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08 Mar 2004

Introducing Leader Ratio

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:


Player Yards Leader Ratio
Jamal Lewis 2066 1.10
Ahman Green 1883 0.91
LaDainian Tomlinson 1645 0.80
Deuce McAllister 1641 0.79
Clinton Portis 1591 0.77
Fred Taylor 1572 0.76
Stephen Davis 1444 0.70
Shaun Alexander 1435 0.69
Priest Holmes 1420 0.69
Ricky Williams 1372 0.66

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:


Year Yards Top non-Brown Yards Leader Ratio
1957 942 Rick Casares 700 1.35
1958 1527 Alan Ameche 791 1.93
1959 1329 J.D. Smith 1036 1.28
1960 1257 Jim Taylor 1101 1.14
1961 1408 Jim Taylor 1307 1.08
1962 996 Jim Taylor 1474 0.68
1963 1863 Jim Taylor 1018 1.83
1964 1446 Jim Taylor 1169 1.24
1965 1544 Gale Sayers 867 1.78

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:


Year Yards Top non-Simpson Yards Leader Ratio
1969 697 Dickie Post 873 0.80
1970 488 Larry Brown 1125 0.43
1971 742 Floyd Little 1133 0.65
1972 1251 Larry Brown 1216 1.03
1973 2003 John Brockington 1144 1.75
1974 1125 Otis Armstrong 1407 0.80
1975 1817 Franco Harris 1246 1.46
1976 1503 Walter Payton 1390 1.08
1977 557 Walter Payton 1852 0.30
1978 593 Earl Campbell 1450 0.41
1979 460 Earl Campbell 1697 0.27

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:


Year Player Yards Leader Ratio
1977 Walter Payton 1852 1.45
1980 Earl Campbell 1934 1.32
1992 Emmitt Smith 1713 1.27
1984 Eric Dickerson 2105 1.25
1994 Barry Sanders 1883 1.22
1986 Eric Dickerson 1821 1.20

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:


Year Yards Top non-Sanders Yards Leader Ratio
1989 1470 Christian Okoye 1480 0.99
1990 1304 Thurman Thomas 1297 1.01
1991 1548 Emmitt Smith 1563 0.99
1992 1352 Emmitt Smith 1713 0.79
1993 1115 Emmitt Smith 1486 0.75
1994 1883 Chris Warren 1545 1.22
1995 1500 Emmitt Smith 1773 0.85
1996 1553 Terrell Davis 1538 1.01
1997 2053 Terrell Davis 1750 1.17
1998 1491 Terrell Davis 2008 0.74

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


Year Yards Top Non-Dickerson Yards Leader Ratio
1983 1808 William Andrews 1567 1.15
1984 2105 Walter Payton 1684 1.25
1985 1234 Marcus Allen 1759 0.70
1986 1821 Joe Morris 1516 1.20
1987 1288 Curt Warner 985 1.31
1988 1659 Herschel Walker 1514 1.10
1989 1311 Christian Okoye 1480 0.89

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:


Year Yards Top non-Emmitt Yards Leader Ratio
1990 937 Barry Sanders 1304 0.72
1991 1563 Barry Sanders 1548 1.01
1992 1713 Barry Foster 1690 1.01
1993 1486 Jerome Bettis 1429 1.04
1994 1484 Barry Sanders 1883 0.79
1995 1773 Barry Sanders 1500 1.18
1996 1204 Barry Sanders 1553 0.78
1997 1074 Barry Sanders 2053 0.52
1998 1332 Terrell Davis 2008 0.66
1999 1397 Edgerrin James 1553 0.90
2000 1203 Edgerrin James 1709 0.70
2001 1021 Priest Holmes 1555 0.66
2002 975 Ricky Williams 1853 0.52
2003 256 Jamal Lewis 2066 0.12

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:


Year Yards Top non-Payton Yards Leader Ratio
1975 679 O.J. Simpson 1817 0.37
1976 1390 O.J. Simpson 1503 0.92
1977 1852 Mark van Eeghen 1273 1.45
1978 1395 Earl Campbell 1450 0.96
1979 1610 Earl Campbell 1697 0.95
1980 1460 Earl Campbell 1934 0.75
1981 1222 George Rogers 1674 0.73
1982 596 Freeman McNeil 786 0.76
1983 1421 Eric Dickerson 1808 0.79
1984 1684 Eric Dickerson 2105 0.80
1985 1551 Marcus Allen 1759 0.88
1986 1333 Eric Dickerson 1821 0.73
1987 533 Eric Dickerson 1288 0.41

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:


Year Yards Top Rusher Yards Leader Ratio
1984 1100 Eric Dickerson 2105 0.52
1985 883 Marcus Allen 1759 0.50
1986 377 Eric Dickerson 1821 0.21
1987 86 Eric Dickerson 1288 0.07
1988 1212 Eric Dickerson 1659 0.73
1989 1137 Christian Okoye 1480 0.77
1990 164 Barry Sanders 1304 0.13

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.

Comments

1
by Tom T. (not verified) :: Wed, 11/02/2005 - 9:48pm

My Dad posed an interesting question to me. What teams had two one thousand yard rushers in the same season? Who were the running backs and who did they play for?