NFL 2007: Pats & Parity

The regular season of the National Football League is now over and, far and away, the biggest story of the year is the New England Patriots' perfect 16-0 record.

As nearly all football fans would know, the last perfect regular season was the 1972 Miami Dolphins' 14-0 campaign; the Dolphins also swept their three post-season games to finish at 17-0. Two Chicago Bear teams from much earlier in NFL history, 1934 and 1942, also won all their regular-season games, but neither squad won the league title.

Before trying to figure out, post hoc, what the probability was of New England completing a 16-0 regular season, however, a brief look at the overall structure of wins and losses in the NFL is in order. If we were simply to flip coins to determine each team's record (i.e., heads = a win; tails = a loss), an infinite number of simulated 16-toss "seasons" would yield the following distribution.


As seen in the next graph, there were a few really good teams (the Colts, Cowboys, and Packers, each at 13-3, were just a cut below the Patriots), one dreadful team (the 1-15 Dolphins), and a lot of mediocre teams clustered around a record of 8-8, during this past season (click here for the final standings).


The actual collection of NFL team records this past season was thus fairly close -- disturbingly close in many fans' minds -- to what would be expected from just flipping coins!

OK, so what was the probability of the Patriots' perfect 16-0 regular season?

Using an approach I developed for my 35th anniversary retrospective on the Los Angeles Lakers' 33-game basketball winning streak during the 1971-72 season, I first attempted to estimate the Pats' chance of winning each of their games this past season, individually, based on the difficulty of the opposition in a particular contest and whether the game was played at home or on the road.

After looking at the final win-loss records of New England's 13 unique opponents (the Pats played their three intra-divisional rivals twice), I grouped the opponents into five levels of difficulty (click here for New England's schedule):

A (hardest opponents) -- The Patriots faced the aforementioned Colts and Cowboys, each of whom won 13 games.

B -- Teams that won 10 or 11 games, comprising San Diego, Cleveland, Pittsburgh, and the New York Giants, formed the second-toughest tier of opponents.

C -- Teams that won from 7 to 9 games, comprising Buffalo, Cincinnati, Washington, and Philadelphia, were deemed to be "mediocre" opponents.

D -- Teams that won 4 or 5 games, specifically the New York Jets and Baltimore, were considered "weak" opponents. The Ravens actually gave the Patriots one of their biggest scares, but that's neither here nor there, given my system of basing opponents' strength on objective win-loss records.

E -- The aforementioned Dolphins were in a class by themselves, providing the Patriots with their easiest opposition.

For each combination of opponent strength and home/away status, I came up with the following (assumed) probabilities of the Patriots' winning any given game (the guidelines below are similar, but not identical, to those I developed for the 1971-72 Lakers). To avoid any confusion, "home" refers to a game at New England.

E opponent at home ---> .95
E opponent on the road ---> .90
D opponent at home ---> .85
D opponent on the road ---> .80
C opponent at home ---> .75
C on road or B at home ---> .70
B opponent on road ---> .65
A opponent at home ---> .60
A opponent on road ---> .55

The 16 individual game-specific Patriot-win probabilities were then multiplied together, according to what is known as the "multiplication rule." Multiplying these 16 probabilities together yielded .006; in other words, the chances of a perfect season like the Patriots' would be 6 out of 1,000 or roughly 1 in 167.

Again, this is just an estimate, based on some convenient assumptions, such as the outcomes of adjacent games being independent (i.e., winning one game does not affect the probability of winning the next game, beyond strength of opposition and game location). Were the distribution of win-loss records throughout the NFL in some future season to be substantially different from this year's (as graphed above), that would also affect the estimated probability, via the strength of opposition.

In any given season, just at a theoretical level, one or two teams (at most) might be expected to contend for 16-0. One must take into account the head-to-head aspect (especially within a conference); having teams play each other directly rules out the possibility of both going 16-0. To take the match-up in Super Bowl XIX (after the 1984 regular season) as an example, the NFC champion San Francisco 49ers had gone 15-1 in the regular season and the AFC champion Miami Dolphins had gone 14-2, so having a pair of teams threaten to go 16-0 in the same season is not totally farfetched.

Thus, if we held out the possibility of two teams per year possibly being able to go 16-0, then we would expect one team roughly every 85 years actually to do so (2 contenders per year X 85 years = 170, similar to the 1-in-167 figure I came up with, above). The 2007 NFL regular season was the 30th played under a 16-game format.

Next, we move on to see if New England can make it to -- and win -- the Super Bowl, and thus finish an unprecedented 19-0...

The L.A. Lakers reeled off a 16-0 run in the first quarter of their game Friday night against the visiting Utah Jazz and never looked back, winning 123-109 (play-by-play sheet). The spurt turned a 13-12 Laker deficit into a 28-13 lead.

Kobe Bryant hit a pair of three-pointers during the run and finished 6-of-9 from behind the arc, for the game as a whole (box score).

Whatever it is that makes some teams get off to fast starts and others, to slow starts, was on display Thursday night at the Staples Center in Los Angeles, as the Phoenix Suns blew out the Clippers.

The Suns dominated the opening minutes of both the first half -- in which they jumped out to leads of 8-0 and 13-2 -- and second half -- in which they outscored the Clippers 18-1. ESPN.com's play-by-play sheet is available here.

The NBA's Portland Trail Blazers, whose rebuilding project suffered a setback with star draft pick Greg Oden having to miss the season due to injury, are now playing at a level few would have expected. Friday night, Portland won its 10th game in a row, outlasting the Denver Nuggets, 99-96. After a 5-12 start, the Blazers are now 15-12.

In keeping the winning streak alive, Portland was aided by a hot stretch within the game. Trailing 76-69 after three quarters, the Blazers went on a 16-2 run to start the fourth (play-by-play sheet for the final period).

There were some substantial team runs in a couple of high-profile basketball games tonight.

In the match-up of NBA superstars Kobe Bryant and Lebron James, the Cleveland Cavaliers used a 16-0 run, spanning the third and fourth quarters, to turn around their game against the L.A. Lakers (play-by-play sheet). The Cavs turned a 78-67 deficit into an 83-78 lead and ultimately won the game, 94-90.

And, in a battle of two undefeated, top 10, men's college teams, Pittsburgh unleashed a 12-0 run to get back into its game against Duke (game article). The game ended up going into overtime, where the Panthers were victorious, 65-64.

The New York Knicks and Coach/President of Basketball Operations Isiah Thomas, who've had their difficulties on and off the court, added to their woes Monday night, in a 119-92 loss to the Indiana Pacers. En route to the loss, the Knicks missed 20 straight field goal attempts in the second quarter. As seen in this play-by-play sheet for the period, many of the misses were from short distance, including layups and tip-in attempts.

A couple of basketball items:

Friday night, with 3:29 left in the games, the visiting Los Angeles Lakers led the Golden State Warriors, 102-94. Golden State then outscored the Lakers 14-2 over roughly the next three minutes, culminating with Baron Davis's three-pointer on a hastily released shot with 0:16 remaining. That shot put the Warriors up 108-104, and they ultimately prevailed, 108-106 (fourth quarter play-by-play).

As discussed in recent postings, team scoring runs such as that pulled off by Golden State do occur fairly frequently. However, I don't recall seeing many that turned a game upside down in the last few minutes, like the one Friday. The win also ended a Warriors' nine-game losing streak to the Lakers.

Switching to the college level, I have noted the Texas Tech men's tendencies this season to shoot well from behind the three-point arc and/or allow their opponents to do the same. Butler, for example, hit 16-24 (.667) against the Red Raiders in the final of the Great Alaska Shootout.

Well, Saturday afternoon, Texas Tech was torched again from three-point land, as New Mexico hit a mindboggling 9 of 11 (.818) treys in an 80-63 Lobo win. Quoting from New Mexico's press release prior to the Texas Tech game:

Before the 3-for-24 performance from long range against Southern Utah, the Lobos were among the nation’s early leaders in 3-point shooting. However, they still lead the league in 3s per game at 9.1 and in accuracy at 42.3%.

The 3s have dropped somewhat, though. Through the first six games, UNM was averaging 10.8 a game and shooting 47.8%, however, the past 4 contests, the Lobos are making an average of 6.5 treys and shooting 32.9% (26-79).

As I've discussed previously, a truly streaky team (or individual) will exhibit pronounced hot and cold spells over a season. It will be interesting to revisit this New Mexico squad at the end of the season to conduct systematic analyses from a larger sample of games.

Now that we've been talking about team runs within basketball games, here are a few more from today's men's action...

The opening 12 minutes of the Arizona-Illinois game featured not so much the trading of baskets, as the trading of runs (ESPN.com play-by-play sheet).

The Illini jumped out to a 12-0 lead, only to see an 11-0 Wildcat run tie the game 16-16. Illinois then scored nine straight, to go up 25-16. Eventually, things settled down with Arizona fighting back via smaller runs. Ultimately, the Wildcats prevailed in overtime, 78-72.

The Purdue-Missouri game featured a big run by each team. As described on the BoilerStation blog:

The Tigers couldn't miss during the first 20 minutes and appeared on the verge of running away with this one, leading 44-36. Back came the Boilermakers, using a 16-3 run to take a 60-51 lead with 7:20 remaining.

Then it was Missouri's turn again. Purdue went ice cold from the field, and the Tigers outscored the Boilermakers 22-3 during the final 7:11.

The second-half play-by-play sheet is available here.

Out west, the UCLA men used runs of 19-6 and 8-0 in overcoming an early 18-point deficit and pulling away from Davidson.

[Update, December 6, 2007: I've now located a complete play-by-play sheet of the Louisiana Tech-Texas Tech game, which allows me to make one little correction from what I stated from memory last night.]

Funny that my previous posting was on team runs in men's college basketball. Tonight's Texas Tech home game against Louisiana Tech was broadcast locally, and I was periodically checking in to see how the game was going. Early on, it was relatively even, with Texas Tech leading 12-10, as I recall. When I checked back a little while later, Texas Tech had pulled out to a 30-12 lead (corrected from last night), and then a while after that, the Red Raiders' lead had grown to 50-13.

According to this wire-service story I found at ESPN.com:

Texas Tech (6-3) outscored the Bulldogs 46-3 [!!!] from midway through the first half to midway through the second half, going up by as many as 45 during the run.

Louisiana Tech (1-5) did not hit a single field goal for more than 19 minutes while turning the ball over 19 times.

[My emphasis added.]

For Louisiana Tech, which ultimately lost 86-31, the box score revealed these lowlights: 13-59 (.220) on field-goal attempts overall; 3-19 (.158) on three-pointers; 10-40 (.250) on two-pointers; and 2-6 (.333) on free throws.

While the game was still going on, after it had become evident that serious statistical analysis would be warranted, I went to Louisiana Tech's statistics page, so I could have the team's percentages entering the Texas Tech game. Such an a priori baseline provides a standard of comparison for how awry the Bulldogs' offense went against Texas Tech. Louisiana Tech's prior statistics were as follows:

Its field-goal shooting was 97-267 (.363) overall; 23-82 (.280) on three-point attempts; and therefore, 74-185 (.400) on two-point attempts. Even with these low prior shooting percentages, Louisiana Tech managed to shoot considerably below them against Texas Tech (since LT had so few free-throw attempts in Lubbock, I didn't bother with the prior percentage). The following figure conveys the above statistics in graphical form.



On Texas Tech's side of the ledger, the Raiders had an overall FG percentage of .545 (36-66) against LT, which is good, but not anything to make fans forget Villanova's shooting in the 1985 national championship game. Texas Tech's 3PT% of .333 (3-9), and FT% of .579 (11-19) were hardly spectacular, either.

There's a lot more that can be analyzed regarding Louisiana Tech's woeful outing in Lubbock, but given the lateness of the hour, that will have to wait... It's Thursday afternoon and I'm now back with more analyses, below...

Now that the play-by-play sheet is available, we can break down what happened to Louisiana Tech during the stretch in which it was outscored 46-3:

Of its 19 two-point attempts, the team made 1 basket, but missed 12 jumpers, 5 layups, and 1 dunk.

It went 0-9 on three-pointers.

It went 1-2 on free-throw attempts.

One way in which a cold streak can be self-perpetuating is that, as a team falls further and further behind, it starts jacking up three-point attempts in a feverish attempt to make a comeback. The Bulldogs exhibited some degree of this tendency, as in a sequence of six shots from right before to right after halftime, five were from behind the arc.

In closing, I want to go back to Louisiana Tech's overall shooting for the game. Using an online calculator, we can determine that under an independence assumption (i.e., one outcome having no bearing on the next, like coin-flipping)...

For a team coming in hitting .400 on two-point attempts (which LT was) to go 10-40 (or worse) in the Texas Tech game has a probability of .035.

And for a team coming in hitting .280 on three-pointers to go 3-19 (or worse) has a probability of .178.

Using the conventions of statistical testing, the Bulldogs were only significantly worse in their two-point field-goal shooting in the Texas Tech game than what their prior baseline was.

Team runs in basketball are when one team outscores the other by a substantial margin (say 10 or more points) within a relatively short timeframe, often (but not necessarily) shutting out the opponent in the process.

I kept a close eye out for notable team runs in the 2004 men's NCAA basketball tournament, and found at least one of them to occur in 75% of the games (47 out of the 63 games, excluding the play-in game). Examples included:

Texas Tech going on a 14-0 run to take control of its first-round game against Charlotte, but then getting eliminated in the second round by St. Joseph's, who reeled off its own 24-2 run against the Red Raiders.

Kansas and Pacific trading runs in their second-round contest, KU's 15-2 first-half spurt being countered by a 12-0 UOP run. Ultimately, a Jayhawks' 15-3 second-half run proved decisive.

UConn unleashing a 12-0 run down the stretch to overtake Duke in a memorable national semifinal contest.

(A full list is available upon request, by e-mailing me through the link to my faculty webpage.)

Though team runs appear to be fairly common, it is quite another matter for the No. 1 team in the country, playing at home, to suffer one. But that's exactly what happened to the top-ranked UCLA men yesterday against No. 8 Texas.

According to this game story:

"Texas outscored the Bruins 26-2, including 17 in a row, in the first half" to take a sizable lead. But, the Bruins came back as, "UCLA opened the second half on a 16-3 run that produced its first lead since early in the game." The game eventually reached an equilibrium, with the Longhorns pulling it out at the end.

I have not attempted to document the rate of team runs in the regular season, but even if they don't occur as frequently as in the NCAA tournament, they still probably occur often enough. Thus, whether your favorite team is leading or trailing in a game, as Yogi Berra said, "It ain't over, till it's over."