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Taylor, Brown, and Simpson (the Paradox, not the Juice)

Posted by Jason Lisk on August 4, 2009

Jim Brown is universally recognized as the best running back of all-time. Jim Taylor is in the Hall of Fame as well, but is probably not as well known by the modern fan. Brown checks in at #1 all-time on Chase's Rushing Value list, with Taylor at #16. The two men were contemporaries, with Taylor born about five months before Brown, and Brown entering the league in 1957, one year prior to Taylor.

Here are the per game rushing yards for Jim Taylor and Jim Brown from the 1960-1965 regular seasons. We have rushing game logs back to the 1960 season, and Jim Brown retired after the 1965 season.

Jim Brown: 103.8 rushing yards per game
Jim Taylor: 83.0 rushing yards per game

Jim Taylor has a pretty impressive rushing average (that would equate to averaging over 1,300 rushing yards over a modern 16 game season, for six seasons), but we see that Jim Brown's numbers are other-worldly, and far in excess of Taylor's numbers. So where does the Simpson's reference come in? It is referring to Simpson's paradox, first discussed by Doug back in this post.

As some of you may know, I have been doing a lot of work on the early 1960s in regard to my AFL versus NFL series. I was generally aware of some imbalance between the NFL Western and Eastern Divisions from the decade of the 1960s. Then, Doug, Chase and I were having some recent discussions about schedule adjustments (teaser alert--this may become part of an upcoming series by Chase), and we noticed some pretty significant schedule adjustments for NFL quarterbacks in the 1960s. For those that don't know, back then the NFL Western and Eastern Divisions were very much like we might think of the AFC versus NFC today in regard to scheduling. Teams played almost all of their schedule within their division (or conference today) with a small percentage of games against the other division (or conference). In 1960, NFL teams played 10 division games, 1 game against the other division, and 1 game against the Dallas Cowboys expansion team. From 1961-1965, NFL teams played 12 division and 2 out of division games.

So, let's turn back to Brown and Taylor. We saw that Brown averaged over 20 yards more per game. Now, let's look at how each did against the respective divisions.

vs. NFL East teams
Jim Brown: 109.6 (70 games)
Jim Taylor: 102.0 (12 games)

vs. NFL West teams
Jim Brown: 74.2 (11 games)
Jim Taylor: 81.7 (68 games)

Now, it's not really a Simpson's paradox, it's more of a quasi-paradox. Jim Brown still had a higher average against the NFL East. Further, the NFL East for Taylor included games against Cleveland, while the NFL West for Brown included games against Green Bay. We do see, though, that Brown averaged 7.6 more yards per game against the East minus Cleveland, compared to Taylor against the East with Cleveland. Conversely, Taylor averaged 7.5 more yards per game against the West minus Green Bay, compared to Brown against the West with Green Bay. A large part of the difference between Brown and Taylor from 1960-1965, at least in terms of rushing yards, can be explained by the schedule each faced.

Brown averaged 4.04 yards per carry against the West, and 5.47 ypc against the East from 1960-1965. The West schedule was pretty balanced for Cleveland during that time, as they played each team at least once over that span and nobody more than twice. Brown had only three 100 yard rushing games out of eleven, and three games with 150+ total yards against the West out of eleven. It's a small sample size, but there is no reason to think it doesn't at least represent playing a cross-section of the NFL West over that period.

How bad was the NFL East versus the NFL West during Jim Brown's career? Well, it ranged from being near equal in a couple of seasons, to being downright lopsided in a few others. Jim Brown entered the NFL in 1957 and played his whole career with the Cleveland Browns and in the NFL Eastern Division. During that time, the NFL West Champion won seven out of nine NFL Championship games. Cleveland was a pretty good team for that entire nine year run. Cleveland went 7-10 (with an average margin of -4.4 points) against the NFL Western Division during Brown's career, compared to 71-24-5 against the other teams in the NFL Eastern Division.

Here is a quick summary listing each year of Brown's career, and the average score margin of the other Eastern Division teams against the Western Division, to get a sense of how Cleveland's division opponents stacked up against the West.

1957	- 1.1
1958	- 2.4
1959	- 6.0
1960	- 3.2
1961	- 3.8
1962	- 8.8
1963	+ 1.3
1964	-20.1
1965	-15.7

Just to be fair, Brown was a much better receiver (or at least more utilized) and adding in receiving yards would separate the two in terms of value. Jim Brown also had three dominant seasons before Taylor had his breakout in 1960, so Brown did it for longer. I'm not providing this to say Taylor was better. People might argue that Taylor had the advantage of Lombardi, and all of the other great players on the Packers. Taylor did play with a great offensive line, but as Chase showed yesterday, so did Brown. They ranked second and third among great running backs most helped by their offensive lines.

I think what it does illustrate is the importance of schedule. Brown is almost universally considered the best running back of all-time. How strong would that hold be if he had instead played his entire career in the NFL Western Division? I have no doubt that most great running back seasons are aided to some extent by the schedule --they are probably not facing the Steel Curtain defense week in and week out. Still, I suspect that Brown’s schedule adjustment is going to be greater than other top running backs. I would guess that he will still rank #1 all-time when Chase prepares his next version of Greatest Running Back of All-Time, with schedule adjustments, but it will interesting to see who gains on him.