ivanvamp

All the Welker talk got me thinking about how to rate the quality of WR. I am 100% bonafide *not* a statistician, but I like to fiddle around with numbers. I have come up with four formulas for determining WR ratings. I won't get too into the formula, but here's the basic idea.

1. Productivity. This measures how, um, productive a receiver is. It takes into account receptions, yards, TD, first downs, and fumbles. Each item is weighted (thus a TD doesn't count the same as a reception, etc.). To give you an idea, here are a few guys and their Productivity Ratings. Note: there were 451 players that caught passes in the NFL this past year. The "AVG" is the average of all 451 players (this includes one reception by Joe Flacco).

AVG: 7.84
Calvin Johnson: 49.11
Wes Welker: 44.59
Deion Branch: 20.82
Mike Wallace: 31.53
Reggie Wayne: 26.10

2. Efficiency. This measures how efficient a player was in turning a reception into a yards, first downs, and touchdowns. So a player that has 1 rec, 20 yds, 1 td is more efficient than a player that has 5 rec, 20 yds, and 1 td. Here are those same players and their Efficiency Ratings:

AVG: 24.52
Calvin Johnson: 33.26
Wes Welker: 27.04
Deion Branch: 27.70
Mike Wallace: 31.58
Reggie Wayne: 25.73

3. Danger. This measures how dangerous a receiver was in turning a reception into a big play, so it takes into account TD/rec, ypc, YAC, etc. Again, the same players and their Danger Rating:

AVG: 19.62
Calvin Johnson: 27.96
Wes Welker: 21.36
Deion Branch: 23.25
Mike Wallace: 27.06
Reggie Wayne: 18.63

4. Total Receiver Rating. This simply adds up the three ratings, with productivity rating being weighted most heavily, followed by efficiency rating, and lastly, danger rating. The reason I weighted them this way is because a player could have just a handful of catches all year but they all go for big plays. Is that player a "better" receiver than a guy with a TON more receptions, yards, and TD, even if his "danger rating" is a little bit lower? Not in my book. But the Danger Rating is a factor. Again, the same guys:

AVG: 72.09
Calvin Johnson: 176.07
Wes Welker: 151.10
Deion Branch: 106.44
Mike Wallace: 137.49
Reggie Wayne: 109.41

I'm sure there are huge flaws in my metrics, but it at least gives me something to go on. Based on these admittedly flawed (but very fun) stats, here's the top ten guys in each category (min 48 rec):

Productivity
1. C. Johnson, Det - 49.11
2. Gronkowski, NE - 46.17
3. Welker, NE - 44.59
4. Graham, NO - 40.40
5. Nelson, GB - 39.13
6. White, Atl - 38.66
7. Cruz, NYG - 37.46
8. Fitzgerald, Ari - 36.21
9. Colston, NO - 31.93
10. Nicks, NYG - 31.92

Efficiency
1. Nelson, GB - 34.80
2. Jackson, SD - 34.12
3. C. Johnson, Det - 33.26
4. Cruz, NYG - 33.25
5. Wallace, Pit - 31.58
6. Gronkowski, NE - 31.51
7. Fitzgerald, Ari - 31.45
8. Smith, Car - 31.32
9. Robinson, Dal - 31.27
10. Jones, Atl - 31.20

Danger
1. Cruz, NYG - 30.10
2. Jones, Atl - 29.97
3. Nelson, GB - 29.91
4. Smith, Car - 28.16
5. Jackson, SD - 27.12
6. Wallace, Pit - 27.06
7. Gronkowski, NE - 26.32
8. Baldwin, Sea - 26.11
9. Foster, Hou - 25.66
10. Smith, Bal - 25.56

TOTAL RATING
1. C. Johnson, Det - 190.65
2. Gronkowski, NE - 176.07
3. Nelson, GB - 165.93
4. Cruz, NYG - 154.90
5. Welker, NE - 151.10
6. Fitzgerald, Ari - 147.49
7. Graham, NO - 144.31
8. Jackson, SD - 141.21
9. Wallace, Pit - 137.49
10. Smith, Car - 137.42

Here's the Pats' key receivers (Welker, Gronk, Hernandez, and Branch) and where they ranked in each category (again, minimum of 48 receptions to qualify):

Productivity
Welker - 44.59, #3
Gronkowski - 46.17, #2
Hernandez - 27.60, #23
Branch - 20.82, #49

Efficiency
Welker - 27.04, #35
Gronkowski - 31.51, #6
Hernandez - 25.20, #51
Branch - 27.70, #28

Danger
Welker - 21.36, #29
Gronkowski - 26.32, #7
Hernandez - 20.47, #35
Branch - 23.25, #19

Total Rating
Welker - 151.10, #5
Gronkowski - 176.07, #2
Hernandez - 113.47, #27
Branch - 106.44, #41

Again, very flawed number-crunching, but when I look at the lists and how the rankings came out, I think they're pretty much in line with what you'd think. The only interesting part was that I figured Hernandez would be more "dangerous" than Welker or Branch, but in reality, his numbers in those key areas weren't as impressive as I thought they would be, and Branch's were better than I thought they would be.

But as a whole group, man, four of the top 41 in the league (again, min 48 receptions)? Well, I guess it kind of makes sense given how prolific the Pats' passing offense was this season.

ivanvamp

Just for fun, I plugged in Randy Moss' 2007 season. Here's where he would be compared with this year's guys:

Productivity
1. C. Johnson, Det - 49.11
2. Gronkowski, NE - 46.17
3. Welker, NE - 44.59
4. Graham, NO - 40.40
5. Nelson, GB - 39.13
6. White, Atl - 38.66
7. Cruz, NYG - 37.46
8. Fitzgerald, Ari - 36.21
9. Colston, NO - 31.93
10. Nicks, NYG - 31.92
2007 Moss - 55.13

Efficiency
1. Nelson, GB - 34.80
2. Jackson, SD - 34.12
3. C. Johnson, Det - 33.26
4. Cruz, NYG - 33.25
5. Wallace, Pit - 31.58
6. Gronkowski, NE - 31.51
7. Fitzgerald, Ari - 31.45
8. Smith, Car - 31.32
9. Robinson, Dal - 31.27
10. Jones, Atl - 31.20
2007 Moss - 31.26

Danger
1. Cruz, NYG - 30.10
2. Jones, Atl - 29.97
3. Nelson, GB - 29.91
4. Smith, Car - 28.16
5. Jackson, SD - 27.12
6. Wallace, Pit - 27.06
7. Gronkowski, NE - 26.32
8. Baldwin, Sea - 26.11
9. Foster, Hou - 25.66
10. Smith, Bal - 25.56
2007 Moss - 22.28

TOTAL RATING
1. C. Johnson, Det - 190.65
2. Gronkowski, NE - 176.07
3. Nelson, GB - 165.93
4. Cruz, NYG - 154.90
5. Welker, NE - 151.10
6. Fitzgerald, Ari - 147.49
7. Graham, NO - 144.31
8. Jackson, SD - 141.21
9. Wallace, Pit - 137.49
10. Smith, Car - 137.42
2007 Moss - 179.42

Here's the Pats' key receivers (Welker, Gronk, Hernandez, and Branch) and where they ranked in each category (again, minimum of 48 receptions to qualify):

Productivity
Welker - 44.59, #3
Gronkowski - 46.17, #2
Hernandez - 27.60, #23
Branch - 20.82, #49
2007 Moss - 55.13

Efficiency
Welker - 27.04, #35
Gronkowski - 31.51, #6
Hernandez - 25.20, #51
Branch - 27.70, #28
2007 Moss - 31.26

Danger
Welker - 21.36, #29
Gronkowski - 26.32, #7
Hernandez - 20.47, #35
Branch - 23.25, #19
2007 Moss - 22.28

Total Rating
Welker - 151.10, #5
Gronkowski - 176.07, #2
Hernandez - 113.47, #27
Branch - 106.44, #41
2007 Moss - 179.42

Very interesting. I'm obviously surprised that Moss' Danger Rating is lower than 2011 Deion Branch's. The things that hurt Moss were his very low YAC per reception number. In 2007, Moss' average YAC per reception was just 2.9. In 2011, the *average* YAC per reception in the NFL was 5.4. Moreover, Moss had just 18 plays of 20+ yards in 2007, and just a 0.18 20+ plays per reception number, which is just slightly above the 2011 NFL average (0.16). So Moss, though he had numerous deep plays, wasn't as productive deep down the field as I had remembered him being. He made a lot of mid-range receptions where he was tackled almost immediately, and a lot of his TDs were in the end zone, which obviously limited his YAC and YAC/Rec numbers.

jmt57

Nice work. I'm glad you included both tight ends and wide receivers, as the distinction between the two becomes more and more blurred with each passing (no pun intended) year. I'm curious: would you consider sharing the complete, specific formulas you used with the rest of us?

ivanvamp

Sure, but I'm kind of embarrassed by the simplicity and utter capriciousness of them. Meaning that yes, I think they tended to produce results that look like they make sense (i.e., the top 10 list seems like it would fit what a reasonable evaluation of receivers in 2011 would look like), but they're hardly robust and based on anything other than what seemed reasonable to me.

TOTAL RATING
1. C. Johnson, Det - 190.65
2. Gronkowski, NE - 176.07
3. Nelson, GB - 165.93
4. Cruz, NYG - 154.90
5. Welker, NE - 151.10
6. Fitzgerald, Ari - 147.49
7. Graham, NO - 144.31
8. Jackson, SD - 141.21
9. Wallace, Pit - 137.49
10. Smith, Car - 137.42

I mean, yeah, that makes sense. Welker was a top-5 receiver this past year, but he wasn't as "good" as Johnson or Gronk or even Victor Cruz, who had just an incredible season.

But sure, here are the formulas, such as they are.....

PR (production rating) = ((10*rec)+yds+(100*td)+(10*1dn)+(-100*fum))/100

ER (efficiency rating) = 10*(rec%+1dn/rec)+ypc+(10*(td/rec))

DR (danger rating) = ypc+yac/rec+(10*20+/rec)+(10*(td/rec))

TR (total rating) = (2*PR)+(1.5*ER)+DR

rec = receptions
yds = yards
td = td
1dn = first downs gained
fum = fumbles
rec% = receptions / targets
1dn/rec = first downs / receptions
ypc = yards per catch
yac = yards after catch

Please, if anyone would like to refine these or make them worlds better, I would love it. This was just my way of trying to have a ratings system that seemed to reflect reality and didn't produce very strange numbers.

I'm sure the real numbers guys and statisticians here could improve this a whole lot. Go easy on me, guys!

jmt57

I like the formula as it gives a nice balance between quantity and quality, and takes into account pretty much any worthwhile metric I can think of. The names on both the overall rankings as well as the sub-rankings bear out that it does seem to be a pretty good way of looking at a receiver's performance and productivity.

patfanken

This was awesome, Ivan. Since a lot of people are taking about him, I'd be interested to seeing how Brandon Lloyd's numbers would look like. As a matter of fact, I'd be interested in seeing where the top ten FA WR's would fit into this formula you've developed.

Again, thanks a lot for the effort,.

VrabelJr

If you won't reveal your formula then this is useless. Which is a very supporting fact to your claim that you are not a statistician.

PatsFanSince74

A lot of work and thought went into that. Thank you.

My quibble is that you are mixing yardage indicators ("yds", "ypc", "yac") with percentage indicators, which latter you then have to adjust by multiplying by a factor of 10 to make them comparable to yardage. That seems artificial to me.

Also, I could figure out what you mean in all of your formulas except for "(10*20+/rec)." How does that read out?

Otherwise, I'll have to think about it a bit. You must have a very good database on the Receivers. Could you give us the source for your raw data so we can play around with it a bit?

Thanks again.

__________________
It is what it is. It wasn't what it wasn't.

PatsFanSince74

Well, "useless" is a little harsh dontcha think? Why not just ask him nicely for it like JMT did?

__________________
It is what it is. It wasn't what it wasn't.

jmt57

The guy with post #7 may want to read post #4