by Michael David Smith

One of my goals as a football researcher is coming up with statistics that let us compare players from different eras. Professional football has changed so much through the years that standard statistics, such as yards or completions, don't do much to help us compare players in 2004 with players in 1934. When I tell you that Jim Brown gained 1,527 yards in 1958, you know that's good, but you don't know how good until I give you some context.

In an effort to address this problem, I'd like to introduce a new stat I'll call leader ratio. It's extremely simple, which means it has some serious limitations, but it also means anyone who attended elementary school should be able to understand it.

Leader ratio is simple: If a player leads the league in a statistic (we'll use rushing yards for the purposes of this article), you divide his total yards by the total yards of the player who came in second. In 1958, when Jim Brown led the league with 1,527 yards, the second-best rusher was Alan Ameche with 791 yards. So that gives Brown a leader ratio of 1.93, which happens to be the best in the history of pro football.

To figure the leader ratio of a player who didn't lead the league, we just switch the dividend with the divisor. So Alan Ameche's leader ratio would be 0.52. (A player who exactly doubled the second-place finisher would get a 2.00; the second-place finisher would get a 0.50.) A limitation is that we're just measuring one statistic at a time, in this case rushing yards. But we could do leader ratios for other positions and other statistics, and if you want to get an idea of who the best run-catch threat as a running back is, you could simply add his rushing leader ratio with his receiving leader ratio. With receiving, it would make more sense to separate running backs from wide receivers.

Let's say we want to compare Jim Brown of 1958 with a player in 2003. Using the traditional statistic of rushing yards, Brown would rank just below Fred Taylor, who had 1,572 yards last year. But, of course, we know it's easier to get 1,500 yards now than it was half a century ago. When we compare Taylor's performance to league leader Jamal Lewis's 2,066 yards, we get a leader ratio of 0.76. Here's how the top 10 rushers of 2003 compare in leader ratio:

Knowing the leader ratio for 2003 doesn't tell you as much about a running back as knowing his DPAR, which is the statistic by which Football Outsiders ranks running backs. But we can only figure DPAR if we have complete play-by-play logs for every game of an entire season, and it seems unlikely that that will ever happen for the majority of the sport's history. So leader ratio is most useful if we want to get an idea of how well players of the past did in their own eras. And no one should be surprised that the best of them all is Jim Brown. Here are Brown's numbers for his entire nine-year career:

Brown led the league in rushing eight of his nine seasons; Jim Taylor was second four of those years and was the only other running back to lead the league during the Brown era. Adding the leader ratios from Brown's nine seasons, he has a career leader ratio of 12.31, which, no surprise, is the best ever. It's truly amazing to compare Brown to the other runners of his era. He rushed for more than 1,500 yards three times; no one else did that until O.J. Simpson got 2,003 in 1973.

Brown has three of the seven all-time leader ratios better than 1.5. The others belong to Simpson, who had 1.75 in 1973, Cliff Battles, who had 1.58 in 1937, Joe Perry, who had 1.54 in 1954, and Steve Van Buren, who had 1.50 in 1947.

Let's take a look at Simpson's leader ratios:

It's hard to believe now, but O.J. Simpson was considered something of a bust after three seasons. It wasn't until new coach Lou Saban decided to make him the focus of the offense in 1972 that he really flourished. And after Saban left in the middle of the 1976 season, Simpson rapidly declined. By his last two seasons he was a washed-up, injured backup in San Francisco. He finished with a career leader ratio of 8.98.

As one would expect, top leader ratios have dropped a bit since the NFL went to the 16-game schedule in 1977. With a larger sample size we don't see as many outliers, but here are the six leader ratios of 1.2 or better in 16-game seasons:

Barry Sanders was remarkably consistent in his leader ratio, never going below 0.74 or above 1.22. That 0.74 represents the best "worst season" any running back ever had. Sanders twice got 0.99 and twice got 1.01, and his career leader ratio is 9.52. Here's how his career looks:

Eric Dickerson started his career with a fury. His first seven seasons looked like this:

That's a total of 7.60 in seven years. It doesn't quite measure up to Jim Brown's total of 9.29 in his first seven years, but it's still quite an accomplishment. (Please note that in 1987, I eliminated the three games that included replacement players, which means league leader Charles White, who crossed the picket line, falls behind both Dickerson and Curt Warner.) Unfortunately, Dickerson battled injuries and never even got up to 0.50 in his last four seasons.

As for the league's all-time leading rusher, Emmitt Smith's career looks like this:

That's a career total of 10.61. I was surprised he was that far ahead of Sanders, although he's still significantly behind Brown. And finally, let's take a look at Walter Payton:

People often forget that Payton, although he retired as the all-time leader in rushing yards, only led the league in rushing once. Smith passed Payton's career leader ratio of 10.50 last year.

I realize that I've dealt here only with Hall of Fame running backs. Perhaps it would help to illustrate leader ratio if we look at a player who had a solid but unspectacular career. Here are the numbers for Greg Bell, who played for the Bills, Rams and Raiders:

Bell gets a career mark of 2.93, which should give you an idea of what kind of career numbers a mediocre back will end up with.

An obvious limitation of leader ratio is that it counts only the league leader and how he compares with the second-place finisher. In 1992, for instance, Emmitt Smith had 1,713 yards, while Barry Foster had 1,690 yards. That gives Smith a leader ratio of 1.01 and Foster a leader ratio of 0.99. But it doesn't take into account that they both had a large margin over the No. 3 ground gainer, Thurman Thomas, who had 1,487 yards for a leader ratio of 0.87. That's a weakness of the statistic, but it still gives us an idea of how well a player performed against the other top players of his era. And when we're trying to compare players from different eras, that's all we can do: Examine how they did against their competition, and try to normalize the stats accounting for how the game has changed. What we have here is a first step toward doing that.

Posted by: Michael David Smith on 08 Mar 2004

1 comment, Last at 02 Nov 2005, 9:48pm by Tom T.