They say age ain’t nothing but a number.

Twenty-one, 26, 31—what’s the significance? Is age merely just a number, or a baseline for seasonal performance? How can we quantify this?

Aging curves—also called aging patterns or age factors—show the relative performance of a group of players for each age, usually either showing how much (in percentage terms) a statistic improves or declines from one age to the next, or how the production at any age compares to the peak age.

One method used for aging curves it to simply add up the stats for every player at each age and look at the resulting sums. This is flawed, however, for it doesn’t account for the fact that there are many more players at age 24 than at age 34—the difference in yards or touchdowns per attempt won’t offset the disparity in attempts.

You can solve this problem by dividing the sum by the number of players at that age, right? Well, technically, yes, but it’s still not enough.

There’s selective sampling issues using this technique: The players who rack up attempts or receptions at age 21 or 22—their rookie season—are usually the best players, and thus it would appear that a player’s first year or two is one of their best.

At 35 and 36, the only guys left are the ones who have had a very successful first 12 years of their career and, as a whole, are typically better than the average player at age 24 or 25...and thus, it would appear that a player also peaks very late in his career.

The solution is to look only at matched pairs: how each player performs from one year to the next. Instead of comparing the average production at age 24 to age 25, you see how those 24-year-olds do the very next year. This way, you are looking at the same players in back-to-back years; previously, not every player was the same in each sample.

So, if those set of 24-year-olds have a completion percentage of 60 percent, and at age 25 that rises to 63 percent, we are fairly certain that completion percentage is 1.05 times higher (63 divided by 60) at age 25 than at age 24.

But we’re forgetting the most important principle at hand: regression to the mean. Observed production is equal to a player’s true talent, plus luck or random noise. What we are trying to do is to eliminate that noise, because, in general, that luck goes away in the next year. (For instance, running backs with over 1,000 yards since 1980 average 6.23 yards per game less the following year, almost 100 yards in a full season.)

We want to regress a player’s Year X stats, but leave the Year X+1 stats alone. The question is, how much should we regress? I found that a quarterback with 512 attempts, a running back with 439 attempts, and a wide receiver with 45 receptions should have their yards per attempt or reception regressed 50 percent to the mean; there are different rates for completion percentage and the like, and the more attempts or catches a player has, the less he’ll be regressed.

Normalize each player’s two years based on the league average, and we’re finished.

Let’s see how these aging curves stack up for each position.

(Note: My data sample ran from 1980 to 2007. I looked at quarterbacks with 50 attempts, running backs with 30 attempts, and wide receivers with 20 receptions in Year X, no matter how many they had in the next year, because I weighed each of the players’ two years by the minimum number of attempts or catches in the back-to-back years. I excluded any players who switched teams mid-year or in the offseason.)

(Another note: Unless otherwise noted, aging curves shown are "chained" and then divided by the peak level. That is, if yards per attempt falls two percent every year from age 21 to age 30, then age 21 would be given a value of 1.00, age 22 would be 0.98, age 23 would be 0.98 x 0.98, or about 0.96, and so on until 0.834 at age 30. The numbers are then divided by the peak value, 1.00 at age 21. In other words, a player’s yards per attempt would be 83.4 percent of what it is at age 21.)

Quarterbacks

Some might say that a quarterback’s best years are in his mid-20s, pointing to common knowledge and the successes of Daunte Culpepper and even Marc Bulger. Others may bring up Tom Brady, Peyton Manning, Kurt Warner, and Brett Favre as guys who succeeded well into their 30s.

Who’s right?

To see this table in graphical form, click here . (The values are adjusted up or down slightly so the lines won’t collide.)

According to the table, a quarterback’s peak age is 25 for all but one of the stats, with 26 to 28 not far behind. There seems to be a steep, upward trend at the beginning of a quarterback’s career, and a gentler fall from their peak.

Notice how the curves of touchdowns and interceptions are much more extreme compared to completion percentage and yards per attempt, which have a moderate slope.

Not coincidentally, touchdowns and interceptions both have a worse year-to-year correlation than do completion percentage and yards per attempts—in other words, it’s more likely for a player to have abnormal numbers in TDs and INTs than in completions or yards.

A quarterback’s biggest statistical jump is from age 24 to age 25: Take a league-average 24-year-old, and the next year (in 450 attempts), he’ll add 1.6 points to his completion percentage, 67 passing yards, almost two touchdowns, and two-fifths of an interceptions.

That equates to 11 more fantasy points over the course of a season—or roughly the difference between the Nos. 13 and 19 quarterbacks last year.

Last year, Jay Cutler and Aaron Rodgers made the leap from their age-24 to their age-25 seasons. This year? Well, Brady Quinn is the only qualifying player who seems to have at least a part of the starting job locked up; Tyler Thigpen, Kevin Kolb, Drew Stanton, and Troy Smith round out the 25-year-olds.

Quinn showed some promise last year, throwing for 239 yards and two touchdowns in a Week 10 game against Denver (though he followed that up with 14 completions in 36 attempts for 185 yards at Buffalo). Think about picking Quinn late in your fantasy draft, and it could pay off.

Age isn’t the only way to split up quarterbacks; experience matters, too. Although an "experience curve" looks roughly the same as an aging curve, we see that rookie quarterbacks have a major increase in production to their sophomore season. (So much for the sophomore slump.)

Rookies had a four percent increase in completion percentage and yards per attempt, a five percent increase in touchdown percentage, and an eight percent decrease in interception percentage.

Both Matt Ryan and Joe Flacco would see a 10-point increase in fantasy points if those percentages held up. Those 10 points wouldn’t have moved Ryan up in his rank among QBs last year (in terms of fantasy points), but it would have moved Flacco from No. 19 to No. 14, right behind Ryan.

Though Ryan and Flacco may regress to the mean, the increase from their second-year experience may offset that regression.

Running Backs

Few running backs have had the late-career outburst that John Riggins did. Riggins had just one 1,000-yard season through age 28, before a miraculous career turnaround that included four 1,000-yard performances in the next six seasons, not including his 533 yards in eight games in the strike-shortened 1983 season.

From age 22 to age 28, Riggins had 4,655 rushing yards and 28 touchdowns; Riggins had 2,000 more yards and almost 50 more touchdowns from 29 to 36 in the same amount of time (he skipped his age-31 season due to contract disputes).

Let’s see if that trend holds steady for every running back.

Click here for this table in a graph.

The vertical lines on the graph show the values at age 29 and 30. You can clearly see that each stat falls after a running back’s age-29 season, but is the myth that 30-year-old running backs see a dramatic decline any true?

Not really. Age-30 backs lose 1.26 percent off their yards per attempt (.937 divided by .949 in the table above, then subtracted from one) and 2.13 percent of their touchdown rate (.862 divided by .881 and subtracted from one)—a drop of 15 yards and one-fourth of a touchdown for a running back with 1,200 yards and 12 touchdowns.

To put it bluntly, don’t downgrade LaDainian Tomlinson, Brian Westbrook, Jamal Lewis, or Larry Johnson on your running back rankings because they are turning 30. That is, unless you’re afraid of losing less than three fantasy points over the course of a season.

Running backs tend to peak around 22 to 25, specifically at 23 and 24. Fantasy points per attempt seem to have, more or less, a triangular pattern from 21 to 26, but then it ever-so-slightly increases with no set pattern until age 32.

This can most likely be attributed to selective sampling. The longer a running back plays, the more chance for them to peak later in their careers, a la John Riggins.

In addition, if a guy is playing into his early-to-mid 30s, chances are he’s been productive late in his career; if a guy fades away at age 31, with, say, a drop of 500 rushing yards from his previous year, he’s going to get little carries the next year—if he isn’t retired by then.

Running backs have a very short period of increasing performance. Rushing yards per carry increase from 21 to 22, but decrease all but two of the next 11 years; touchdowns per carry increase from 21 to 23 but decrease four of the next five years.

Of course, the largest overall increase for a running back is between his age 22 and 23 seasons, in which his touchdowns go up almost 12 percent and fantasy points increase by 2.7 percent. (Rushing yards, however, decline by about 1.2 percent.)

Steve Slaton, Marshawn Lynch, and Kevin Smith headline this year’s age-23 class. That said, don’t expect a huge breakout: If we adjust each of their 2008 stats based on their expected increase, all of them would have a four- or five-point increase in fantasy points.

Neither Slaton nor Smith would have their rank among running backs in fantasy points changed, while Lynch would move up three spots from No. 15 to No. 12.

Thirty-two-year-old running backs had the biggest decline in production, losing 10 percent of their yards per carry, 16 percent of their touchdowns, and 12 percent of their fantasy points. This year, however, only two New England backs are turning 33: Fred Taylor and Kevin Faulk.

I think it’s safe to say that neither will perform as the top-10 backs you expected in May.

Wide Receivers

Conventional wisdom says that wide receivers have a longer peak than most other positions.

Take one look at the best receivers in the NFL today—Larry Fitzgerald, Randy Moss, Steve Smith, Reggie Wayne, Chad Johnson, to name a few—and it becomes clear that the best wideouts typically have numerous 1,000-yard seasons during their prime.

The numbers, unsurprisingly, back up this notion.

A graph of this data can be found here.

Wide receivers have the latest and longest peak of any skill position. Their best year is at age 27, but ages 24 to 30 aren’t far behind. In fact, in terms of yards per receptions, all but one of those six years (excluding age 27) are within one percent of the peak level.

In other words, a wide receiver with a true talent level of 1,000 yards in a constant number of catches will be within 10 yards of that level all but one year from 24 to 30. (He’d be within 13 yards in that one year.)

This also suggests that a receiver’s breakout or banner year is more reliable in establishing a new talent level compared to those of quarterbacks or running backs. (As well, receiving yards per catch has a higher year-to-year correlation than any passing or rushing stat.)

A receiver’s largest statistical jump unquestionably occurs from age 23 to age 24, when yards per catch increases by 3.2 percent and touchdowns per catch goes up 7.7 percent.

That means a receiver with 1,200 yards and seven touchdowns—who’d rank No. 12 among receivers in fantasy points—would gain almost 40 yards and half a touchdown (seven fantasy points), and would jump four spots to No. 8.

If you didn’t respect him before, it’s hard not to now: Calvin Johnson is turning 24. The second-year receiver finished fifth in the league in receiving yards with 1,331 and tied for first in receiving touchdowns with 12. In addition, Johnson’s average of 17.1 yards per catch was the second-highest of any receiver with 60 catches since 2006.

Applying the aforementioned age adjustments, Johnson gains over 40 yards and one touchdown to his already absurd statistics.

Another receiver turning 24 is Miami’s Ted Ginn Jr. The ninth pick in the 2007 draft, Ginn started 14 games last year and caught 56 balls for 790 yards, 570 more than his rookie season total. Ginn finished No. 33 among receivers in fantasy points last year, but most Web sites rank him around No. 40 for the upcoming season.

Ginn could beat out those prognostications by a large margin if the age-24 increase comes about.

Interestingly, both Johnson and Ginn are also entering their third season. We hear fantasy analysts claiming that receivers break out in their third season, because it takes two to acclimate to the NFL. Is this belief actually a renaming of the age-24 jump?

If so, the increase from a receiver’s second to third season would not be as large as the increase from age 23 to age 24.

And we see just that.

You can find a graph of this data here.

A receiver’s yards and touchdowns both peak in their third year—though that doesn’t necessarily confirm the myth. From their second year to their third, wideouts gain 1.4 percent to their yards and 4.2 percent to their touchdowns, compared to 3.2 and 7.7, respectively, from age 23 to age 24.

It appears as if the third-year wide receiver myth is actually the age-24 increase in disguise.