes of regulation to tie the game 28-28. The sudden-death touchdown for the 34-28 win seemed almost inevitable after New England won the coin toss to start overtime.

My interest in using this graph went beyond simply portraying the path of the game. What could it show about comparison of this Super Bowl to earlier ones? Could it yield any insight beyond the laudatory comments by post-game analysts and other commentators in the next few days?

My first step was a compilation on the same grid of the ten most recent Super Bowls, XLII-LI. In addition to the dashed black line indicating the locus of tie scores, I have also added two dashed red lines that demarcate a plus-or-minus 10-point band (in the directions that the game score can be moved by the teams). Roughly speaking, game scores within this band are “close,” which one might expect a priori for well-matched teams. (Pop quiz: Just to be sure you understand how this graph is constructed, can you locate the infamous “Bevell Gap”? Hint: Follow the gray line to its terminus….)

Indeed, eight of the ten games are roughly within the red band (but see below). The exceptions are the 43-8 rout (yellow) of Denver by Seattle in Super Bowl XLVIII and the New England win over Atlanta (light blue). As the scoring path shows, this year’s game was unprecedented, at least in the last decade, not only because of the overtime win, but also because of the amount by which the path exceeded the upper red line before the seeming loser actually became the winner.

Someone more interested than I in the long-term history of the NFL and the Super Bowls (or with access to results in a database rather than Wikipedia) may want to check out the first forty-one contests to see if this distinction holds up. I decided to look instead at how this game compared to the others played by the “Big Four” — Pittsburgh (PIT), 6 wins; and Dallas (DAL), New England (NE), and San Francisco (SF), 5 each. After all, these 21 games span 45 years of that history and represent some of the most stable combinations of owners, styles of play, and coach-quarterback duos. Asked differently and colloquially, what might this graph show about the collective or cumulative Super Bowl play of the four top-winning dynasties (with all due respect to the Green Bay Packers and New York Giants with 4 wins each)?

In chronological order (by when each franchise won its first Super Bowl), here they are:

Note: Final score of DAL-BUF in Super Bowl XXVII is off-scale at 52-17

Note: Final score of SF-DEN in Super Bowl XXIV is off-scale at 55-10

Let’s dispense immediately with the reason we all have gathered around this page — Tom Brady and the Orthogonal Pivot remain unique through the 18 additional games in these four diagrams; together with the ten in the first decade that covers more than half of the 51 Super Bowls.

With respect to the collective play of each franchise, this plot highlights at least two things. Firstly, the patterns for DAL and SF are “flattened” out to the right. Like the rout of SEA over DEN in Super Bowl XLVIII (above), this indicates a much stronger scoring performance by DAL and SF than their respective opponents. In contrast, the patterns for PIT and NE fall much more nearly within the red band, indicating much closer contests; the Orthogonal Pivot is actually the exception that proves this rule, since games don’t get any closer than a tie at the end of regulation!

Secondly, the location of the point for the final score of each game also gives a succinct view about defensive play for each of the four teams. From the top down, DAL allowed no opponent above the 20-point line; PIT allowed one above 20 and one above 30 points; SF allowed two opponents above 20 points; and NE allowed four above the 20-point line.

Here is a composite of all four diagrams, arranged L-to-R in order of increased flattening of the overall pattern, that is, from closest to most one-sided scoring:

Click for a large version

It’s a qualitative judgment, of course, but the gradation seems (to my eye) to be clear. Whether it means anything substantive from a dynastic perspective depends on many things, first and foremost whether or not the idea of long-lived dynasties is meaningful. Of course, there is also the correlation-causation question of whether a graph like this, instead, provides evidence that should be used to define and categorize dynasties. I have no answer to that conundrum.

The diagram has the virtue that every visualization strives for, compressing a lot of information into a simple, readable form. Notice, however, that the information itself already exists in some other format, which makes any new portrayal subject to the I-already-knew-that objection, no matter how helpful or lucid it might be visually. Case in point: If the L-to-R flattening of the scoring patterns for each of the four teams is reflective of their overall scoring prowess, then you would expect that a common measure such as total point differential against their respective opponents would change similarly. In fact, it works moderately well: NE won their five Super Bowls by a total of 19 points; PIT by 45; DAL by 100; and SF by 99. Not bad for comparing a qualitative visual judgment to a single numerical metric, especially when aggregated across a span between 13 years (SF) and 34 years (PIT).

The major unanswered question that I’m left with is this: Are there measures of team performance that are worth examining and comparing for the life of a franchise? I mean in-game metrics, not simply wins and losses or number of post-season appearances, which are the kinds of things I’m used to seeing. It’s one thing to try it, and see that it apparently works, for championship-caliber teams, where dynastic momentum could be a real thing. But for middling teams, or worse yet say the Cleveland Browns of the last decade, does it make any sense to construct lifetime metrics? On the face of it, it seems like a waste of time. But then, so do many games until they’re actually played.

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