Rating Quarterback Decision Making

[JeffHCross]

Originally posted on Utopia, and modified after discussions with several members over there. The concept does apply to both Pro and College Football in my mind.

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Over the last month or two, I've poured a lot of time and interest into the usefulness of statistics in football. Sabermetrics, if you will, for the gridiron. There are a lot of places already doing this research, such as FootballOutsiders.com, the PFR Blog, and the very interesting book Mathletics.

One of the frequent topics of these analyses is the QB Rating. Most of the writings I've seen have argued that the QB Rating is antiquated and uses numbers that once had meaning but are arbitrary to today's standards. 8.4 x YDS? 330 x TDs - 200 x INTs? Apparently, when the formula was created for the NCAA, the 330 x TDs and 200 x INTs were supposed to negate each other for an "average" passer. That means for every 10 TDs, the "average" passer threw 16.5 INTs. Ew.

Originally, I was going to use QB Rating to be the determination for my quarterback's AWR in my "Historical Players" thread. So I looked at the various suggestions for improving the Passer Rating, but none of them sat quite right with me. They were good for QB Ratings, but weren't what I was looking for. AWR, I believe, should be a measure of a quarterback's decision making.

The Hayes Rating
So I decided to create The Hayes Rating. Hayes, of course, is a hattip to Ohio State coach Wayne Woodrow Hayes, who is credited with saying "There are three things that can happen when you throw a pass, and two of them are bad."

The Hayes Rating is a measure of the things that can go wrong on a pass, and how often a quarterback does one of them, given the number of chances he has.

The original formula: (-Incompletions * Yds Per Comp. - 45*Interceptions - Sack Yards Lost ) / (Attempts + Sacks Taken)
The (modified/final) formula: ( -(Incompletions - Interceptions)*5 - Interceptions*30 - Sack Yards Lost ) / (Attempts + Sacks Taken)
The explanation: The easiest way to measure mistakes by a quarterback is in yardage, so all of these measures is in that unit. Incompletions * 5 yards is based on the fact that, over the last decade in College Football, the average play has gained somewhere between 5.0 and 5.5 yards per play. An incompletion is, therefore, a loss on, at least, an 'average' play. I used 5 yards just to make it a rounder number.

Interceptions is subtracted from Incompletions so an Interception doesn't count as both an Incompletion and an Interception.

Interceptions*30 is a modification of the 45 yards per interception cost originally researched in 1988's The Hidden Game of Football. This modification was made to keep a 6:1 ratio of interception cost to incompletion cost, based on other research that would have put the value of an incompletion at 10 yards and interceptions at 60 yards.

Sack Yards lost should be self explanatory. Likewise, dividing everything by Attempts + Sacks Taken should be self explanatory. Sack Yards is left without modification because the sacks average out around 7 lost yards per sack, which puts them as slightly worse than an incompletion. This is a logical outcome.

Now to the results ... the top 15 seasons of 2007-2009:

1. Zach Collaros, 2009: 75%, 2 INTs, 2 sacks in 126 plays
2. Colt McCoy, 2008: 76.7%, 8 INTs, 24 sacks in 457 plays
3. Graham Harrell, 2008: 70.6%, 9 INTs, 13 sacks in 639 plays
4. Dan LeFevour, 2009: 69.7%, 7 INTs, 17 sacks in 473 plays
5. Kellen Moore, 2009: 64.3%, 3 INTs, 5 sacks in 436 plays
6. Graham Harrell, 2007: 71.8%, 14 INTs, 16 sacks in 729 plays
7. Jimmy Clausen, 2009: 68%, 4 INTs, 24 sacks in 449 plays
8. Sam Bradford, 2008: 67.9%, 8 INTs, 11 sacks in 494 plays
9. Case Keenum, 2009: 70.3%, 15 INTs, 16 sacks in 716 plays
10. Kirk Cousins, 2008: 74.4%, 1 INTs, 2 sacks in 45 plays
11. Pat White, 2007: 66.7%, 4 INTs, 8 sacks in 224 plays
12. Tim Tebow, 2007: 66.9%, 6 INTs, 13 sacks in 363 plays
13. Tyler Sheehan, 2009: 64.9%, 7 INTs, 29 sacks in 604 plays
14. Tim Tebow, 2009: 67.8%, 5 INTs, 27 sacks in 341 plays
15. Dennis Dixon, 2007: 67.7%, 4 INTs, 13 sacks in 267 plays

[Rudy]

Where do yards and TDs come in that formula? I'm a math guy and I like reading that stuff but I can't get on board with a formula that only accounts for negative plays and doesn't account for the positive TDs and yards produced.

[JeffHCross]

They don't, but that's because I don't want to account for positive plays. Maybe a better title would have been rating quarterback's "bad" decision making, but I'm concerning myself with only negative plays. I'm not looking to offset them with "well, he makes good plays X amount of the time" ... just looking to see who makes the most bad plays.

It's not designed to replace Passer Rating, which would take into account TDs and yards. I have a different formula I've been exploring for that. This is designed to supplement.

[Rudy]

OK, cool. I'd like to see your positive rating. One thing that kills the QB rating stat though is 3rd down conversion. Throwing a 5 yard swing pass on 3rd and 8 is a positive but in reality should at least be neutral. I'd love to see a formula factor that in as well as rushing yards for a true QB rating.

[JeffHCross]

Since you said you're a math guy, you should check out this page: http://www.aaronschatz.com/info/methods#dvoa Namely look at the 5th paragraph under DVOA Explained.

Unfortunately, the statistics necessary for what you're talking about is something we don't really have for college football. The NFL stats guys do, and that's where things like DVOA have come from.

I've got my own Passer Rating as well as several others on my laptop. I'll grab them the next time I'm on it.

[JeffHCross]

Rudy, here you go.

Creator|Equation
NCAA|[ { (8.4 * yards) + (330 * touchdowns) - (200 * interceptions) + (100 * completions) } / attempts ]
Mathletics|1.543 * ((passing yards – sack yards)/pass plays) – 50.0957(interceptions/pass attempts)
The Hidden Game of Football|((Passing Yards – Sack Yards) + 10(touchdowns) – 45(interceptions))/attempts + sacks
Wages of Win|Passing Yards – 3(passing attempts) – 30(interceptions)
JHC (me)|( (passing yards - sack yards) - 3*(attempts + times sacked) - 37.5*(interceptions) ) / games ) * 12 games

[Rudy]

What were the top QBs in college football last year based on that system?

[JeffHCross]

Rudy, didn't see your reply until just now. Keep in mind that I used my own qualifying method (10 attempts per game, minimum 4 games) rather than the NCAA's official qualifier. So my ranking using their system is not going to match the official one.

NCAA
1. Zach Collaros, Cinc
2. Steven Sheffield, TexT
3. Tim Tebow, Fla
4. Kellen Moore, BoSt
5. Jimmy Clausen, ND
6. Max Hall, BYU
7. Greg Alexander, Haw
8. Kyle Padron, SMU
9. Nathan Enderle, Ida
10. Case Keenum, Hou

Mathletics
1. Zach Collaros, Cinc
2. Josh Nesbitt, GT
3. Andrew Luck, Stan
4. Kellen Moore, BoSt
5. Jimmy Clausen, ND
6. Greg Alexander, Haw
7. Tim Tebow, Fla
8. Ryan Mallett, Ark
9. Nathan Enderle, Ida
10. Kyle Padron, SMU

Hidden Game
1. Zach Collaros, Cinc
2. Kellen Moore, BoSt
3. Josh Nesbitt, GT
4. Andrew Luck, Stan
5. Jimmy Clausen, ND
6. Tim Tebow, Fla
7. Ryan Mallett, Ark
8. Greg Alexander, Haw
9. Nathan Enderle, Ida
10. Kyle Padron, SMU

Wages of Win
1. Case Keenum, Hou
2. Levi Brown, Troy
3. Jimmy Clausen, ND
4. Kellen Moore, BoSt
5. Ryan Mallett, Ark
6. Tyler Sheehan, BGSU
7. Blaine Gabbert, Mo
8. Max Hall, BYU
9. Dan LeFevour, CeMI
10. Jerrod Johnson, TAMU

Mine
1. Case Keenum, Hou
2. Greg Alexander, Haw
3. Jimmy Clausen, ND
4. Levi Brown, Troy
5. Kellen Moore, BoSt
6. Ryan Mallett, Ark
7. Christian Ponder, FLSt
8. Kyle Padron, SMU
9. Tyler Sheehan, BGSU
10. Nathan Enderle, Ida

[oweb26]

QB rating to me has always been one of those weird formulas and stats that I never really got, maybe for judging all-time QB's but season in and season out it never made sense to me.

[JeffHCross]

oweb, it gets even more interesting when you find out the history of the QB Rating. The numbers in the formula (8.4 * yards, 330 * TDs, 200 * INTs), I think it was in college, were developed when the TDs and INTs would have cancelled themselves out for the "average" passer. So the "average" Quarterback when the rating was developed would have been throwing 33 INTs for every 20 TDs (because you have to take the inverse to cancel). Essentially a 3:2 ratio! That's just nuts.

Wages of Win's method is probably my favorite. The 3 * Attempts is to recognize that for every pass you throw, you're spending a limited quantity: downs. I think that's a very cool twist.

[JeffHCross]

Another interesting tidbit: In 1979, when the college Passing Efficiency rating was created, the average rating was 104.49. In 2007, it was 127.35.

[Rudy]

It should be noted that Jimmy Clausen was in the Top 5 in every category. They guy had a great year on a bad foot. The kid rubs most people the wrong way but he allegedly matured at Notre Dame and I think he will be an absolute steal for the Panthers.

[JeffHCross]

Yep. He should be great for the Panthers, if he can get over the leadership hump. He's incredibly talented, but I never saw any leadership out of him or Golden Tate. I'm expecting Jimmy Clausen to mature and become a leader, and Golden Tate to be a locker room nightmare (like TO, or Randy Moss for a while) for most of his career.

[JeffHCross]

The Hayes Rating is a measure of the things that can go wrong on a pass, and how often a quarterback does one of them, given the number of chances he has.
The formula: ( -(Incompletions - Interceptions)*5 - Interceptions*30 - Sack Yards Lost ) / (Attempts + Sacks Taken)

Minimum requirements: 10 attempts per game played, minimum of 2 games played.

2010 Hayes Rating as 10/2/10 (includes games that have already been played on 9/30 & 10/1)
1. Dan Persa, N.W.
2. Zach Collaros, Cinc
3. Cotton Turner, Hou
4. T.J. Yates, UNC
5. Ricky Stanzi, Iowa
6. Ryan Griffin, Tula
7. Terrance Broadway, Hou
8. Ben Chappell, Ind
9. Terrance Cain, Utah
10. Stephen Garcia, SCar
11. Jordan Webb, Kan
12. Jerome Tiller, IASt
13. Ryan Colburn, FrSt
14. Danny O'Brien, Md
15. Scott Tolzien, Wis

40. Terrelle Pryor, OHSt

127. Jacory Harris, MiaF

[Rudy]

Wow @ Jacory Harris. Look how high Stephen Garcia is rated and yet Spurrier is always chewing that guy out. You wonder why he doesn't get premium QBs to want to play for him. He's a jerk to most of them.

[JeffHCross]

Well, Spurrier had seemed to be okay with Garcia this year until Stephen had two consecutive fumbles against Auburn. His stat line from that game looked great, but he was a major contributing factor to the Gamecocks loss. Garcia is admittedly a surprise this season ... much like TJ Yates and Ricky Stanzi.

[JeffHCross]

May have had a slight bug in last week's list, but it should be corrected for this week.

Hayes Rating through Oct 2 Games. 10 Att / Gm, Minimum 2 Gm
1. Terrance Cain, Utah
2. Cotton Turner, Hou
3. Dan Persa, N.W.
4. Ben Chappell, Ind
5. Denard Robinson, Mich
6. Colin Kaepernick, Nev
7. Kellen Moore, BoSt
8. Chandler Harnish, NIU
9. Ross Jenkins, LT
10. Cody Endres, Conn
11. Ryan Colburn, FrSt
12. Blaine Gabbert, Mo
13. Nick Foles, Ariz
14. Jordan Wynn, Utah
15. Bryant Moniz, Haw

34. Terrelle Pryor, OHSt

107. Jerrod Johnson, TAMU
122. Joshua Nesbitt, GT
132. Jacory Harris, MiaF
137. Jordan Jefferson, LSU

[Rudy]

Chappel got helped out big time by playing Michigan last week. Denard has been making very good decisions but he also missed two wide open receivers last week. The play action for Michigan kills teams since they are so concerned with the run. DR usually hits those easy ones but last week missed a couple.

[JeffHCross]

Chappell definitely got a boost by playing UM, but he was #8 before last week's games.

The top 2 players have only played in 3 games, and 3 others in the Top 15 have only played in 2. There'll be a bit of a shakeup if they don't play in any more. The Top 15 still looks pretty good right now, but this is definitely one rating that gets more defined as the season progresses.

[JeffHCross]

Hayes Rating through Oct 15 Games. 10 Att / Gm, Minimum 2 Gm
Top 15 and other notables

1. Terrance Cain, Utah
2. Cotton Turner, Hou
3. Dan Persa, N.W.
4. Chandler Harnish, NIU
5. Kellen Moore, BoSt
6. Colin Kaepernick, Nev
7. Ben Chappell, Ind
8. Mike Hartline, UK
9. Scott Tolzien, Wis
10. Robert Griffin, Bay
11. Geno Smith, WVU
12. Nick Foles, Ariz
13. Jordan Wynn, Utah
14. Blaine Gabbert, Mo
15. Greg McElroy, Ala

19. Terrelle Pryor, OHSt
24. Stephen Garcia, SCar
27. Ryan Mallett, Ark
30. Denard Robinson, Mich

114. Taylor Martinez, Neb
115. Jerrod Johnson, TAMU
126. Joshua Nesbitt, GT
128. Jacory Harris, MiaF
136. Jordan Jefferson, LSU