Most Exciting NFL Week Ever? Monday, May 18 2009

The 12th week of the 2003 NFL season might have been the most exciting ever. Featuring improbable comebacks and overtime thrillers, not a single game was decided by two touchdowns or more.  Indeed, if all the games were replayed, just two-thirds would have been won by the same teams.

The first game of the weekend was a 30-27 overtime game between St. Louis and Arizona.  The Rams squandered a 24-0 lead in the late third quarter, letting the Cardinals take a 27-24 lead. But in the final three minutes the Rams drove 83 yards, including a fourth-and-seven conversion, to set up a 24-yard field goal as time expired. In overtime the Rams drove to the winning 49-yarder. Marc Bulger, the the Ram’s QB, threw 4 interceptions but still threw for 329 yards.

The next game was a 38-31 comeback win by Tennessee over Atlanta. The Falcons held a 21-0 lead at the end of the first quarter, but the Titans countered with a 14-point second quarter. Tennessee then had a 24-3 run to take a commanding 38-24 lead with seven minutes left, but a 41-yard touchdown made the score 38-31. Atlanta got the ball back but were stopped on downs to prevent overtime.

Indianapolis triumphed 17-14 over Buffalo despite the  Bill’s 14-3 lead in the fourth quarter. But Edgerrin James scored on a 14-yard rumble and then scored the game-winner on fourth-and-one after the Colts had been stopped for no gain on the previous two downs.

The next game was yet another comeback, this one an ugly 13-6 AFC North matchup between Pittsburgh and Cleveland. Both defenses did a great job, with Cleveland limiting the Steelers to 168 yards and Pittsburgh forcing 5 turnovers that led to all 13 Steelers’ points. Cleveland led 6-0 with three minutes left in the half, but a fumble recovery allowed the Steelers to score a touchdown and a quick field goal to take a 10-6 lead they would not relinquish.

Next came a 24-20 thriller between Dallas and Carolina. The teams were tied three times during the game, including a tie at 17-17 before Dallas scored on an option-wishbone play to take the lead for good in the fourth quarter.

Then came a 19-10 Chicago triumph over Denver. Paul Edinger kicked 4 field goals, but the key play was a fourth-and-one quarterback sneak that just got in for a touchdown. Denver might have had a chance for a comeback had the snap for a field goal not been fumbled.

Green Bay needed 243 yards rushing to defeat the 49er’s 20-10. Brett Favre threw two touchdowns and Green Bay converted three third downs to run out the clock. Terrell Owens made a great fourth-down touchdown catch to make the score 17-10, but three other times San Francisco was unable to convert in Packer territory.

New England scored with 41 seconds left in overtime to defeat Houston. The Patriots had a much better game offensively, but committed three turnovers that kept the Texans in the game. A last-minute touchdown pass by Tom Brady tied it up. After two possession changes Adam Vinatieri won it 23-20 on a 28-yard field goal.

Morten Andersen kicked a 45-yard field goal with just four seconds left to give the Chiefs a 27-24 victory over Oakland. The game-winning drive included a crucial 16-yard pass on fourth-and-14 just two minutes after Sebastian Janikowski’s 41-yarder to tie it up.

Minnesota pulled an incredible comeback to win over Detroit 24-14. After a fourth-quarter field goal, Minnesota ran an interception back for a touchdown, then three plays later, they did it again. Scoring 17 points in the final three minutes, the Vikings averted overtime in a thriller.

A 94-yard drive in the closing minutes gave the Jets a 13-10 victory over the Jaguars in an otherwise unimportant AFC matchup. Chad Pennington completed 9 of 11 passes on the crucial drive and found Santana Moss on a 3-yard touchdown pass with 27 seconds left to left the Jets to the top.

Philadelphia was never pressured in a 33-20 win over the Saints, but the game featured some thrilling moments. Deuce McAllister broke a 76-yard run and a 22-yard ramble. The Saints might have won had it not been for a crucial stop by the Philly defense and a fumble at the Eagles’ 1-yard line.

Cincinnati survived a rally from San Diego to win 34-27 on a great performance by Jon Kitna, who threw four touchdown passes and ran the clock out to save the win in the final seconds. Chad Ocho Cinco caught 3 touchdowns of 4, 5, and 12 yards.

Miami rallied from a two-touchdown deficit in the fourth quarter to win 24-23. Ricky Williams scored on runs of 1 and 24 yards to givve the Dolphins their slim one-point lead, but they nearly lost it after the Redskins forced a punt from the Dolphin’s nine-yard line.

Tampa Bay beat New York 19-13 on Monday night. Though the Bucs’ defense allowed just 212 yards and forced 4 turnovers, the Giants nearly triumphed as Tampa Bay forced a fumble as halftime expired and later intercepted a pass in the end zone. ‘

By far the most exciting game of the week, however, was a thrilling 44-41 overtime victory by Baltimore over Seattle. The game featured nine touchdown passes in just 29 minutes and 11 seconds, four of them second-half receptions by Baltimore’s Marcus Robinson. The Ravens were down 17-3 at halftime and faced an impossible 41-27 deficit with just 6:41 left and the ball in Seattle’s possession. But star back Ed Reed blocked the Seahawks’ punt and returned it for a touchdown. Then Ray Lewis recovered a fumble at the Raven’s 29 with just 4:16 left. Robinson scored again to put the Ravens just three behind. Seattle recovered the onside kick, seemingly dooming Baltimore. But Matt Hasselbeck was stopped on fourth-and-one to give Baltimore one last shot, and a 44-yard pass interference penalty on a play intended to go to Robinson set up the game-tying 40-yard field goal as time expired. In overtime, the Ravens forced a punt and Matt Stover kicked his third field goal of the game, but not before being set up by a 19-yard pass on third and 15 that went to, of course, Robinson, who fiished the game with 131 yards recieving and 4 touchdowns on just 7 receptions.

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Football and Baseball Defensive Statistics: A Parallel Tuesday, Feb 10 2009

While reading the New Bill James Historical Baseball Abstract, a curious similarity between football and baseball defense struck me. James discusses the difficulty of analyzing baseball defense, especially the effects of the pitching staff and how a field full of great defensive players will produce just as many outs as a field with slow-footed DH’s. Just as in baseball, football players compete for a certain number of sequence-ending plays (outs in baseball, tackles in football). Similarly, defensive statistics are influenced by an independent factor, the groundball-flyball tendencies of a pitcher or the run-pass tendencies of an opposing offense.  Not surprisingly, fly balls and passes are similar. Both come down to a single defensive player (a defensive back or an outfielder) and mistakes are most costly on these plays. Groundballs and running plays also share characteristics: multiple players are necessary and speed is tested in the offense. Many statistics are similar. Defensive backs are rated on their interceptions, outfielders on their putouts. Therefore, in both analysis and statistics, football and baseball defense is very similar.

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Special Teams: Which Position is Most Valuable? Friday, Dec 19 2008

Specialists are generally divided into punters, placekickers, and returners. Which of these positions is most valuable? It might seem like placekickers are most valuable because they are called on for crucial last-minute field goals. But is this in fact accurate? I selected the 2004 NFL season to find out.

Kickoff returners usually return about 40 kicks a season. In 2004 the leader in return average was Willie Ponder with 27.6 yards per return. The league average was 21.7, so a star returner would be worth around 240 yards, or 20 points, to a team each season.

Punt returners average 30 returns per years and 2004 leader Dennis Northcutt typically returned his punts 12 yards. The league avearage was 8.6, so a returner of his ability would contribute 102 yards or 8.5 points per season.

A star placekicker like Adam Vinatieri would make all of his 40 extra points, but so would most other kickers in the league. So only field goals contribute to a kicker’s value. Supposing a player attempts 25 field goals per season, he should make 94% of them versus the league average of 80%. This is just 8.9 points.

Punters may have the least glamorous job on a team, but stars such as Mitch Berger can average a net of 39 yards. Since the league average was 35.8 yards in 2004 and punters would probably dropkick 75 times over the course of the season, they would contribute 240 yards or 20 points.

Therefore, star talent is most valuable at the returner position because a returner doing punts and kickoffs would net 28.5 points per season. Punters are second with 20 points of value, and surprisingly, kickers are last with just 8.9.

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Larry Csonka and the Miami Dolphins Thursday, Dec 11 2008

Star fullback Larry Csonka left the Miami Dolphins in 1975 for the new World Football League. He slumped in 1974, with just a 3.8 yards-per-rush average, down from 4.6, 5.2, and 5.4 in his previous three seasons. Reports suggest his performance was worse because he was switching leagues. How would the Dolphins have done if Csonka was up to form?

The Dolphins that year had an 11-3 record and averaged just 3.8 yards rushing. If we assume Csonka would have averaged at least 5.0 yards per rush, and Jim Kiick had been up to form as well, the Dolphins might have been able to put up 5 yards per rush as in their previous two seasons. Since the Dolphins had the most rushing attempts of any team in the league, they could have significantly improved their performance. In fact, they probably would have scored more than 50 points more than they actually did.

But would this really make a difference? According to the Pythagorean Record system, the Dolphins would have won fewer games than they actually did! This is true because the Dolphins overacheived that year by about 1 1/2 games. So, even if Larry Csonka had been up to form in 1974 and the Dolphins had redid their season, in the long run it would make no difference in their record.

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My NFL Playoff Predictions Sunday, Dec 7 2008

This weekend I analyzed every remaining game for the playoff contenders to come up with what I think is the most likely seeding and playoff results. I treated 17th week games, where many teams that have clinched playoff spots rest their starters, just like regular games, favoring the stronger team.

AFC Seeding:

1. Tennessee (15-1)
2. New York Jets (12-4)
3. Pittsburgh (11-5)
4. Baltimore (11-5)
5. Miami (9-7)
6. Denver (9-7)

NFC Seeding:

1. New York Giants (14-2)
2. Tampa Bay (13-3)
3. Atlanta (11-5)
4. Arizona (11-5)
5. Carolina (10-6)
6. Green Bay (10-6)

Playoff Results:

Wild Card Round:

Denver @ Pittsburgh, Pittsburgh wins

Green Bay @ Atlanta, Atlanta wins

Miami @ Baltimore, Baltimore wins

Carolina @ Arizona, Carolina wins

Division Round:

Pittsburgh @ New York Jets, Pittsburgh wins

Baltimore @ Tennessee, Tennessee wins

Atlanta @ Tampa Bay, Tampa Bay wins

Carolina @ New York Giants, New York Giants win

Conference Championships:

Pittsburgh @ Tennessee, Tennessee wins

Tampa Bay @ New York Giants, New York Giants win

Super Bowl XLIII: Giants beat the Titans, 30-21.

Also, I have chosen the five best remaining games in the NFL schedule:

1. Pittsburgh @ Tennessee, 1 PM, December 21
2. New York Giants @ Dallas, 8:15 PM, December 14
3. Dallas @ Pittsburgh, 4:15 PM today, December 7
4. Pittsburgh @ Baltimore, 4:15 PM, December 14
5. Baltimore @ Dallas, 8:15 PM, December 20

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Crazy Statistics Thursday, Dec 4 2008

Hopefully this will become the first in a series of posts of crazy statistics I’ve noticed, with no purpose other than fun.
1. The Colts’ head coach, Tony Dungy, played cornerback and quarterback for the Pittsburgh Steelers about 30 years ago. His career offensive statistics were 8 yards on 3 attempts rushing and 3 completions on 8 passing attempts
2. Kicker Dean Biasucci played 11 years in the NFL, with season attempts ranging from 5 to 32 and hitting anywhere from 50 to 85% of his attempts. Yet his longest field goals are incredibly consistent: 50, 52, 50, 53, 55, 55, 54, 52, 53, 50, and 51.

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Tom Brady’s Injury: How Many Wins Will it Cost the Patriots? Sunday, Sep 14 2008

Tom Brady’s injury in the first game of the 2008 football season is expected to cost fantasy team owners about 150 million dollars. But how much will his injury cost the Patriots, who are coming off a perfect 16-0 regular season? Pythagorean records and some elementary football knowledge allows us to calculate with great accuracy.

First of all, how many points will Brady’s injury cost the Pats? It seems reasonable to assume that his injury will cost them about 100 offensive yards per game, because the Patriots will lose about 60-80 yards of passing (they still have Randy Moss!) and the rest will result from the inability to set up the run. 100×15 games left in the season is 1500, so that is 1500 fewer yards of offense. This seems like a lot, but remember that Brady is the reigning MVP, and backup Matt Cassel has thrown a pass precisely 61 times in his NFL career.

Then, we can use the knowledge that 12 yards equal one point (discovered by statisticians Pete Palmer and Jim Thorn) to calculate the Pats will lose 125 points on offense.  Using the Pythagorean formula, we can then calculate that Brady’s injury will cost the Patriots about 2.5 wins (if they started out with a 13-3 record.) In a now highly competitive division, this is the difference between winning the division and being the wild card or not making the playoffs at all.

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Rating the NFL’s Great Teams by Pythagorean Records Monday, Aug 4 2008

June 2008

More than any other sports teams, great NFL teams are assessed by how many championships they win. The 1969-1971 Baltimore Orioles are considered a fantastic baseball dynasty, but they won just one World Series. The Detroit Pistons have been one of the best teams in the NBA, but perennially come up short in the playoffs. Football’s notion of greatness, winning Super Bowls, is unique but it is also nonsense. The Super Bowl is one game, and the evaluation of a team should not rest on a short sixty minutes of play. Teams should not receive as much credit for beating up on a poor team, as happened in Super Bowl XX, as they do for defeating another great team, like Dallas’s win in VI.

Rating teams by Super Bowls is inaccurate, so another popular way of rating great teams is by their regular season record. But this method also has weaknesses, despite the sixteen-game sample size. A team may kick a game-winning field goal in overtime that would make no difference in a 42-0 rout. A team that many wins games by small margins but loses routs will make the playoffs ahead of a superior team that wins games by huge amounts but loses a few close games in overtime. Thus, the regular season record should be discarded as a method for rating great teams.

Since the two most popular methods for rating football dynasties are both inaccurate, we must turn to a method developed by baseball statistician Bill James. James invented a formula for estimating a team’s record based on points scored and allowed. The system, called the Pythagorean record, is as follows

Expected W = G x P²

P²+PA²

where W is wins, G games, P points, and PA points allowed. By factoring out luck, the Pythagorean record calculates how many games a team should win. The formula also makes an automatic adjustment to sixteen game seasons, which is helpful for analyzing the performance of early teams that played shorter schedules.

What NFL teams qualify as great dynasties? The Chicago Bears of the 30s and 40s were consistently outstanding. They once scored more than 300 points while allowing just eighty-four. The Monsters of the Midway dominated for eleven seasons, and another great team didn’t emerge until 1950. The Cleveland Browns of that era started in an upstart league, the AAFC. Under coach Paul Brown and quarterback Otto Graham, the Browns won the AAFC championship for four years and joined the NFL when the AAFC disbanded. They appeared in six consecutive NFL championship games and won three. Vince Lombardi’s Green Bay Packers are probably the most famous football dynasty ever. They won three straight championships, including the first two Super Bowls.

As soon as their run ended, the Johnny Unitas Baltimore Colts became the NFL’s premier team. Their 258-point differential in 1968 is one of the best ever. They appeared in Super Bowls III and V, and were just seven points from having a better season than division champion Los Angeles in 1967. The New England Patriot’s bid for a perfect season renewed interest in the Miami Dolphins of the 70s. The 1972 Dolphins went 17-0, and according to their Pythagorean record, they did even better the following year. The Dolphins won two consecutive Super Bowls and had perhaps the strongest group of running backs in history. Miami boasted Larry Csonka, Mercury Morris, and Jim Kiick in their backfield. Another great dynasty started their run in 1971. The Dallas Cowboys reached four Super Bowls and won two. Their streak of winning seasons lasted until 1983, making the thirteen-season period the longest run of any team in this study. The Cowboys’ nemesis was the Pittsburgh Steelers. The Steelers won four Super Bowls in six years and had a 200-point scoring differential for two straight years. Their defense, the Steel Curtain, is often considered the best in NFL history.

The Joe Montana San Francisco 49ers tied the Steelers by winning four Super Bowls in one decade. If not for the strikes in 1982 and 1987, the 49ers would very likely have won another and become the only NFL dynasty to win five championships. The 49ers had 100-point differentials for ten of eleven seasons, and topped 150 in six of those seasons. After 1992, Montana went to Kansas City and Steve Young took over at quarterback. With Young, Jerry Rice, and running back Ricky Watters, the 49ers won Super Bowl XXIX and their division for three straight years. The Buffalo Bills of the early 90s are the only team to reach four consecutive Super Bowls. Quarterback Jim Kelly and running back Thurman Thomas were the stars of the revolutionary Hurry-Up offense. In Super Bowls XXVII and XXVIII, the Bills lost to the Dallas Cowboys. The Cowboys had a short run but dominated the NFL for four years.

Some teams not in the study include the Bears, Redskins, and Broncos of the 80s. Washington and Chicago were impressive in the years they won championships, but otherwise nothing special. The Broncos were more consistent, but topped the 100-point scoring differential barrier only twice and had several mediocre years. The Minnesota Vikings were unbelievable in 1998, scoring more than 550 points and allowing less than 300. However, they were great for just one season. The New England Patriots have won three Super Bowls in four years and went 16-0 in the regular season last year. However, their scoring differentials are mediocre and their videotaping of opponent’s signals casts suspicion upon their record.

After narrowing the field to eleven dynasties, I applied the Pythagorean Formula directly. The results were skewed towards early teams, as eight of the ten best seasons were from the early Chicago Bears. Modern teams like the Cowboys or Bills were at the bottom of the group. Because the margin of scoring in games has continuously decreased throughout history, so have seasonal margins between the best and worst teams. Early teams should not have this advantage and perhaps should be penalized because of the differences between early run-oriented football and the balanced modern version. The Monsters of the Midway would have much more trouble defending against a wide receiver like Randy Moss than would a defense of similar ability today. After making the adjustments, teams of all eras were evenly distributed throughout the list of teams. The adjustment reduced the wins of every team, so I added 2.82 wins to every team. These adjustments gave the leading team, the 1976 Steelers, exactly sixteen wins.

To rank dynasties, I used four measurements: average wins in best three consecutive years, average wins in best five consecutive years, average wins per year in the period considered, and the total wins in the period. I adjusted the latter component so that it was comparable with the other three, i.e. it was on sixteen-win scale. I weighted the five-year run most heavily, because it represented both the short-term ability and the consistency of the team. The next most important factor was the three-year run, measuring the peak of the team. The average and total were rated equally.

The final computation showed the greatest NFL dynasty ever was the 1980s 49ers. They finished in the top four in every rating component. In addition, the team led in average and total, an incredible feat considering that the two have a very strong negative correlation. Great teams tend to either have short, brilliant runs or long, consistently very good ones. The 49ers had the best aspects of both. In second were the Miami Dolphins. They were one of only two teams to have three consecutive seasons of 14 wins or better. The Pittsburgh Steelers had the best scores for 3 and 5 years, but did poorly in the average category. They were almost tied with the Dallas Cowboys of the 70s, who had the best total of any team. Surprisingly, the Vince Lombardi Packers finished last. The team had fantastic actual records but poor scoring differentials. They were the opposite of the 49ers, finishing in the bottom four of every category. The complete results of the study:

Dynasty	Start	End	Best 3	Best 5	Avg.	Total	Adj. Tot.	Rating
San Francisco M	1981	1992	14.55	14.66	14.33	143.31	15.58	14.751
Miami	1970	1975	15.05	14.43	14.02	84.16	12.78	14.173
Pittsburgh	1972	1979	15.12	14.78	12.15	97.21	13.47	14.077
Dallas	1971	1983	14.02	13.42	13.15	157.89	16.18	14.068
San Francisco Y	1993	1998	14.63	14.29	14.19	85.18	12.84	14.065
Baltimore	1966	1971	14.22	13.67	13.42	80.54	12.58	13.539
Dallas	1992	1996	14.52	13.42	13.42	67.08	11.80	13.371
Buffalo	1988	1993	13.64	13.37	13.33	79.98	12.55	13.266
Chicago	1934	1944	13.42	12.32	11.72	129.00	14.97	13.005
Cleveland	1950	1955	13.25	13.00	12.88	77.29	12.40	12.919
Green Bay	1963	1967	13.34	13.16	13.15	65.78	11.72	12.917

The best dynasty in NFL history is clearly the 49ers. The Pythagorean formula establishes the strengths of the 49ers: consistency, high peaks, and durability. Pythagorean records are a powerful way to analyze sports performance. By removing factors of luck that bias championships or regular-season records, they analyze how a team really should have done. Thus, Pythagorean records expose overachievers and show which teams deserve to win based on their points scored and allowed.

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An Original Method for Statistical Analysis of Defensive Football Players Monday, Aug 4 2008

February 2008

Who is the best defensive player of all time? Is it a defensive lineman, such as Reggie White, a linebacker, like Lawrence Taylor, or a back, like Ronnie Lott? This is a very difficult question to answer since most defensive ratings are built on reputation, which is largely inaccurate. We should be able to statistically and impartially rate defensive players. Curiously, though, the only defensive statistics currently used have serious flaws. But by breaking down team statistics and using simple and obvious but rarely used individual measures, defensive players can be cleanly and accurately analyzed.

First, let’s see what is wrong with the most common defensive statistics today. A very popular method of rating the secondary is interceptions They are valuable but also rare. In fact, it is unusual to record more than six or seven in a season. However, this scarcity makes them almost random, so they are subject to fluctuation. To illustrate this, take a good safety who intercepts five of 160 passes thrown to receivers he is covering. Using a random statistical database, I computed that chances are less than eighteen percent he will duplicate this performance in the next season, even with exactly the same chance of an interception and the same number of opportunities. Returns of interceptions for touchdowns are even more random.

The skill of the opponent can also bias a player’s number of interceptions. A division loaded with bad quarterbacks may seem to have superhuman secondaries. Strange as it may seem, good defensive backs may also benefit if the division has better passers. Since they cover their receivers closely, it is easy for them to catch well-thrown passes. Wide receivers also have an effect. Other than catching passes, they are also the first ones to be able to tackle a back. This puts strong safeties at a disadvantage for touchdown returns. They typically cover the tight end, who is almost always the best tackler among the receivers.

Interceptions also depend on defensive teammates. Linemen and linebackers pressure the quarterback into misthrows by breaking through the line and threatening to sack him. Other players in the secondary can limit a quarterback’s options and force him to throw when his timing is off or to an inferior receiver. The position a player plays often changes interception results. As we have seen, strong safeties rarely return interceptions for touchdowns since they cover tight ends. The free safety has more interception opportunities since he often guards receivers on deep passes, which are likely to lead to bad throws. Good players are disadvantaged since offenses try to throw away from them. Finally, note that interceptions are not always important plays. On fourth down they are not much better than an incompletion or a completed pass saved by a good tackle. Similarly a touchdown return makes no difference if a team is already ahead by twenty points.

The other most popular defensive statistic is sacks. This statistic is primarily designed to measure the performance of linemen and outside linebackers. While it is a better statistic than interceptions, it has many fundamental weaknesses that limit its use.

Sacks do have some advantages. Since they are more common than interceptions, they are less likely to vary from year to year. They also reflect skills other than just rushing the passer. Players with lots of sacks tend to be good at getting past the line on running plays and tackling backs. Players with sacks also harass quarterbacks into bad passes even when they don’t sack him. Tackles and ends that are good at rushing the quarterback pick up more fumbles. More general qualities are also reflected in sacks, since to tackle quarterbacks a player must be both big, to get past 300-pound linemen, and agile, to tackle smaller, faster quarterbacks.

Like interceptions, though, sacks also depend on the skill of other players. If the rest of the line is good, then additional linemen or running backs may be called up to help with the blocking. With fewer opposing players, it is easier to break through the line and get to the quarterback. The secondary also helps. If all the receivers are well covered, the quarterback keeps the ball longer since there is no good place to throw. This gives a lineman time to tackle the quarterback before he passes. Even the coaches can help a player accumulate sacks. A good scouting report will help players to determine where and when to rush.

Both sacks and interceptions have serious flaws. How can we design ways to evaluate defensive players without bias? One solution uses common team statistics to evaluate units, such as the secondary or the linebackers. These stats often correspond to the efforts and skills of a particular group of players.

The first of these statistics is a simple breakdown of points scored by opposing offenses. If high numbers of field goals are scored, this indicates clutch performance by the defense. Once the offense threatens to score a touchdown, the defense forces a field goal on fourth down. Takeaways on fourth down also reflect clutch ability. More specifically, high numbers of touchdowns can indicate weaknesses in the secondary. Touchdowns almost always depend on one or two long plays, which are usually the fault of the safeties.

Yards-per-scoring-drive helps analyze how much of a defense’s success is really due to its own play. The defense is obviously at a disadvantage if they have a weak offense. Then they tend to come onto the field when the opposing team has the ball in good field position. Yards-per-scoring-drive doesn’t work to evaluate a defense on its own, but it can help to identify when a defense is overrated or underrated.

Another team stat is the percentage of plays longer than fifteen yards on scoring and non-scoring drives. If a defense tends to allow a much greater margin on scoring drives, it indicates that offenses need big plays to succeed. This is a sign of a good defense. If there is very little difference, then offenses can score by consistently calling short plays. Defenses like this are weak against the run, so offenses use that approach against them. The percentage of plays longer than fifteen yards is very useful for evaluating the secondary. Since it is their job to make the tackle on long plays, this measures their ability both to read a play and their ability to tackle. If they tend to be good at defending against long passes, the percentage of plays longer than fifteen yards should be low. Running and passing statistics also help to evaluate parts of a defense. If the percentage of running plays for a loss is high, this reflects well on the skills of the line and linebackers, especially their rushing abilities. To measure the relative abilities of the defense, the percentage of running and passing plays called by the offense is an accurate statistic. This works especially well when several defensive players have been injured in the course of the season. Then the percentage called can be compared to the offense’s overall average. From this, it is easy to see how this compares to before the injury. A big difference indicates that that player is good either against the run or the pass.

However, most of these statistics work only to evaluate groups of players. How can we rate individual players? Surprisingly, many good individual ratings branch off of interceptions and sacks. But since these stats are either more common, less biased because of teammate or opposition performance, or more representative of other skills, they provide an accurate assessment of a player’s performance.

Probably the best measure of a cornerback or safety’s skill is incompletions. These are similar to interceptions, but have many advantages. They are much more common and therefore they are less random and fluctuate less from year to year. Incompletions also depend less on the opponent’s skill. They are much more likely to be good defense than bad passes, which often hit the ground untouched. Thus, the quarterback is less important, as is the defensive line. Also, incompletions can occur anywhere on the field. It is as common to bat down a pass right in front of the pocket as it is to knock one away from a receiver. These plays depend only on individual abilities, not on the skills of others.

Another good statistic to measure backs is the number of yards that a receiver gains after a catch. Not only does this statistic measure tackling ability, it evaluates how closely a back covers a receiver. Close coverage is important because it saves yards on passing plays and puts a back in excellent position for an incompletion or interception. Raw tackles are also an effective statistic. Tackles measure how well a back reacts to the run and how often he is able to catch the ballcarrier. In addition, they show a safety or cornerback’s ability to make a quick tackle after a catch.

Incompletions are also an effective measure of linebackers. If he covers receivers, they measure his coverage ability. If an outside linebacker rushes the quarterback, sacks judge his ability to call the pass and knock it down right after it is released. This statistic reflects his ability to read the play as a pass and try to stop it. Tackles inside the line of scrimmage rate a player’s rush ability well. Not only is key-reading important, so is rushing the line and tackling the running back. Pursuit ability is also measured, if a chase goes on before the tackle.

Even defensive linemen can be measured by incompletions, for reasons similar to those for linebackers. If in a rare event they are called into pass coverage, it measures their pass coverage ability. They also occasionally knock down throws when rushing the quarterback, which requires timing and good rushing ability. Tackles are also a helpful statistic. They indicate skill on plays right at a lineman, as well as speed on plays in a different direction.

With the most popular defensive statistics, it is almost impossible to rate defensive players. As we have seen, sacks and interceptions have serious flaws. But it is not hard to accurately analyze defensive players. Individual statistics like incompletions and tackles coupled with team statistics to analyze groups of players can give an accurate statistical representation of a player’s skills.

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Comprehensive Ratings in Pro Football Monday, Aug 4 2008

December 2006

The most complicated statistic in pro football today is certainly Passer Rating, a measure of quarterback effectiveness. Although it does not include running, play calling, and other factors that contribute to a quarterback’s success, this is still a very helpful tool if used correctly. Also, it has a standard benchmark of superiority (100) that is easy to remember, a good feature in any statistic.

But what about the other offensive stars, running backs and wide receivers? They clearly deserve such sophisticated measures. This article features some of the author’s statistics in this line using yards gained and touchdowns.

For both positions, the main statistics that can be used are:

• Yards gained per attempt (for speed, ability, etc.)
• Yards gained (for durability, reliability)
• Touchdowns (for “ability to make the big play”, morale, etc.)

The key in Passer Rating is calculating the percentage of important stats including completions and touchdowns, but in this case, a simpler way might be to just divide by the league total. This way we also get an automatic adjustment to the league context and era. But then players from eras with less teams will have a significant advantage, which we don’t want. The obvious solution is to first divide the league total by the number of teams.

Now we just need to find what performance 100 should get. For running backs, 1,600 yards, 12 touchdowns, and 5.3 yards per attempt; for wide receivers 1,100 yards, 10 touchdowns, and 11.6 yards per reception. Both are good general benchmarks of superiority.

For running backs the overall formula is:

Yards + Yards per attempt + Touchdowns x 45

Yards _(L/T) Yards per attempt_(L/T) Touchdowns_(L/T)

(Note: (L/T denotes the average per team.)

Let’s use this statistic to compare Shaun Alexander in 2004 with Ahman Green in 2003:

Player	Yards/Att.	Yards	TD’s	Rating
Alexander 2004	4.8	1,696	16	148
Green 2003	5.4	1,883	15	150

At first glance, Green appears to be vastly superior to Alexander. He has more than half a yard more per attempt, and Alexander’s one touchdown advantage is hardly enough to overcome that. However, Runner Rating shows that it is actually closer then we might think: Green has only a slight lead.

Runner rating is hardly a tell-all statistic. It has weaknesses like limited playing time, playing surfaces, and experience, but if used correctly can be very powerful.

We can use a similar method to rate wide receivers. In this case, since teams generally use more receivers than running backs, the multiplying factor, instead of being 45, should be higher.

Yards + Yards per reception + Touchdowns x 57

Yards_(L/T) Yards per reception_(L/T) Touchdowns_(L/T

Now let’s use this to compare Darrell Jackson in 2003 with Torry Holt in 2004:

Year	Yards	Yards/Recep.	TD’s	Rating
Holt	1,372	14.6	10	118
Jackson	1,119	16.7	9	129

They seem very close. Jackson has a large edge in yards per reception, but Holt has more yards and touchdowns. Jackson has a much higher rating, though, because the pass was used less in 2003, and so he had a higher performance compared to the league.

These examples have shown that running backs generally have higher ratings then receivers or even quarterbacks. But this is realistic; running backs do have a higher value since they have more carries. Running back performance also depends more on individual skill more than do receivers and quarterbacks. It’s true that getting the right blocks helps a lot, but quick, accurate decision-making and speed are the majority of the job.

Passer rating is a very powerful statistic reflecting most of a passer’s qualities. Similar ratings can be created for receivers and running backs. By combining a few important measures of a player’s ability and multiplying, one gets a useful statistic.

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