Cardinal Numbers: "Bend, But Don't Break"

For those of us obsessed with the collection, analysis, interpretation and presentation of data, The Bootleg's Contributing Columnist & Senior Statistician Terry Johnson examines the validity of the widely-held view among fans that the Stanford's "D" has been one of a "bend, but don't break" variety during this 2007 season. While it may have been true against WSU, we shouldn't rush to conclusions.

During Stanford's game with Washington State, the television announcers described Stanford's defense as a "bend but don't break" defense. That's an old, often misused, football cliché. But in this case, there was some truth to it.

Stanford's defense repeatedly allowed Washington State to drive into the Stanford end of the field. Washington State had 12 possessions in the game, not counting the kneel-downs to run out the clock at the end of each half. Remarkably, the WSU offense drove inside the Stanford 25-yard line on 11 of those 12 possessions. WSU punted just once.

However, once Washington State got inside the Stanford 25-yard line, the Cardinal defense repeatedly stiffened, stopping WSU drives short of the goal line. The Cougars came away with no points at all on five of their 11 trips inside the Stanford 25-yard line, due to two fumbles and three failed fourth down conversion attempts. WSU had to settle for field goals on four other drives inside the Stanford 25. The WSU offense got into the end zone only twice:

Washington State Drives
(excluding kneel-downs)
QuarterStarting Point
of Drive
Farthest Point
of Drive
Result of
1WSU 20Stanford 3Fumble
1Stanford 30Stanford 23Field Goal
1WSU 12Stanford 20Failed on 4th down
2WSU 34Stanford 0Touchdown
2Stanford 39Stanford 21Failed on 4th down
2WSU 40WSU 41Punt
2WSU 36Stanford 24Fumble
3WSU 25Stanford 5Field goal
3WSU 29Stanford 0Touchdown
3WSU 18Stanford 21Failed on 4th down
4WSU 21Stanford 15Field goal
4WSU 31Stanford 14Field goal

There's good news and bad news here. The bad news: Stanford played appallingly bad defense last week. Washington State shredded the Cardinal defense, rolling up 561 yards of total offense and moving the ball deep into Stanford territory on almost every drive. The good news, such as it is: despite all those yards, and despite numerous scoring opportunities, the Cougar offense managed to put only 26 points on the board. (WSU's other seven points weren't scored by the Cougar offense, coming on an interception return.) "Bend but don't break" may indeed have been an apt description of the performance of the Stanford defense last Saturday.

In thinking about this, I began to wonder whether there is a good statistical way of evaluating whether a defense is indeed a "bend but don't break" defense.

The "bend but don't break" label seems to be used to describe defenses that give up a lot of yards, but don't give up as many points as one might expect – as Stanford's defense did against Washington State. There are various ways in which one could attempt to measure the "bend but don't break" tendency statistically. For present purposes, I'm going to focus on just one way of looking at this issue. We can compare the number of points allowed by a defense to the number of yards allowed: does the defense give up a relatively low number of points, in comparison to the number of yards given up?

To make that comparison, we first need to figure out the "normal" relationship between points allowed and yards allowed. Then, we can determine whether a particular team's defense gives up fewer points than would be expected, based on the number of yards allowed. So, what is the statistical relationship between points and yards?

There is a reasonably consistent, well-established relationship between points and yards. So far this season in the Pac-10, totaling up all of the offensive and defensive statistics for all of the teams in the conference combined, there has been one point scored for every 14.3 yards gained. I've looked at this statistic several times in previous years, and this relationship between yards and points is reasonably consistent from year to year, coming out in roughly this same range each year.

The ratio of one point for every 14.3 yards gives rise to perhaps the most elegant statistic in college football: on average, there are about seven points scored for every 100 yards gained. Statistics don't always make practical sense, but this one does. A football field is 100 yards; a touchdown is seven points. This stat has an intuitive simplicity to it.

Sadly, but inevitably, nothing can remain quite that simple. The average of seven points for every 100 yards includes all points allowed by the team, not just points allowed by the defense. The defense is not responsible for points allowed on interception returns, fumble recoveries, kickoff returns, punt returns, and safeties. To judge the performance of the defense, we should remove from the analysis the points that were not allowed by the defense.

I adjusted the cumulative Pac-10 offensive and defense statistics for the season to date to include only points scored by the offense and allowed by the defense. Making that adjustment gives us a less aesthetically pleasing, but more precise, average of 7 points for every 107 yards. That is, so far this year, for all Pac-10 offenses and defenses combined, there have been about seven points scored by the offenses and allowed by the defenses for every 107 yards gained.

Now, back to the "bend but don't break" issue. We might expect a "bend but don't break" defense to give up a relatively high number of yards while allowing a relatively low number of points. Now that we have established that the average for a Pac-10 offense or defense is about seven points for every 107 yards, we can use that average to come up with an "expected" number of points for a team in a given game, based on the number of yards gained. We might expect a "bend but don't break" defense to allow fewer than the "expected" number of points.

For example, in the Washington State game, the Stanford defense got sliced and diced to the tune of 561 yards. If the Stanford defense had given up points at the average Pac-10 rate of seven points for every 107 yards, then the "expected" number of points allowed by the Stanford defense would have been 37 points. However, the Stanford defense gave up only 26 points, well below the "expected" 37 points. Thus, it appears that Stanford's defense did fit the "bend but don't break" description in this particular outing.

That's just one game. What about the season as a whole? Does Stanford's defense consistently merit the "bend but don't break" label?

Not really. For the season, the Stanford defense is allowing 455.3 yards per game. At the average rate of seven points for every 107 yards, the "expected" number of points allowed by the defense would be 29.8 points per game. Stanford has allowed 305 points this season, but 14 of those points came on interception returns and were not allowed by the defense. So, the Cardinal defense has allowed 291 points, or 29.1 points per game. That's very close to the "expected" figure of 29.8 points allowed. Thus, Stanford has given up about as many points as one would expect based on the number of yards it has allowed.

There have been a few Stanford games in which the "bend but don't break" label seemed to fit – particularly the games against USC, Washington, and WSU. In each of those games, Stanford gave up a lot of yards, but allowed fewer than the "expected" number of points. However, there also have been some games in which Stanford's defense bent until it broke, allowing as many points as expected or more:

Actual Points Allowed by Defense
vs. "Expected" Points Allowed by Defense
("expected" points based on
7 points per 107 yards allowed)
San Jose St.163110-11
Arizona St.4402934+5
Oregon St.3152123+2
Washington St.5613726-11
Season average455.329.829.1-0.7

These numbers don't seem to support the idea that Stanford's defense consistently has been a "bend but don't break" defense for the season as a whole. Rather, I would conclude that Stanford's defense has been giving up both a shocking number of yards and a lot of points as well.

Looking at the Pac-10 as a whole, here's how the defenses around the conference stack up against their "expected" number of points allowed, based on the average of seven points for every 107 yards (point totals are adjusted to exclude points not allowed by the defense):

Actual Points Allowed by Defense
vs. "Expected" Points Allowed by Defense
("expected" points based on
7 points per 107 yards allowed)
Arizona St.318.920.915.7-5.2
Oregon St.302.019.821.8+2.0
Washington St.415.827.229.3+2.1

As it turns out, most teams in the conference come pretty close to their "expected" number of points allowed, based on the ratio of seven points for every 107 yards. For five of the teams in the conference, their actual number of points allowed is within one point of their "expected" number of points allowed. Seven of the teams' actual points allowed are within 2.1 points of their "expected" figures.

Three defenses allow substantially fewer than the "expected" number of points – Arizona State, USC, and Oregon. Arizona State and USC really aren't "bend but don't break" defenses, because they don't "bend" – that is, they don't give up many yards. They're just very good defenses. Oregon's defense, on the other hand, does look like a "bend but don't break" defense. Oregon's defense allows a lot of yards – 404.6 yards per game. But the Duck defenders do not allow a lot of points – 22.0 points per game. So, if we want to find a "bend but don't break" defense in this conference, we should look north to Eugene.

Random Numbers

Mark Bradford's 12 receptions against Washington State give him 157 career receptions, moving him up to sixth on Stanford's career receptions list, ahead of Justin Armour and Jeff James (154 receptions) and behind Vincent White (162 receptions). Bradford's 141 receiving yards against WSU give him 2,236 career receiving yards, moving him into tenth place in career receiving yards, ahead of Tony Hill (2,225 yards) and behind Jeff James (2,265 yards)...

Bradford's 12 receptions against WSU were the most receptions in a game by a Stanford receiver since Luke Powell had 12 catches against San Jose State in 2003. The school single-game record of 14 receptions is shared by Eric Cross, Vincent White, Brad Muster, and Jim Price...

Stanford has scored just 13 points in the first quarter this season, with just one first quarter touchdown (against TCU). The first quarter has been by far Stanford's lowest-scoring quarter. Stanford has scored 81, 50, and 57 points in the second, third, and fourth quarters respectively...

Stanford has scored on its first possession of the game just once this season, a field goal against San Jose State. In each of the last two games, Stanford moved the ball into the opponent's red zone on its first possession but came away with no points, missing a field goal attempt each time...

Stanford's leading tackler against Washington State was Taylor Skaufel with 11 tackles. It was the first game this season in which Bo McNally, Pat Maynor, or Clinton Snyder was not the team leader or co-leader in tackles...

Excluding yards lost on sacks, Tavita Pritchard ran for 104 yards in his first two games as a starter, with 10 carries for 49 yards against USC and 11 carries for 55 yards against TCU. Since then, however, Pritchard has run for just 18 yards, with three carries for -9 yards against Arizona, four carries for 10 yards against Oregon State, one carry for six yards against Washington, and five carries for 11 yards against Washington State...

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