Some Clarification is in Order: What Does One Yard Cost?

This off-season we've discussed a very large number of topics as we've tried to keep busy during the down time. Now my desire to learn more about topics has lead me to do a lot of my own research. This have lead to a lot of articles, one of which dealt with salary and winning. It was started by a fanshot that Kirk posted with a quote from former GM Brian Xanders about how the Broncos would be more active in free agency. The comments quickly developed into a great discussion of the balance of spending and it's affect on wins. I wrote my article to build upon the discussion with a few numbers and discussion points. The main conclusion I gained from my earlier study was this:

Here we see a bit clearer picture, teams that spent efficiently also won. Teams that spent a lot of money AND spent it well won games more than those who just SPEND or those who just use money EFFICIENTLY. This is the key, while spending money is very likely to help you win, there is more volatility, or a larger difference between the top 10 when just looking at spending compared to a low volatility in the Cost per Win.

To summarize, if you spend you are more likely to win, but if you spend and spend that money efficiently, you are set.

But there is more to this than just base salary numbers. I wanted to see which players were cost efficient, which players produced but cost a lot and which players were just overpaid and never played well. To do this I set out to try a variety of metrics to measure cost efficiency.. Now this won't be a comprehensive study across all positions since some positions are incredibly hard to look at, but I hope this provides a starting point of discussion, and I will be trying to complete a study of all positions, when that happens I'll publish the results at that time.

Methodology:

This study went through a large number of phases and I'll only be presenting my most current form due to space. Now I wanted to look at this from a few different sides. The first was I wanted to look at a team and see which players on that team played up to their contract, and also see those that didn't. Secondly I wanted to see the level of efficiency of all the players at a certain position, quarterback or running back for example. We'll start by looking at a single team, we'll look at the Broncos for obvious reasons. On this table well be organizing the table in this order:

*How the column will be labeled on the table will be in ()*

- Players name (Player)
- Position the player plays at (Position)
- 2011 Salary effect on the teams cap (2011 Salary Cap Hit)
- Whether the player was drafted to the team or whether they came through other methods (Draft/Other)
- Approximate Value based on Pro Football References studies (AV)
- Approximate Value of that player divided by the teams total Approximate Value (AV %)
- Percentage of the total salary cap that the player occupies (% of Total Salary Cap Hit)

Before we begin I should explain a few things and issue a few clarifications. The first thing I want to discuss is something some of you may be already thinking about, "Why are there no other categories like sacks, touchdowns, etc?" Well the reason for this was I wanted to be able to compare the whole team looking for value, but you make a valid point, especially if you wanted to find the best value at linebacker or running back on the team. And this will be something we'll discuss in the second part of this series. But for now I just wanted to compare the whole team.

The second thing I wanted to discuss deals with the salary numbers. now I got them from Rotoworld, which is considered the most reliable place for these numbers. But that isn't the main point, what I want to discuss here is the nature of contracts.

Contracts, Experience and Value

When Chris Johnson first came into the league he was making decent money for a running back, but after two outstanding seasons, he knew his value was just too good for his contract and he held out of the 2011 season as a result until he got a new contract. Rookie players are always going to be a better value than experienced players because while they may be producing at a similar level, or just below, very good players, they are still riding on their rookie contracts which are usually lower than veterans. Let's look at Andy Dalton and Rex Grossman. Last season Dalton earned $495,000 while Grossman earned $1,500,000. Now that just may seem strange considering the struggles of Grossman compared to Dalton's production and potential, but it is even more complex than that. The Bengals paid Dalton $23,571 per touchdown while the Redskins paid Grossman $88,235 per touchdown. I simply divided the players salary by the number of touchdowns to create this number. Dalton had 4 more touchdowns than Grossman and was paid less to do it. Now this is where one of the key struggles begins.

When looking at this just in terms of yards or touchdowns, while it is a useful metric since it helps us bring conformity to the scale, but it struggles since a contract isn't just purely for touchdowns or yards or sacks (unless you are a kicker or a punter then you are literally paid per field goal or punt), most players are paid to accomplish a number of tasks. Having said that dollars per yard or tackle are still viable methods of measuring value, though they are flawed, and I'll gladly admit that.

But getting back to contracts, to put it simply, rookies will almost always be a good value with a few notable exceptions. The two biggest will be Sam Bradford and Matt Stafford since they were the final two #1 picks at quarterback so their contracts are massive. Stafford had a great season so he still had solid value, but considering Bradford struggled this season, his value is greatly reduced due to his massive contract. But as we look at the tables in these next few articles, you'll be able to clearly see who is still on their rookie contract compared to those who are on their second or third contracts.

Approximate Value:

Having noted the weaknesses of dollars per yard, I wanted to find a better metric that could be applied across all positions so there would be conformity. I studied a variety of metrics ranging from Pro Football Focus's ratings to Advanced NFL Stats Win Probability Add and Football Outsiders' Defense-Adjusted Yards Above Replacement, in th end I ended up using a few of these depending on the position, but one that stuck and was reliable with little variance was Pro Football Reference's Approximate Value (AV).

Now I won't get into the nitty-gritty of AV with you since the math is fairly complex and time consuming, but here are the links to how it is formed for those who want to check it out:

- Overview
- Methodology
- Applications of AV, along with Part 2, Part 3 and Part 4.
- Adjustments

AV was created by Doug Drinen and refined by Neil Paine and Chase Stuart, AV was created with the purpose of creating a metric that allows the comparison of differing positions. Prior to AV their weren't really any overarching metrics for this. DYAR and DVOA can't be applied to every positions, same can be said for WPA and EPA. That really just leaves games started, Pro Bowls and All-Pros. Even these have weaknesses since games started does indicate some value, it doesn't say that J.D. Walton was a worse center than Jeff Saturday despite both playing 16 games. The Pro Bowl is just a popularity contest that still does a decent job of measure talent, while All-Pro is very limiting since only one quarterback can achieve it per season. Before I go much further I want to insert the introduction the creator of AV had for his product:

AV is not meant to be a be-all end-all metric. Football stat lines just do not come close to capturing all the contributions of a player the way they do in baseball and basketball. If one player is a 16 and another is a 14, we can't be very confident that the 16AV player actually had a better season than the 14AV player. But I am pretty confident that the collection of all players with 16AV played better, as an entire group, than the collection of all players with 14AV.

Essentially, AV is a substitute for --- and a significant improvement upon, in my opinion --- metrics like 'number of seasons as a starter' or 'number of times making the pro bowl' or the like. You should think of it as being essentially like those two metrics, but with interpolation in between. That is, 'number of seasons as a starter' is a reasonable starting point if you're trying to measure, say, how good a particular draft class is, or what kind of player you can expect to get with the #13 pick in the draft. But obviously some starters are better than others. Starters on good teams are, as a group, better than starters on bad teams. Starting WRs who had lots of receiving yards are, as a group, better than starting WRs who did not have many receiving yards. Starters who made the pro bowl are, as a group, better than starters who didn't, and so on. And non-starters aren't worthless, so they get some points too.

As Doug said, this isn't a be-all, end-all metric, but it is the best way I've found at comparing a players value across positions, no other metric or number of even eye test does that. Now I don't have the space here to go into the detail, that took the author dozens of articles to cover, but the basis of AV is a top down approach to grading. A team's offense and defense are assigned a number of "points" based on the level of success of each unit. So a team like the 2011 Patriots offense would have more points than their defense due to the offense being better than their defense. Using these unit totals (which are formed from a formula derived from a huge amount of data and research by nearly a dozen researchers) the totals are broken up among the players on that unit based on more formulas for each position. While I won't list each formula (they are under the methodology article above) they are accurate.

While I know many don't care for stats, which is fine, almost everyone can agree on one thing, measuring success, or failure, is the only real point of stats, and AV is incredible accurate at this. Since 2000 the team that has the high AV won the game 93% of the time. AV is an incredibly powerful, accurate and useful metric since it measures a teams overall strength as well as players on that team. As Doug stated, a 16 won't always be better than a 14, but they will USUALLY be better. The wider the margin between two AV's the more often the player is better, same can be said for teams.

I understand that some will not like this metric, that's fine, but it is the best one out there for comparisons so I'll be using it anyways. Another thing to note, AV doesn't track special teams so we'll be missing a few players who only saw the field on ST:
-Quan Crosby
- Matt Prater
- Britton Colquitt
- Lonie Paxton

The Table:

Now I didn't take every player the Broncos had on their roster last season, rather I only listed those who saw 50 or more snaps or players that were at key positions but may have not seen the field (Brady Quinn for instance).

Notes

Now obviously the fact that Robert Ayers outplayed his contract is nice, but that doesn't mean he was a better player than Champ Bailey, whose contract was so big that it would really be impossible to balance out his AV and contract. So finding a balance of good AV and outplaying salary is key. We'll use Ayers again, he had a solid season with 6 AV (3.19% of the team's total AV) and did it with a fairly cheap contract (0.89% of the team's total cap hit). Whereas someone like Virgil Green didn't contribute much with 1 AV (0.53% of the teams total AV) but the standards weren't very high either due to his draft spot (7th round) and his salary (0.38% of the teams total cap hit). Other players, like Elvis Dumervil had a massive contract (14.66% of the teams total cap hit) but due to a slow start and injuries wasn't able to live up to his contract. Doesn't mean he was bad, just didn't play at the level he was paid too.

With this we get into another discussion point, is it worth it to overpay a player at a key position because you can't risk losing him? That is the whole idea behind the Franchise Tag. Along those lines I know that when we resigned Champ Bailey that our own John Bena wasn't a big fan of the move because at that time we really didn't have a pass rush and he felt we could acquire another corner at the top of the draft. Now whether he was right or not really doesn't matter, but many feel that overpaying, especially at non-premium positions, can hurt the team overall. I don't have a clear answer, I don't think anyone does, outside of it depends on the situation and the player.

Overall, while this method does have weaknesses, I feel it is a good place to start. I wouldn't dream of saying this is the final, complete look at the Broncos roster and value. I know I am personally looking a number of ways to improve this model:

- Introducing league averages per position
- Long term looks at positions and players
- How various coaches and GM's handle it
- Tracking a players value across multiple seasons and contracts

These are a few of the things we'll be discussing in future articles, hope that this can start a discussion and hope to answer more questions as we work our way through this topic together.