LaDainian Tomlinson had one of the greatest rushing campaigns in the history of the NFL according to the WCSN Rusher Rating System.

## Neglected rushing

It’s a sign of just how passing-centric the NFL is that the league has had a passer efficiency rating since the 1970s and yet to this day still does not have a rusher efficiency rating. But considering the fact that the ground attack has almost as much effect on wins and losses as passing, it seems only right that we should be evaluating the performances of rushers as well as passers, if we desire to develop a more complete understanding of what happens in games.

Your friendly statheads at WCSN are always looking to fill needs, and since no one else has taken it upon themselves to create a rusher rating, we decided that the task had fallen to us.

Our criteria for a good rusher rating were straightforward:

- It must be simple.
- It must be elegant.
- It must be easily calculated from readily available statistics.
- It should be descriptive, not evaluative.

The first three criteria are easy to understand, but the fourth might need a bit of explanation.

There are plenty of rating systems out there that seek to quantify how “good” or “bad” a play, player, or team is. That was not the goal of this rating system. Trying to weight, in an absolute sense, just how “good” a touchdown is or how “bad” a fumble is would inevitably involve some kind of value judgment that someone was bound to take issue with. Rather, we sought strictly to rate rushing performances in a relative sense — that is, in relation to all other rushing performances — without making judgments as to what a player “should” or “should not” do.

## Methods

To accomplish this, we used much the same methodology that the NFL and NCAA used when creating their passer ratings all those years ago. We collected a large body of data — specifically, rushing statistics from the 2002 divisional realignment to the present — all of which was freely available on NFL.com, and distilled it down to the three statistical categories the NFL provides not only in season-by-season charts but also in weekly box scores: average yards per carry (Avg), touchdowns, and fumbles. This allows us to calculate not just year-to-date or career ratings, but also in-game ratings.

Because we were looking to create an efficiency rating, as opposed to a measure of raw output, we converted touchdowns and fumbles to touchdown percentage (TD%) and fumble percentage (FUM%).

To improve the accuracy of this rating as a realistic measure of performance for a typical running back, we only looked at rushers who had at least 100 carries in a season. This helped to prevent skewing of the averages by situational backs and backs who happened to have one or two superb games in relief. (Similarly, if we were creating a passer rating, we’d leave out punters who threw one pass for a touchdown all season and thus ended up with a perfect rating.) This left us with 501 rusher-seasons over 11 calendar years, more than enough for a reasonable sample size.

For each of the statistical categories, we calculated the average and set that equal to a rating of 50. We used a very stringent definition of “elite,” setting 100 on the scale to equal the mean plus two standard deviations. In other words, to attain a rating of 100 for a category, a rusher must be in greater than the 95th percentile; that is, he must do better than 95 percent of all other rushers. Similarly, we set 0 on the scale to equal the mean minus two standard deviations, roughly equal to the 4th percentile.

The ratings for each of the statistical categories was then weighted by principal component analysis to better reflect the effect on total variation, *not *to make a value judgment as to “goodness” or badness.” The average of the weighted ratings was calculated and then adjusted as follows to give the final rating for the rusher:

A rushing performance that is exactly average in all three categories — Avg, TD% and FUM% — is rated 50.0. A performance that averages above the 95th percentile in all three categories will have a rating of 100.0 or above. A performance that averages below the 4.5th percentile in all three categories will have a rating of 0.0 or below.

This rusher rating differs from the NFL passer rating and resembles in the NCAA passer rating in that it is not capped; it is bound only by the physical constraints of the field. The maximum possible rating is 1,393.17, which equates to an average of 99 yards per carry, one touchdown per carry, and no fumbles. The lowest possible rating is -1,416.45, which equates to an average of -99 ypc, no touchdowns, and one fumble per carry. Needless to say, while it’s theoretically possible we could see a maximum rating, never in the history of the league has a rusher run all the way from the opponent’s one-yard line to his own end zone, so it’s not likely we’ll ever see anything close to the lowest-possible rating. It would take a dreadful performance for a rusher to even earn a rating below zero, although it has happened.

## WRR formula

The final formula looks like this:

[latex]14.19A+3.95T -9.64F -11.639 [/latex],

where A = YPC, T = TD%, and F = FUM%.

The formula is quite simple and can be plugged easily into a spreadsheet to calculate rusher ratings for a game, a season, or a career.

Now that we’ve laid out the technobabble behind the formula, let’s see the formula in action.

## How it stacks up

The following table lays out the top ten rusher ratings for running backs with at least 300 carries in a season since the 2002 divisional alignment.

Rank | Year | Player | Team | Att | Yds | Avg | TD% | FUM% | WRR |

1 | 2006 | LaDainian Tomlinson | SD | 348 | 1,815 | 5.2 | 8.0 | 0.6 | 88.39 |

2 | 2002 | Priest Holmes | KC | 313 | 1,615 | 5.2 | 6.7 | 0.3 | 85.57 |

3 | 2003 | Priest Holmes | KC | 320 | 1,420 | 4.4 | 8.4 | 0.3 | 81.11 |

4 | 2012 | Adrian Peterson | MIN | 348 | 2,097 | 6.0 | 3.4 | 0.9 | 78.81 |

5 | 2010 | Rashard Mendenhall | PIT | 324 | 1,273 | 3.9 | 11.0 | 1.0 | 77.51 |

6 | 2005 | Shaun Alexander | SEA | 370 | 1,880 | 5.1 | 7.3 | 1.4 | 76.53 |

7 | 2010 | Arian Foster | HOU | 327 | 1,616 | 4.9 | 12.0 | 3.0 | 76.37 |

8 | 2009 | Chris Johnson | TEN | 358 | 2,006 | 5.6 | 3.9 | 0.8 | 75.19 |

9 | 2007 | LaDainian Tomlinson | SD | 315 | 1,474 | 4.7 | 4.8 | 0.0 | 73.86 |

10 | 2003 | LaDainian Tomlinson | SD | 313 | 1,645 | 5.3 | 4.2 | 0.6 | 73.81 |

With even a quick glance at the table, two things stand out immediately: The first is how few names are on it. LaDainian Tomlinson occupies three slots, while Priest Holmes occupies two, indicating an impressively sustained level of success. The second is how low the top rating is. No one comes even close to breaking 100, which shows just how difficult it is to attain such a lofty rating. This is a good thing, in that it indicates the rating will not become easily inflated and outdated the way the NFL’s passer rating has in recent years.

An astute observer might also notice that there are two 2,000-yard seasons represented in the top ten. Considering an efficiency rating like this inevitably favors third-down and situational backs, who have more opportunities to steal touchdowns and fewer chances to fumble or be stuffed in the backfield, that shows just how remarkable Adrian Peterson’s 2012 and Chris Johnson’s 2009 campaign really were.

Tomorrow we will look at rushing efficiency trends leaguewide over the past decade and also test the rusher rating system some of the greats like O.J. Simpson and Eric Dickerson.