Statistics


The first version of my Open Source Draft Simulator I wrote in time to analyze the draft of 2001, and it was based on C++. Later on, in 2007, while trying to get a job, I rewrote the simulator in Ruby because I was trying to impress people that I could learn the language. I didn’t get the job. The Ruby simulator isn’t as statistically versatile, but it works on multiple sports.

I pulled out that ten year old code, in part to see if it still works, and part to see if I could make use of the data I had received from Ourlads. Ourlads does a 32 team needs list, which in general is the hardest part of setting up a draft simulator.

The ruby code, as downloaded, has a dependence on the module ‘rdoc/usage’. It is not essential, and I recommend you comment out or delete the line that says ‘require ‘rdoc/usage”. At that point you’ll have a working program. If all the warnings at the beginning bother you, remove the -w flag from the hash bang (first) line.

On Linux create all the files and then get rid of the ^Ms at the end of the lines. I had originally developed this sim on Windows. You can use perl to remove the ^M characters with something like perl -pre ‘s/\r//g’.

Data sources? Sports Illustrated has a top 100 list that works well. The top 100 list from NFL Draft Scout also yields useful results. I used Ourlads as my ‘serious’ set of needs, but Lance Zierlein has a set, as do other sites.

A typical rule file in my current setup is:

#
# rule file for Cleveland Browns.
#
rule need
#
needlist QB RB OL DB DE
#
cond QB max 1 high 
#
cond RB max 1

To note, with the SI top player set, if you don’t set QB to a “high” need, you’ll end up drafting Saquon Barkley number one. That’s one of the things I like about my own code. Slight changes in the needs of a single team can cause ripple effects throughout the draft.

A typical mock draft using this setup is:

ruby rubysim.rb -y 2018 -s football

This mock draft was made by rubysim.rb on 2018-04-16


Round 1.

1. Cleveland Browns select Sam Darnold, QB.
2. New York Giants select Bradley Chubb, DE.
3. New York Jets select Baker Mayfield, QB.
4. Cleveland Browns select Saquon Barkley, RB.
5. Denver Broncos select Josh Allen, QB.
6. Indianapolis Colts select Quenton Nelson, G.
7. Tampa Bay Buccaneers select Minkah Fitzpatrick, S.
8. Chicago Bears select Roquan Smith, LB.
9. San Francisco 49ers select Calvin Ridley, WR.
10. Oakland Raiders select Denzel Ward, CB.
11. Miami Dolphins select Vita Vea, DT.
12. Buffalo Bills select Josh Rosen, QB.
13. Washington Redskins select Josh Jackson, CB.
14. Green Bay Packers select Derwin James, S.
15. Arizona Cardinals select Connor Williams, OT.
16. Baltimore Ravens select Mike McGlinchey, OT.
17. Los Angeles Chargers select Tremaine Edmunds, LB.
18. Seattle Seahawks select Marcus Davenport, DE.
19. Dallas Cowboys select Da'Ron Payne, DT.
20. Detroit Lions select Harold Landry, DE.
21. Cincinnati Bengals select Leighton Vander Esch, LB.
22. Buffalo Bills select Courtland Sutton, WR.
23. New England Patriots select Derrius Guice, RB.
24. Carolina Panthers select Isaiah Oliver, CB.
25. Tennessee Titans select Maurice Hurst, DT.
26. Atlanta Falcons select Taven Bryan, DL.
27. New Orleans Saints select Christian Kirk, WR.
28. Pittsburgh Steelers select Rashaan Evans, LB.
29. Jacksonville Jaguars select Kolton Miller, OT.
30. Minnesota Vikings select Arden Key, DE.
31. New England Patriots select Isaiah Wynn, G.
32. Philadelphia Eagles select Justin Reid, S.

Round 2.

33. Cleveland Browns select James Daniels, C.
34. New York Giants select Lamar Jackson, QB.
35. Cleveland Browns select Mike Hughes, CB.
36. Indianapolis Colts select Jaire Alexander, CB.
37. Indianapolis Colts select Ronnie Harrison, S.
38. Tampa Bay Buccaneers select Carlton Davis, CB.
39. Chicago Bears select D.J. Moore, WR.
40. Denver Broncos select Hayden Hurst, TE.
41. Oakland Raiders select Donte Jackson, CB.
42. Miami Dolphins select Ronald Jones II, RB.
43. New England Patriots select Mike Gesicki, TE.
44. Washington Redskins select Will Hernandez, G.
45. Green Bay Packers select Orlando Brown, OT.
46. Cincinnati Bengals select Billy Price, C.
47. Arizona Cardinals select Chukwuma Okorafor, OT.
48. Los Angeles Chargers select Rasheem Green, DT.
49. Indianapolis Colts select Sam Hubbard, DE.
50. Dallas Cowboys select James Washington, WR.
51. Detroit Lions select Brian O'Neill, OT.
52. Baltimore Ravens select Jessie Bates, S.
53. Buffalo Bills select Deon Cain, WR.
54. Kansas City Chiefs select Tim Settle, DT.
55. Carolina Panthers select Lorenzo Carter, DE.
56. Buffalo Bills select Martinas Rankin, OT.
57. Tennessee Titans select Armani Watts, S.
58. Atlanta Falcons select Harrison Phillips, DT.
59. San Francisco 49ers select Uchenna Nwosu, LB.
60. Pittsburgh Steelers select Dallas Goedert, TE.
61. Jacksonville Jaguars select Anthony Averett, CB.
62. Minnesota Vikings select DeShon Elliott, S.
63. New England Patriots select Tyrell Crosby, OT.
64. Cleveland Browns select Ogbonnia Okoronkwo, DE.

Round 3.

65. Buffalo Bills select Darius Leonard, LB.
66. New York Giants select Sony Michel, RB.
67. Indianapolis Colts select Desmond Harrison, OT.
68. Houston Texans select Mark Andrews, TE.
69. New York Giants select Mason Rudolph, QB.
70. San Francisco 49ers select Dante Pettis, WR.
71. Denver Broncos select Kerryon Johnson, RB.
72. New York Jets select Nick Chubb, RB.
73. Miami Dolphins select Jerome Baker, LB.
74. San Francisco 49ers select Equanimeous St. Brown, WR.
75. Oakland Raiders select Malik Jefferson, LB.
76. Green Bay Packers select Michael Gallup, WR.
77. Cincinnati Bengals select Ian Thomas, TE.
78. Washington Redskins select Frank Ragnow, C.
79. Arizona Cardinals select Geron Christian, OT.
80. Houston Texans select Kyzir White, S.
81. Dallas Cowboys select Jamarco Jones, OT.
82. Detroit Lions select Jeff Holland, DE.
83. Baltimore Colts select Josh Sweat, DE.
84. Los Angeles Chargers select Trenton Thompson, DT.
85. Carolina Panthers select D.J. Chark, WR.
86. Kansas City Chiefs select Braden Smith, G.
87. Los Angeles Rams select Kemoko Turay, DE.
88. Carolina Panthers select Dorance Armstrong Jr., DE.
89. Tennessee Titans select Tarvarus McFadden, CB.
90. Atlanta Falcons select Chad Thomas, DE.
91. New Orleans Saints select Jordan Lasley, WR.
92. Pittsburgh Steelers select Shaquem Griffin, OLB.
93. Jacksonville Jaguars select Rashaan Gaulden, CB.
94. Minnesota Vikings select Tre'Quan Smith, WR.
95. New England Patriots select Anthony Miller, WR.
96. Buffalo Bills select Simmie Cobbs Jr., WR.
97. Arizona Cardinals select Joseph Noteboom, OT.
98. Houston Texans select Nick Nelson, CB.
99. Denver Broncos select Rashaad Penny, RB.
100. Cincinnati Bengals select Jaylen Samuels, RB.
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I’ll continue posting my odds, though this has not been the best season for them. Jacksonville continued to be best modeled by their median point spread, as opposed to their playoff formula. Philadelphia outperformed any reasonable prediction of their play once Wentz went down.

My system gives an edge to New England. Philadelphia played a tougher schedule but lacks playoff experience by my system. There is no home field in the Superbowl.

Super Bowl Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
New England Patriots Philadelphia Eagles 0.586 0.642 4.3

Outside of the New England game, all the games were good and exciting, from the final goal line stand by the Eagles, to the win with ten seconds left by the Vikings. The Jacksonville Jaguars are just not well managed by this system. It was easy to see that through the year that they were a boom or bust team. They could win big or lose big, and in the game with the Steelers, they were enough in “win big” mode that the Steelers could not keep up.

Philadelphia won because of their stout defense, a Nick Foles that gave them a AYA of 8.2 for the game, much akin to Carson Wentz’s average.

To remind people, the 2017 worksheet is here, and the methodology is here. The odds for the next round are below.

Conference (NFC/AFC) Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Philadelphia Eagles Minnesota Vikings -0.604 0.353 -4.5
New England Patriots Jacksonville Jaguars 1.872 0.867 13.9

The first round is over and in terms of predicting winners, not my best (by my count, 1-2-1, as we had Jax and Bills in a de facto tie). I was pleased that the model got Rams and Atlanta correct, and the Sunday games all came down to the wire. One or two plays and my formal results would have been impressive. Still, back to the predictions for this week.

To add some spice, we will predict results for New Orleans normally, and also as if Drew Brees is elite. Values in parentheses are the elite numbers. With elite status or no, Minnesota is still favored in this data set.

The only home team not favored is Philadelphia. We discussed this in part in this article.

Second Round Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Philadelphia Eagles Atlanta Falcons -0.878 0.294 -6.5
Minnesota Vikings New Orleans Saints 1.231 (0.484) 0.774 (0.619) 9.1 (3.6)
New England Patriots Tennessee Titans 1.674 0.842 12.4
Pittsburgh Steelers Jacksonville Jaguars 1.915 0.872 14

Summary: Replacing Wentz with Foles removes about 6.5 points of offense from the Philadelphia Eagles, turning a high flying offense into something very average.

Last night the Atlanta Falcons defeated the LA Rams. Now we’re faced with the prospect of the Falcons playing the Eagles. I have an idiosyncratic playoff model, one I treat as a hobby. It is based on static factors, the three being home field advantage, strength of schedule, and previous playoff experience. And since it values the Eagles as 0.444 and the Falcons as 1.322, the difference is -0.878 (win probability in logits). The inverse logit of -0.878 is 0.294, which is the probability of the Eagles winning, and an estimated point spread would be a 6.5 point advantage for the Falcons.

Another question that a Falcons or Eagles fan might have is how much is Carson Wentz worth as a QB, in points scored? We can use the adjusted yards per attempt stat of Pro Football Reference to estimate this, and also to estimate how much Carson Wentz is better than Foles. We have made these kinds of analyses before for Matt Ryan and Peyton Manning.

Pro Football Reference says that Carson Wentz has a AYA of 8.3 yards per attempt. Nick Foles has a AYA of 5.4. Now lets calculate the overall AYA for every pass thrown in the NFL. Stats are from Pro Football Reference.

(114870 yards + 20*741 TDs – 45*430 Ints) / 17488 Attempts
(114870 yards + 14820 TD “yards” – 19350 Int “yards”) / 117488 Attempts
110340 net yards / 17488 yards
6.31 yards per attempt to three significant digits

So about 6.3 yards per attempt. Carson Wentz is 2 yards per attempt better than the average. Nick Foles is 0.9 yards less than the average. The magic number is 2.25 which converts yards per attempt to points scored per thirty passes. So Carson, compared to Foles, is worth 2.9 * 2.25 = 6.5 points per game more than Foles, and 4.5 points more than the average NFL quarterback.

This doesn’t completely encompass Carson Wentz’s value, as according to ESPN
‘s QBR stat
, he account for 10 expected points on the ground in 13 games, so he nets about 0.8 points a game on the ground as well.

Now, back to some traditional stats. The offensive SRS assigned to Philadelphia by PFR is 7.0 with a defensive SRS of 2.5. If Carson Wentz is worth between 6.5 and 7.3 points per game, then it reduces Philadelphia’s offense to something very average, about 0.5 to -0.3. That high flying offense is almost completely transformed by the loss of their quarterback into an average offense.

Note: logits are to probabilities as logarithms are to multiplication. Rather than multiplying probabilities and using transitive rules, you just add the logits and convert back. Logarithms allow you to add logarithms of numbers rather than multiplying them.

One of the ESPN folks posted FPI odds today, retweeted by Ben Alamar. The numbers are very different from my playoff formulas. The nature of those odds made me suspect that FPI is intrinsically an offensive stat, with the advantages and disadvantages of such a stat.

One of the issues I’ve has with offensive stats is that the confidence interval of any I’ve looked at, in terms of predicting playoff performance, is that those confidence intervals are on the order of 85%. Whatever flaws of my formulas, they fit to confidence intervals of 95%. The effects they touch on are real.

But still, the purpose of this is to compare FPI odds to the odds generated by some common offensive stats. We’re using Pythagorean expectation, as generated by my Perl code, SRS as generated by my Perl code, and median point spread, also calculated by my code.

Results are below.

FPI Odds versus Other Offensive Stats
Game FPI Pythag Simple Ranking Median Pt Spread
Kansas City – Tennessee 0.75 0.75 0.79 0.73
Jacksonville – Buffalo 0.82 0.89 0.86 0.73
Los Angeles – Atlanta 0.62 0.75 0.74 0.68
New Orleans – Carolina 0.70 0.73 0.74 0.78

 

The numbers correlate too well for FPI not to have a large offensive component in its character. In fact, Pythagorean odds correlate so well with FPI I’m hard pressed to know what advantages FPI gives to the generic fan.

Note: the SRS link above points out that PFR has added a home field advantage component to their SRS calcs. I’ll note that our SRS was calibrated against PFR’s pre 2015 formula.

 

This would have been done earlier, but Pro Football Reference dropped its very handy chart of draft position versus AV. I started missing it more and more, and using the Wayback Machine I found it here.

The three major QB trades of 2017 were the trade for Mitch Trubisky, Patrick Mahomes, and Deshaun Watson. We will analyze them in sequence.

Mitchell Trubisky Trade
Chicago Bears 49ers Results
Pick Average AV Pick Average AV Delta AV Risk Ratio
2 46 3 45
67 21
111 13
(71) 13
Total 46 Total 92
46 2.00

 

The Bears have a trade risk comparable to a typical trade for a #1 draft choice and a quarterback at that. The trade has less fundamental risk than Goff or Wentz. The comparable that comes to mind is Eli Manning. By contrast, the delta AV of the other two trades are substantially less.

Patrick Mahomes Trade
Chiefs Bills Results
Pick Average AV Pick Average AV Delta AV Risk Ratio
10 41 27 25
91 20
(25) 24
Total 41 Total 69
28 1.68

 
Mahomes merely has to give six seven good years, and the trade ends up warranted. The issue in the case of Deshaun Watson is keeping him upright. A fistful of whole years almost as good as his freshman year in the NFL and he would end up bordering on Hall of Fame numbers.

Deshaun Watson Trade
Texans Browns Results
Pick Average AV Pick Average AV Delta AV Risk Ratio
12 35 25 24
4 44
Total 35 Total 68
33 1.94

 

So here is wishing Deshaun Watson a healthy career from now on.

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