Sports and STEM

# How NFL Statistics Lead to Wins, Pt. 2: Quantifying Player Stats into Wins

Zach FeinAnalyst IMay 28, 2009

In Part I of this series, we saw how various stats correlated with wins and points scored. Among the observations:

Rushing attempts correlate better with wins than do passing attempts, because teams with the lead will rush the ball to run out the clock late in the game; but passing statistics—including yards and touchdowns per pass attempt—lead to wins more than rushing stats per attempt do.

Tackles have a negative correlation with wins, meaning that as tackles go up, wins go down. This is possibly due to the fact that worse teams have less three-and-outs and are on the field on defense longer than better teams; however, if we normalize this by dividing tackles by opponent plays from scrimmage, we get no significant results—solo tackles per play have a -0.18 correlation with wins, and that correlation is only -0.05 using tackles per play.

Special teams have relatively no effect on team wins.

You can find a table with every one of the 127 stats I took from Pro-Football-Reference and its correlation with wins, points scored, points allowed, yards, and yards allowed here. I also included the difference in each stat for every team, such as points scored minus points allowed.

REGRESSION

Correlation is a fine measure of how important a statistic is in terms of wins or points or yards.

What it doesn’t tell you, however, is how many wins a stat is worth to a team. Using a regression, we can find out the number of wins a team adds to its record by completing an extra pass, or throwing an extra touchdown, or intercepting the opposing quarterback once more.

A regression spits out an equation to estimate a set of values (team wins, in this case) based on independent variables (in this case, a team’s stats). In Part I, I went over this in greater detail.

The regression included 14 reasonable player stats: completion percentage, passing touchdown percentage, interception percentage, net yards per attempt (pass yards minus sack yards divided by attempts plus sacks), rushing yards per attempt, rushing touchdown percentage, and fumble rate (fumbles divided by completions plus sacks plus rush attempts), all for both offense and defense.

I neglected to add stats such as points scored and allowed because they only add up at the team level and not the player level; they can be estimated for players as touchdowns multiplied by six or seven, but in the end, you’d be counting touchdowns twice (for points and touchdowns, obviously).

The table below shows the results of the regression in terms of wins. The first column represents the actual number of wins each stat is worth. The second represents the coefficient after standardizing each stat; this column shows the relative value of each stat compared to all the others.

The equation ends up like so: Wins = O Comp % x 1.34 + O Pass TD % x 45.98 + … + 8.02.

The regression equation says that for every extra point added onto completion percentage, you add 0.0134 wins, and so on. (One full point—which would make the completion percentage about 1.60, an impossible number—is 1.34 wins, and in this situation, every point is equal to one hundredth of a full point; 1.34 divided by 100 is 0.0134. For all the percentage stats, it’s easier to look at it this way than by the actual coefficient.)

We can look at the equation in simpler terms by converting the percentages into totals. The average team last year attempted 516 passes and completed exactly 61 percent of them. To complete 62 percent, the average team would have had to complete 5.16 more passes than they actually did. We can then say that 5.16 completions equals .0134 wins, or that 385 completions equals one full win.

(Note: This means that you would have had to complete 385 more passes in the same amount of attempts to equal one win—not that completing 385 of the next 385 attempts equals one win. That would be impossible to do using last year’s average stats, but that just shows how unimportant completion percentage is to wins.)

Using this technique, we can find how many of each stat equals one win.

Look at it this way: A team completely average in everything—same number of pass attempts, completions, etc.—will win eight games. That same exact team, but with 11 more touchdowns, will win nine games.

INTRODUCING WINS ABOVE AVERAGE

With the exception of video games, the idea of player ratings for the NFL has never been sold to the general public. You’ve got passer rating and…fantasy points? There’s no definitive stat that ranks running back, wide receivers, or even quarterbacks. (Passer rating is flawed. The weights are unbalanced and completely arbitrary, and since the league average rating increases almost every year, you can’t compare past generations.)

Think about this: Which quarterback’s statistics are better—Quarterback A, who throws for 4,500 yards, 35 touchdowns, 20 interceptions, and a completion percentage of 60 percent; or Quarterback B, who throws for 3,800 yards, 27 touchdowns, 10 interceptions, and a completion percentage of 67 percent?

Or how about this: Running Back A, who runs for 1,500 yards and 10 touchdowns; or Running Back B, who has 1,200 rushing yards and 12 touchdowns in 50 less attempts?

Quarterback B has a better passer rating than Quarterback A, and Running Back B is slightly better on a per-carry basis than Running Back A. But Quarterback and Running Back A have more fantasy points than their counterparts, and in this fantasy-crazy world, chances are they may be labeled as the better players.

With the lack of useful, comparative stats available, we can never quantify how much better one player is than the other.

With the regression equation above, however, we can.

We saw that completion percentage is worth 1.34 wins, passing touchdown percentage is worth 45.98 wins, and so on. Thus, we can estimate player wins as 1.34 x completion percentage + 45.98 x touchdown percentage + … — 33.20 x fumble rate.

For wide receivers (and running backs’ receiving stats), we use targets as “attempts,” and receptions as “completions.” The coefficients of the passing statistics stay the same, so for a receiver, the equation for wins can be estimated as 1.34 x (receptions ÷ targets) + 45.98 x (touchdowns ÷ targets) — 33.20 x fumble rate.

But there’s one caveat: We must account for the fact that a receiver’s targets do not solely comprise a team’s 500-plus pass attempts. Once we find a receiver’s unadjusted wins, we multiply that number by the percentage of attempts that were targeted to the receiver (or, targets ÷ team pass attempts).

We can express wins as points or point differential as well. Since it takes about 34.5 points to make a win (see end of article for details), we can multiply wins by 34.5 to find how many points a player has created; or, equally, wins above average multiplied by 34.5 equals points above average.

If we divide the latter number by 16, we find how many points that player adds over the average player at his position per game. In other words, if you were to take a team full of average players that scores 21 points per game, and swap that team’s running back for one that is four points above average per game, they would score 25 points per game after the switch.

I have also used these ratings to show which players were underpaid or overpaid last year, using salary earned based on individual wins. For quarterbacks, each win was worth \$0.75 million; for running backs, \$1.70 million; and for wide receivers, \$1.72 million. These numbers were found by dividing the combined salary of all qualifiers (200 pass attempts, 100 rush attempts, and 40 receptions) by the total number of wins between them.

QUARTERBACKS

Without further ado, here are the wins above average for every quarterback with 200 attempts last year. I took player wins and subtracted 8.10, the average for the 34 quarterbacks.

Here’s a simple explanation to wins above average: Philip Rivers, for instance, is 2.65 wins above average. If you take a team full of average players (as in the example for points above average per game), and swap their quarterback for Rivers, they would win 10.65 games—the eight prior to the switch plus the 2.65 added on by Rivers.

(That may be not fully correct, though; Rivers is benefited from playing with one of the best running backs in the game in LaDanian Tomlinson, as well as Vincent Jackson and Antonio Gates. The figures shown below are not team-independent, per se, as it’s nearly impossible to separate Rivers from his receivers, running backs, coaching staff, or playbook.)

For quarterbacks, fumble rate was defined as fumbles ÷ (incompletions + sacks + rush attempts). I included rushing yards, but took out rushing touchdowns because some quarterbacks—such as Kyle Orton, who has three rushing touchdowns in 24 attempts—have such high rushing touchdown rates that it completely skews their wins total; as well, most quarterback rushing touchdowns are from inside the five-yard-line and are a result of other factors that lead the possession to the five—e.g., the quarterback’s passing, the rushing game, penalties, or good field position resulting from a defensive stop.

Two names that stand out are Tony Romo and Kurt Warner, Nos. 14 and 15. Their inability to hold onto the ball (over 11 fumbles for each of them) knock off 1.8 wins from Romo’s total and 1.5 from Warner’s. In fact, if I disregarded rushing stats altogether, Romo and Warner would be Nos. 3 and 4, respectively; their rushing drops them both 11 spots.

The three most underpaid quarterbacks last year were Matt Cassel (paid \$5.87 million less than he deserved), Tyler Thigpen (\$5.85 million), and Seneca Wallace (\$5.39 million).

Ben Roethlisberger (paid a whopping \$22.9 million more than he deserved), JaMarcus Russell (\$11.3 million), and Brett Favre (\$7.09 million) were the three most overpaid quarterbacks in 2008. Roethlisberger was the highest-paid player from any position last year, and JaMarcus Russell just showed how badly the league needs a rookie wage scale.

RUNNING BACKS

Third—that’s where LenDale White would have ranked if wins were calculated just as the regression showed.

Sixth—that’s where Tim Hightower would have ranked if wins were calculated just as the regression showed.

You can see where this is heading. Because the regression equation placed so much emphasis on rushing touchdowns, backs that get the load of the red zone carries for their team—such as White, Hightower, and Brandon Jacobs—would place among the league’s best.

Rushing touchdowns are a valuable measure at the team level, but not at the player level, in which the Mike Alstotts of the world can earn nine or ten wins from their touchdown percentage alone. (Alstott’s six touchdowns in 34 attempts in 2005 would have been worth 9.8 wins.)

The solution to this is to find the percentage of his team’s total rushing touchdowns that a running back’s touchdowns make up, and then multiply this figure by the number of wins created by a back’s rushing touchdowns (55.71 x touchdowns ÷ attempts). Add this to the rest of his wins, and subtract 2.15 wins—the average for those with 100 rush attempts—and you have wins above average.

Fantasy football owners will recognize Pierre Thomas’s name at No. 7. Thomas had a touchdown in each game and over 100 total yards in all but one from Weeks 11 to 16. He averaged 17 touches for 113 total yards per game, with a total of nine touchdowns and one fumble during the stretch.

Adrian Peterson and his league-leading 1,760 rushing yards rank No. 30 and below average. Let’s go through each stat one-by-one to see why.

Yards per carry: Peterson had a 4.85 YPC, good for 1.31 wins. The average of the 49 backs with 100 attempts was 4.21, or 1.14 wins. Peterson is +0.17 wins so far.

Rushing touchdowns per carry: Peterson had 10 rushing touchdowns in 363 attempts; the league average, prorated to 363 attempts, was just over 12 touchdowns. But including the fact that the Vikings had less rushing touchdowns than the average, Peterson gained 0.24 wins over the average. He’s now at +0.41 wins.

Fumble rate: Peterson fumbled nine times in 384 attempts and receptions. In that many fumble chances, the league average back would have fumbled 4.1 times, half of Peterson’s total. Peterson’s minus-0.78 wins from his fumble rate means he was 0.42 wins less than the league average. He’s at minus-0.01 wins.

Receiving: Peterson averaged just 3.9 receiving yards per target, had no receiving touchdowns, and caught 54 percent of his targets. His receiving game earned him just 0.35 wins, or 0.27 wins below league average. All combined, Peterson was 0.28 wins below average in 2008.

DeAngelo Williams (worth \$5.45 million more than his actual salary last year), Pierre Thomas (\$4.80 million), and Maurice Jones-Drew (\$4.74 million) were the three most underpaid running backs last year.

The three most overpaid were Michael Turner (whose production was worth \$11.3 million less than he actually received), Marion Barber III (\$8.90 million), and Steven Jackson (\$8.04 million).

The standard deviation of the 49 running back’s wins above average is 0.78, while for quarterbacks it is 1.27. That suggests that running back production is more tightly packed than quarterbacks, and that there’s a steeper drop-off for quarterbacks than running backs.

Wide receivers were explained in greater detail above. Here’s how the 59 wideouts with at least 40 catches rank.

According to their wins above average, the most underpaid receivers last year were Roddy White (paid \$6.31 million less than what he actually “earned”), Greg Jennings (\$4.98 million), and Vincent Jackson (\$4.75 million).

Larry Fitzgerald (deserved \$11.3 million less than his actual salary), Randy Moss (\$9.33 million), and Terrell Owens (\$8.81 million) were the three most overpaid.

Now, that isn’t to say those three were actually that bad. If you graph actual salaries against worth, you find that actual salary drops three times faster than worth. For instance, the fifth-highest salary was \$11.82 million, but Larry Fitzgerald—who was No. 5 in WAA—was worth only \$5.73 million. This is because deserved salary based on WAA is linear (in that you multiply WAA by a constant to get worth) and not exponential.

In addition, Fitzgerald is hurt by the fact that wins are found by adjusting for team pass attempts. If every wideout’s team had 516 attempts (the league average), Fitzgerald would have ranked No. 1 in wins above average, but would have been worth only \$6.91 million because of linear calculation.

In Part III of this series, I’ll apply individual wins and worth to the team level to see which teams are the most cost-efficient and get the most production out of their payroll.

How did I come up with 34.5 points?

The simple answer: Take a team that both scores and allows 21 points per game. Using the Pythagorean formula—which estimates a team’s record based points scored and allowed—they’d be expected to win eight games no matter what exponent you use (2.37, 2.64, or a floating exponent based on total points per game).

Now, if you add 34.5 points to that team’s points scored, you get about 23.16 points scored and 21 points allowed per game. Run them through the Pythagorean formula, and you exactly nine wins.

(In the second scenario, the exponent I used was (total points scored and allowed per game)0.25, which yields better results than any other exponent.)

The complex answer: The formula to find points per win is PPW = 2 x (Pts-PtsAll) x (Ptsx + PtsAllx) ÷ (Ptsx — PtsAllx), where x is the floating exponent as given above and points and points allowed are per game. That equation comes from David Smyth and Patriot.

I applied this equation to every team season since 1994, and the average points per win was 34.3; the median was 34. I stuck with 34.5 after performing the test above.

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