## What is a Hall of Fame Player Worth?

Posted by Jason Lisk on August 9, 2010

I was watching the Hall of Fame enshrinement ceremony for Dick LeBeau, John Randle, Russ Grimm, Rickey Jackson, Jerry Rice, Floyd Little and Emmitt Smith on Saturday and among all the accolades from the pre-ceremony commentators to the introductions to the speeches, it got me wondering, "what is a Hall of Fame player worth?"

I suppose one answer is "priceless", if you are a twelve year old boy who grew up watching one of your favorite stars. Players also may have value beyond what they bring to the field in productivity, in terms of goodwill, fanbase support, and franchise recognition. I want to try to focus, though, on how valuable they were compared to an average player during their careers. Of course, there is no prototypical Hall of Famer, as this year's class showed. We had a class that ranged from two of the all-time greats at their position, to others that were not as clear cut for choices in Canton. Positions may have different value in different time periods, and some may just be more valuable than others as well. Recognizing that the answer I may be seeking is only true in aggregrate and needs to be adjusted up or down based on position, era, and the quality of the player, I still tried to come up with an answer.

Before I get to what I did, what do you think a Hall of Famer is worth in terms of points per game, versus having an average NFL starter at the same position? Try to think of this in terms of the Hall of Famer's entire career, from rookie, to star in his prime, to maybe holding on for a few more years. Now, let's see if it is similar to what I came up with.

I looked at every team from 1970-1989, separately on the offensive and defensive side of the ball, and recorded how many Hall of Famers with a season approximate value of 5 or higher were on that unit. I chose 1970 because bringing in the 1960's would have brought in two competing leagues and rapid expansion, and I settled on 1989 at the other end to make sure we had teams that had no active players and most of the stars are in the Hall of Fame already.

I then recorded each team's simple rating system (SRS) rating for those seasons, so I could compare the number of Hall of Famers on a team with the points per game above or below the league average. Here are the results for all offensive teams:

HOF'ers | SRS avg | Team Total | Difference |
---|---|---|---|

0 | -1.69 | 242 | |

1 | 0.65 | 182 | 2.34 |

2 | 1.47 | 76 | 0.82 |

3 | 3.36 | 27 | 1.89 |

4 | 4.29 | 10 | 0.93 |

5 | 4.08 | 11 | -0.21 |

And here is the same table for defensive units:

HOF'ers | SRS avg | Team Total | Difference |
---|---|---|---|

0 | -1.09 | 313 | |

1 | 0.77 | 155 | 1.86 |

2 | 2.28 | 50 | 1.51 |

3 | 3.40 | 18 | 1.12 |

4 | 4.03 | 12 | 0.63 |

That difference column shows the difference between the average SRS for a team with N number of Hall of Famers versus one with N-1 Hall of Famers. When we weight those differences (since there are far more teams with exactly one Hall of Famer than three), we get an average difference of +1.79 points per game on offense, and +1.67 points per game on defense, per Hall of Famer.

I think that number is a good low end estimate. The method I used only looked at season totals, so while I set a low end limit of an approximate value of 5, we could have Hall of Famers who miss a few games with injury but still play most of the year, and since the value is based on the complete season SRS, it might undervalue them because the SRS was likely higher in games they actually played and did not miss with injury. If you wanted to round up to a nice integer, when considering that factor, I think we can say that the average Hall of Famer is worth about 2 more points per game than an average non-Hall of Fame starter over the course of his career.

Keep in mind, though, that number is the average for the entire career. Careers come in all sorts of shapes. I would estimate that the prime years are closer to a 2.5 to 3 points per game improvement versus an average starter, while seasons at the end or beginning may be much closer to average-some even below average.

What does 2 ppg translate to in terms of win percentage?

I suspect that the Hall of Famer is worth more than that -- I think you've simply looked at their effect on the side of the ball they play on, and not factored in the help they provided to the team as a whole. Jerry Rice or Emmitt Smith both increased their team's scoring, but they also decreased their opponents' scoring by keeping their offense on the field longer and giving their defense better field position when they gave up the ball.

Of course, that's a bit more difficult to calculate....

Jiffy, I didn't run the numbers specifically, but in this post by Doug on quarterbacks, he said that 2.3 points was almost exactly 1 extra win.

Jeremy, I can re-run the numbers with both sides of the ball. I'll try to do that later tonight. The teams that had a hall of famer on both sides of the ball are already accounted for in the estimate. For example, Mia 1972 had 5 on offense and Buoniconti on defense. If I look at overall SRS, it simply becomes the sum of those two numbers divided by 6, and the effect is the same. Now, we can see what it is for teams with HOF on only one side of the ball. Looking at the offenses with multiple HOF but with none on defense, I'm not sure total SRS will help the Air Coryell Chargers, the Dan Marino Dolphins, or the early 70's Jets.

Getting a HOF player can help you out draft-wise too. Look at the Dolphins using a 2nd round pick three years in a row on a QB. That's just bad drafting. Get that one guy that can be the franchise, and even if he's not HOF-caliber, that still can save you more picks in the future.

I wonder about causation here -- There's some selection bias in the HOF. Take Joe the very-good-player. Put him on a great team and give him a long career, and he'll have the opportunity to put up some gaudy stats for several years, maybe get a ring or two... and he may end up in the HOF. Put him on a miserable team, and while he may still stand out as better than his teammates, his stats won't be quite as impressive, he won't have the opportunity to shine in the playoffs...

I agree with Mattieshoes. The more succesful teams have a higher degree of HOF players because their best players get more recogntion. The analysis, while interesting, does not show a causal relationship and thus clouds determining the value of a HOF player to team success. The two factors are intertwined. Some other way of teasing out this relationship is needed.

Reply to Postings #1 @ 3

Obviously, I don't know much about math and particularly regressions, but Brian Burke pretty much tore apart Doug's regression analysis that Jason pointed us to in the link he gave us---and Doug agreed with him that he had made mistakes.

During his early writings, Burke pointed out that most regressions are useless because their authors almost always combine two or more dependant variables in their regressions. In 1981, Pete Palmer ran a wonderful article on "Yards, Points, and Wins" in the PFRA's Coffin Corner series Vol 3, Annual. One thing he wrote struck me: "One very important thing to remember with regression is that variables used are often not really independant and that incorrect conclusions can be reached from the results. In football, points scored and allowed are really not independant because of the interaction between offense and defense."

Despite his own cautionary note, Palmer looked at games played between 1970-80 and ran a regression---thus raising questions about his own analysis. He concluded that, on average, it takes about 37 additional points scored on offense or not allowed on defense to result in one more win. However, within sub-groups, it could take as many as 40 points for very strong or very weak teams and 30 points for the "average" team.

Palmer's article was quite long and provided many interesting notes. I will paraphase: "Yards per drive correlated best with wins; better than yards per pass attempt." "Time of possession has virtually no correlation to wins." "Kick and punt return yardage have a very slight correlation to wins." "Winning leads to rushing; not the other way around." "Interceptions do not lead to defeat; defeat is more likely to lead to interceptions. Approximately two-thirds of a loser's interceptions occur when the team is behind and has little chance of winning." "Fumbles and interceptions are equally damaging to a team's chances of winning."

What all this means, with respect to this posting, I'm not sure. My impression is that, even stud players such as HOFers, make very little difference between actual results and expected results. As always, team merits trump individual merits.

I recommend reading Palmer's article for a more detailed explanation of his conclusions.

Mattieshoes, I agree there is some selection bias. If you notice, the value of each additional "Hall of Famer" goes down as we add. The largest jump is going from 0 to 1. The 11 teams that had 5 offensive Hall of Famers had a slightly worse average SRS than those with 4, and only a little better than 3.

One explanation is that the value of adding another Hall of Famer is not as valuable as adding the first. Another is that some of those Hall of Famers probably shouldn't be in, and were able to get in because their teammates who should be in put them in position to get noticed.

Still, way more teams had 1 or 2 Hall of Famers and did not win rings than had 4 or more, so even if we took out the 10 most questionable picks on either side of the ball based on rings, I don't think it changes it too much.

I looked at this Hall of Fame induction and I loved it, especially the senior nominees because I did not pick either one of them. I knew Jerry Rice, who could arguably be the greatest reciever of all-time and Emmith Smith, who is considered the standard to what every running back will be measured, was getting in. However, we has John Randle, Ricky Jackson, underrated players who were very good throughout their careers elected in. I did not pic Russ Grimm and the senior nominees. To see their families cry and hear the speeches given by these three gave me goosebumps. So no I did not get what I wanted but it was close to it. It was a great day for Canton!