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What’s a starting QB worth? Part II

Posted by Doug on August 19, 2008

Yesterday I asked you to speculate on how many points per game teams have historically lost when their starting quarterback was replaced by a backup.

Before I tell you the results, let's walk through a theoretical exercise....

If you take an average offensive team, let's say the 2008 Redskins, and you assume that they lost ALL their offensive starters for the season, how many points do you think they'd score per game in 2008?

They'd be rolling with the likes of Todd Collins, Ladell Betts, Devin Thomas, Malcolm Kelly, Fred Davis, and a backup offensive line. Arguably, you might give them the services of Antwaan Randle El instead of Kelly. They might go out and sign some veteran Shaun Alexander-type players off the street.

I'd say that offense scores about 12 points per game. They couldn't be that much worse than last year's Chiefs or 49ers, who averaged about 14 points per game. The last three expansion teams combined have averaged 16 points per game and all were above 13. Twelve points per game would be the second-lowest figure of the last seven seasons (thank you 2006 Raiders) and would have been last in the league in seven of the last ten years.

If you're willing to buy 12 points per game, then you've just agreed that an entire average offensive starting eleven is worth about 9 or 10 points per game.

Now, what percentage of an average offense does the quarterback account for? 20%? 30%? 40%?

If you say 30%, then the other ten are worth a combined 70%, or 7% each on average. That makes the QB worth more than four times as much as a typical non-QB offensive player. Is the QB worth more than the two guards, the center, and the right tackle combined? Is he worth more than the tight end, both wide receivers, and the running back combined? I don't think so.

I'm not sure how reliable the data accompanying these purty pictures are, but this link (and those that follow) give the average salaries by position as follows:

QB - 1.97 million
OL - 1.27 million
WR - 1.05 million
RB - .96 million
TE - .86 million

That would imply that 16% of the total salary paid to offensive players goes to quarterbacks. I believe that includes all players, not just starters, but I don't see why the starting-eleven ratio would be too much different.

In short, if NFL General Managers believed that quarterbacks were worth (more than) four times more than wide receivers, why do they only allocate twice the resources to quarterbacks? And if NFL GMs don't think quarterbacks are worth four times more than wide receivers, then why do you?

Anyway, if you don't agree, fill in your own number and go with it. My number would be around 20% or 25%, which would make the QB worth about two-and-a-half to three times what a typical non-QB offensive starter is worth.

So a typical QB accounts for about 20% to 25% of the offense, and a typical starting eleven is worth about 10 points per game. Thus, a typical starting quarterback is worth around two to two-and-a-half points per game.

The result of the study I described yesterday is the empirical verification of the theoretical observations above. Actual teams who have replaced their starter with a backup have on average dropped off by 2.3 points per game.

As I mentioned yesterday, I tried lots of different variations on the definition of a starting quarterback. These tweaks made the sample sizes grow or shrink, and they made the "average starting quarterback" better or worse. But in virtually every case, the number was between 2 and 3.

How does that translate to wins?

A regression of Simple Rating System rating to wins says that adding one point per game will add about .45 wins over the course of a season. So a typical starting quarterback is worth 2.3 points per game, and 2.3 points per game is worth just about one win per season. (A Pythagorean calculation, by the way, would give a very similar result.)

If this still seems too low, let me rattle off some examples:

In 2007, the Texans scored more points with Sage Rosenfels starting than with Matt Schaub starting.

In 2006, the Eagles scored more points with backup Jeff Garcia than with Donovan McNabb.

In 2005, the Jags were better with backup David Garrard than with starter Byron Leftwich.

If you're tempted to raise an objection on the grounds that David Garrard is too good a backup to be considered typical, I will overrule it. Part of the point of this is that sometimes, backups are better than you think they are. David Garrard was the very definition of a backup quarterback when he replaced Byron Leftwich in 2005. And Leftwich, who had an 8-3 record as a starter and a 15/5 TD/INT ratio, certainly looked like an above average starting quarterback.

The 2001 Vikings scored more points (per game) with Spergon Wynn and Todd Bouman than with Daunte Culpepper.

The 2000 Saints' offense was much more productive with a young backup named Aaron Brooks than it was with veteran starter Jeff Blake, who had been having a fine season.

The 1998 Broncos scored more with Bubby Brister playing than with John Elway.

The 1996 Dolphins scored more with Craig Erickson than with Dan Marino.

And the list goes on.

There are, of course, lots of examples of the opposite thing happening. But when you add them all up, it comes out to an average of 2.3 points per game.

In closing, I'll mention that you could run through the same exercise for a particular QB that we just did with an average QB. It'll still just be conjecture, but it'll be fun. Take Tom Brady for instance.

If the Patriots lost their entire starting eleven tomorrow, how many points would they score? I'm inclined to say maybe 16 per game, because Belichick is a genius and the Patriots do everything The Right Way and John Lynch would probably move to tight end and all that sort of thing. With their actual starting eleven, I'd go ahead and give them credit for the 36 points per game they scored last year. On one hand, they probably caught a bit of lightning in a bottle last season and can't keep up that pace. But on the other hand, they weren't playing with their actual starting eleven all season either. If they had all eleven guys for 16 games this season, they probably could match last season's output. So I'll estimate that the Patriots' starting offense is worth 20 points.

Brady is probably a bigger part of the Patriots' offense than a typical quarterback is to a typical offense, so maybe give him credit for a third of that. Then round up, and you're at 7 points per game. That's right around three wins. I believe Vegas is currently showing an over/under of 12 or 12.5 wins for New England, so the above says that the Patriots would be a 9- or 10-win team if they lost Brady tomorrow.

[EDIT: it just occurred to me that the Vegas lines have some probability of a Brady injury already built into them. If New England were assured of Brady's services for 16 games, the over/under would probably be 13 wins. Maybe 13.5, though I don't think it would go that high. So I think that means that my estimate is that New England would be a solid 10-win team (maybe 11) without Brady.]

Does that sound about right?