Wednesday, June 5, 2013

NEW QUARTERBACK PASSING RATING FORMULA.

Updated March 7, 2018

As posted on a wiki talk page, the popularly used quarterback rating formula is so far from adequate measure that I put upon myself to make one that is more sensible. My aim is to make reasonable models of the major categories involved in assessing a quarterback's PASSING performance. Certainly, until which time the NFL decides to parse certain statistics like no-fault passer incompletions and not counting spiked balls used to stop the clock, my proposed model below is working off of traditional statistics. Overall quarterback performance would be far more involved and would have much obfuscating aspects involved such as the play caller, coach calls, errors by the offense (such as delay of game not caused by the quarterback, off-side penalties as well as other play action penalties), running, dodging sacks, etc.

My objections five years ago of the NFL adopted passer rating index include:
1) the bizarre numerical rating of 158.3 to be the highest figure possible,
2) the 10 pass minimum to qualify for a perfect rating, as if snowy day and most all plays are on the ground, and with a weak defense, the offense is able to only have say, 30 total plays, it would not be the quarterback’s failure to not pass extensively.
3) averaging 12.5 yards per attempt as “perfect” which means throwing for more yardage would not be any better
4) the 11.875% touchdown passes percentage which could be highly dependent on what the quarterback is told to do.

I opted to make 100 the number considered to be perfect. In my first formula, in using exponential functions, the 100 number would be impossible to be obtained but could get to practically that number. In this newer model, I am allowing the 100 number to be achieved.

I originally gave greater points to quarterbacks doing extensive passing but opted to avoid this. Besides the scenario of a snowy day as mentioned prior, suppose a first-string quarterback gets injured and the replacing quarterback makes only 9 passes and all were completions of 20+ yards - would that make the second quarterback not be considered perfect? And so, any number of passes would qualify for perfection and this would not hurt anything as besides trivial short-lasting presence on the field, the yearly or career statistics could have basic requirements to be included.

The NFL's adopted formula using 12.5 yards per attempt qualifying for perfect, I find this to be about right and thus am incorporating this figure in the newer formula.

I am fine with the 77.5% completion percentage but I am adopting herein a 75% completion percentage to account for spiked balls and receiver dropped balls. I’d up the number to 90% if basic statistics honed in more to the quarterback’s passer performance that would not be unduly affected by confounding factors.


The newer formula I am proposing deals with three items only:
1) Percentage completions per attempt
2) Yards per attempt
3) Interceptions


Proposal for Quarterback Rating:

Passer Rating = 100*F1*F2*F3

Where:
F1=(27/32)*(C/A)^3/(729/4096+(C/A)^6) for C/A<=0.75, F1=1 for C/A>0.75
F2=5^(3/2)*2^(¼)*(Y/A)^(¾)/(125/4*2^(½) + (Y/A)^(3/2)) for Y/A<=12.5, F2=1 for Y/A>12.5
F3=1-(200*I/Y)^3/(7+(200*I/Y)^3)

where A=attempts, C=completed passes I= interceptions, Y=total yards passing.


The numbers in the formula may appear to be complicated but it’s really not so. The numbers have been chosen to enable curves of the individual passer rating components to have a zero slope at certain critical points or other defining properties to maintain flow without any cusps.


Here are the break-down graphs of the components used in the formula (use of wolfram alpha):

Pass completion percentage (function of complete passes per attempt):

completionpercentage


Production (function of yards per attempt):

yardsperattempt


Interceptions (function of interceptions relative to counterpart of passing yards - shown here using 200 passing yards as a basis):

interceptions



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COMPARE THIS NEW FORMULA WITH THE CURRENTLY USED FORMULA. COMPARE THE STATS AND YOU DETERMINE THE BETTER FORMULA! LOOK CLOSELY AT THE SEVERAL PLAYERS WITH MUCH DISPARATE RANKINGS AND INSPECT THE STATS TO SEE WHICH FORMULA YOU JUDGE THE PLAYERS TO BE MORE ACCURATELY PLACED.

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Preferred Rating FormulaCurrently Used Rating Formula            
RankRatingRatingRankPLAYERTEAMCOMPATTPCTYDSYDS/ATDINTSACKGYDS/G
189.99105.82Peyton Manning, QBDEN40058368.64,6597.9937112116291
288.481081Aaron Rodgers, QBGB37155267.24,2957.783985116268
387.899.15Matt Ryan, QBATL42261568.64,7197.6732142816295
487.55102.43Robert Griffin III, QBWSH25839365.63,2008.142053015213
581.821004Russell Wilson, QBSEA25239364.13,1187.9326103316195
681.3798.76Tom Brady, QBNE401637634,8277.583482716302
781.1390.79Matt Schaub, QBHOU35054464.34,0087.3722122716251
880.8690.510Tony Romo, QBDAL42564865.64,9037.5728193616306
980.07977Ben Roethlisberger, QBPIT28444963.33,2657.272683013251
1077.8896.38Drew Brees, QBNO422670635,1777.7343192616324
1175.2688.611Philip Rivers, QBSD33852764.13,6066.8426154916225
1273.185.316Carson Palmer, QBOAK34556561.14,0187.1122142615268
1372.4687.712Joe Flacco, QBBAL31753159.73,8177.1922103516239
1471.7787.413Andy Dalton, QBCIN32952862.33,6696.9527164616229
1571.479.123Nick Foles, QBPHI16126560.81,6996.4165207243
1670.4887.214Eli Manning, QBNYG32153659.93,9487.3726151916247
1769.979.822Matthew Stafford, QBDET43572759.84,9676.8320172916310
1869.2881.221Christian Ponder, QBMIN30048362.12,9356.0818123216183
1969.0786.215Cam Newton, QBCAR28048557.73,8697.9819123616242
2068.6582.618Sam Bradford, QBSTL32855159.53,7026.7221133516231
2166.4583.317Ryan Fitzpatrick, QBBUF30650560.63,4006.7324163016213
2264.9676.127Ryan Tannehill, QBMIA28248458.33,2946.8112133516206
2364.0381.320Jay Cutler, QBCHI25543458.83,0336.9919143815202
2463.4378.124Michael Vick, QBPHI20435158.12,3626.7312102810236
2563.0777.425Blaine Gabbert, QBJAC16227858.31,6625.98962210166
2658.3272.629Brandon Weeden, QBCLE29751757.43,3856.5514172815226
2757.7881.619Josh Freeman, QBTB30655854.84,0657.2927172616254
2857.027428Jake Locker, QBTEN17731456.42,1766.9310112511198
2955.4776.526Andrew Luck, QBIND33962754.14,3746.9823184116273
3050.7866.732Matt Cassel, QBKC16127758.11,7966.48612199200
3150.4172.230Chad Henne, QBJAC16630853.92,0846.7711112810208
3245.9166.931Mark Sanchez, QBNYJ24645354.32,8836.3613183415192