October 6, 2010

Demystifying the passing efficiency stat

Good luck finding a coach who says he doesn't value a quarterback who throws a lot of touchdown passes, for a lot of yards and has a high completion percentage. The more efficient the quarterback, the better.

Now try to find a coach -- or any fan without a calculator -- who can determine a quarterback's passing efficiency rating. For that matter, try to find a coach who can explain the NCAA's formula.

Comparing the passing prowess of Boise State's Kellen Moore to Georgia Tech's Josh Nesbitt to Michigan's Denard Robinson isn't easy, but the NCAA has been trying for nearly 30 years.

"Most people -- most general fans, probably the quarterbacks themselves, the coaches -- don't really understand the formula," NCAA director of statistics Jim Wright said. "Unless you've got a calculator and a lot of time, you can't figure that out yourself."

The NCAA's passing efficiency rating contains four basic factors -- completion percentage, yards per pass, touchdowns per pass and interceptions per pass -- computed to give a quarterback and/or a team a rating to measure effectiveness. The rating is intended to create a level playing field on which to evaluate passers who play in different systems. (See chart for the full formula.)

In theory, the rating can be used to compare the performances of a pass-first quarterback such as Houston's Case Keenum with a pro-style signal-caller such as USC's Matt Barkley with an option quarterback such as Nesbitt.

Bill Connelly, a columnist with Football Outsiders, a Web site that examines and analyzes advanced college football and NFL statistics, said the NCAA's efficiency statistic tends to overvalue completion percentage and touchdown passes while not punishing sacks. For example, a good play on the field -- such as avoiding a sack and throwing the ball away -- is punished in the efficiency formula.

But to calculate down, distance and situation in a single statistic or series of statistics would become far more complicated than the efficiency rating already is.

"Of the stats you can find on a major sports site, this is probably the best one. But it's far from perfect," Connelly said. "It's only as useful as it is understandable."

Wright, 63, was a member of the NCAA's statistics staff when it came up with the passing efficiency rating in the late 1970s. Before the efficiency rating, the NCAA ranked quarterbacks based on total number of completions (1937-69), then number of completions per game (1970-79). But over time, those ratings became less and less reliable in evaluating and ranking a quarterback's effectiveness. That's when the NCAA decided to develop its own passing efficiency rating, eight years after the NFL came up with its rating system.

The NFL rating evaluates the same four factors, although with different multipliers. Their formula also awards "bonus points" for certain statistical benchmarks.

Want to find out how your team's QB has done? Here's a calculator to get you the answer fast (You'll need a Flash plug-in). Just fill in the attempts, completions, yards, touchdowns and interceptions. The full formula is a little farther down the page.
The maximum in the NFL's passer rating formula is 153.8; the NCAA's maximum is almost limitless. The NCAA's single-game record is 403.4, set by Indiana's Tim Clifford against Colorado in 1980. He was 11-of-14 for 345 yards, with five touchdowns and no interceptions.

The rating was the brainchild of the late Jim Van Valkenburg, the NCAA's director of statistics from 1968-92. (Van Valkenburg also helped to develop the Ratings Percentage Index -- better known as the RPI -- which is one metric used to determine at-large teams in the NCAA basketball tournament and other postseason events.)

Van Valkenburg wasn't a mathematician or a statistician. Instead, he was a former sports reporter with The Associated Press before joining the NCAA. All of the other members of the NCAA's department of statistics were former sports information directors.

The statistics department determined the four factors that would be used in the rating; they also determined that the baseline rating would be 100. Then, the NCAA's research department, a group comprised of mathematicians, determined the multipliers and the final formula.

"The only magic to '8.4,' '3.3' and '2.0' [see chart] is that's how we got to 100," Wright said. "It could have been almost anything else."

Obviously, if the NCAA had developed the passing efficiency rating 10 years later, those three multipliers would have been drastically different.

The rating was intended to give an average passing quarterback a rating of 100. Van Valkenburg and his team compiled passing statistics over the previous 15 years to determine the numbers for a so-called "average" quarterback. After that, the NCAA determined the four multipliers that would lead to an average rating of 100.

Times clearly have changed. An efficiency rating of 100 may have been "average" during the late '70s, but it wouldn't get a team or quarterback very far these days.

Thanks to the rise of more sophisticated passing offenses and continuing with the spread offenses of the past decade, an "average" passer from 1970s likely would be benched in 2010.

While a 100 rating was "average" in 1979, it is anything but now. Last season, five teams of 120 had team passing efficiency ratings of less than 100. All of them -- Eastern Michigan, Ball State, Army, Vanderbilt and New Mexico State -- had losing records.

In 1979, the average efficiency rating of all teams was 104.49. The average team that season completed fewer than half its passes (49.1 percent) and attempted 21.6 passes per game. By 2009, the average passing efficiency rating of the 120 teams was 129.27. Collectively, teams completed 59.1 percent of their passes, the best completion rate on record, while attempting 31 passes per game.

Oklahoma's Sam Bradford (175.6) and Florida's Tim Tebow (170.8) left college after last season as the top two quarterbacks in career passing efficiency.

In 1980, BYU's Jim McMahon set the single-season passing efficiency (176.9.) That mark stood for 15 years, until Florida's Danny Wuerffel broke it in 1995. But since 1998, six quarterbacks have broken Wuerffel's single-season record; the last was Hawaii's Colt Brennan in 2006.

While baseball statistics are skewed by the "dead ball era" and by the "steroids era," followers of football stats mull over the contrasting statistics from the heyday of the wishbone and "3 yards and a cloud of dust" offenses to the current trends in spread and pro-style offenses.

As offenses have evolved, the NCAA has contemplated changing the multipliers in the pass efficiency rating to re-establish a rating of 100 as the average. But almost unanimously, the members of the statistics department have elected to stay with the formula developed more than 30 years ago.

"The dilemma we face is that, clearly, quarterbacks are becoming more efficient and the game is becoming more pass-oriented than it was in the late '70s or early '80s," Wright said. "If we tweak the efficiency rating, you're not going to be able to compare past years with current years because clearly to do that, you'd have to change the multipliers."

Here is the formula used to determine the NCAA's passing efficiency statistic:
Utah's Terrance Cain leads the nation in passing efficiency. We will use his passing statistics to show how the NCAA computes passing efficiency.
Factor one: Completion percentage
Pass completions divided by pass attempts times 100
Cain: 37 49 x 100 = 75.5102

Factor two: Yards per attempted pass
Yards passing divided by pass attempts times 8.4
Cain: 486 49 x 8.4 = 83.3142

Factor three: Touchdowns per attempted pass
Touchdown passes divided by pass attempts times 100 times 3.3.
Cain: 5 49 x 100 x 3.3 = 33.6734

Factor four: Interceptions per attempted pass
Interceptions divided by pass attempts times 100 times 2.0
Cain: 0 49 x 100 x 2.0 = 0.0

Add factors one, two and three
Cain: 75.51 + 83.31 + 33.67 = 192.4978

Subtract factor four from subtotal
Cain: 192.4978 - 0.0 = 192.4978

Cain's pass efficiency rating, rounded up, is 192.50

Source: NCAA Official 2010 Football Statistics Rules
Since 1990, the NCAA has calculated a team's passing efficiency defense. At the time, the NCAA was based in Kansas City, and Wright and others noticed that nearby Kansas State had led the nation in pass defense (passing yards allowed per game) in 1989. It wasn't because the Wildcats' defense was particularly good; in fact, they led the nation in fewest passing yards allowed simply because their run defense was so bad. Few teams bothered to pass on the Wildcats that season because opposing offenses could win by running the ball.

Yards per game, then, hardly was an effective measure of the quality of a team's performance against the pass. The next season, the NCAA created a statistic that focused on how inefficient a defense made a passer.

Just because the statistic is widely available doesn't mean it is used, though.

"I don't even know what that is," said Arizona coach Mike Stoops, who was a defensive coordinator before becoming a head coach. "[Instead] you look at touchdown passes, points, passing percentages, what are we giving up as pass completions. I don't put a lot of stock in a lot of statistics."

By definition, though, the pass efficiency defense rating takes all of Stoops' favorite factors into account.

From the offensive end, Syracuse coach Doug Marrone said efficiency one of the top things he looks for in quarterbacks -- in games, practice and recruiting.

"We put a lot of stock into it," said Marrone, a former New Orleans Saints offensive coordinator. "We do it on a daily basis. We keep track of quarterback efficiency daily in practice, as we do with receivers, tight ends, running backs."

Even coaches who say they pay little attention to the efficiency rating itself keep an eye on the components that go into efficiency.

For coaches, the truth is on tape, not in the numbers.

"I don't get too caught up in stats," California coach Jeff Tedford said. "There are so many variables at the quarterback position that can be misleading. You really need to look at how they play and what is happening -- is the ball tipped off somebody's hands for an interception?

"You can look at the stats themselves and then look at the tape. That's still the key, to watch the tape and understand what they're doing good or bad to be efficient."

It makes sense that coaches wouldn't be too concerned with how their quarterbacks compare with others around the country based on a formula generated for general consumption. When coaches evaluate the performance of their own offense, they may have different ways to gauge success in their own systems, Connelly said.

He recalled listening to Missouri coach Gary Pinkel in an interview this season refer to the efficiency of the Tigers' running game in a particular game. Pinkel may not have been using a statistic generated by the NCAA or anyone outside of his coaching staff, but it was a statistic nonetheless.

"I do think they come up with their own ways to evaluate things a lot," Connelly said. "I doubt they would use QB rating. With the plays they call, they're going to define their own version of success."

The passing efficiency rating has trended upward since it was first a recorded statistic in 1979. Here's a look at the average passing efficiency for all passers in the Football Bowl Subdivision as well as the individual leader.
Year All passers Individual leader (rating)
1979104.49Turk Schonert, Stanford (163)
1980106.63Jim McMahon, BYU (176.9)
1981107Jim McMahon, BYU (155)
1982110.77Tom Ramsey, UCLA (153.5)
1983113.56Steve Young, BYU (168.5)
1984113.02Doug Flutie, Boston College (152.9)
1985114.58 Jim Harbaugh, Michigan (163.7)
1986115Vinny Testaverde, Miami (165.8)
1987112.67Don McPherson, Syracuse (164.3)
1988114.32Timm Rosenbach, Washington State (162)
1989118.35Ty Detmer, BYU (175.6)
1990117.39Shawn Moore, Virginia (160.7)
1991117.94Elvis Grbac, Michigan (169)
1992114.5Elvis Grbac, Michigan (154.2)
1993122.43Trent Dilfer, Fresno State (173.1)
1994120.59Kerry Collins, Penn State (172.9)
1995120.17Danny Wuerffel, Florida (178.4)
1996120.24 Steve Sarkisian, BYU (173.6)
1997122.86Cade McNown, UCLA (168.6)
1998 122.97Shaun King, Tulane (183.3)
1999120.5Michael Vick, Virginia Tech (180.4)
2000119.66Bart Hendricks, Boise State (170.6)
2001123.8Rex Grossman, Florida (170.8)
2002123Brad Banks, Iowa (157.1)
2003125.89Philip Rivers, N.C. State (170.5)
2004125.36Stefan LeFors, Louisville (181.7)
2005126.13Rudy Carpenter, Arizona State (175)
2006127.54Colt Brennan, Hawaii (186)*
2007127.35Sam Bradford, Oklahoma (176.5)
2008127.89Sam Bradford, Oklahoma (180.8)
2009129.27*Tim Tebow, Florida (164.2)
*denotes single season record; Source: NCAA

David Fox is a national writer for Rivals.com. He can be reached at dfox@rivals.com.


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