The Toolbox: Secondary Point Values

So we've covered that each yard line has a specific point value, and we've covered that an EqPts Per Play (PPP) measure is extremely useful in terms of both evaluation and the tearing apart and piecing together of a given game.  But a "one value per yard line" concept ignores quite a bit of context.  So let's take it down a level.

Click to embiggen.

Here's what I said about secondary (or second-level) point values when I first wrote about them at Varsity Numbers:

The concept behind EqPts is a simple one. Each yard line has a point value assigned to it based on the number of points an offense can expect to score in a possession involving a play from that yard line. The 20-yard line is worth 1.179 EqPts. The opposing 20-yard line is worth 3.898. Each play is assigned a point value based on where the play started and where it finished. The slope is different throughout the field. A gain of five yards from your 20 to your 25 is worth 0.064 EqPts. From the opponent's 40 to the opponent's 35: 0.441 EqPts. From the opponent's 10 to the opponent's 5: 0.582 EqPts. The concept of EqPts is intended to give more weight to more important gains.

Second- and third-level EqPts are in essence derivatives of the EqPts concept. Second-level EqPts take two factors into account: yard line and down. First down from your 20 (1.488) has a different point value than third down from your 20 (0.808). Another example: First down from the opponent's 10 is worth 4.881 EqPts, second down is worth 4.477, and third down is worth 3.818. It's not a hard concept to explain; the points you can expect to score go down as the down markers go up.

With second-level EqPts, a play can have a negative value without losing yards. As mentioned in the quote above, second-level EqPts don't tie as closely to actual point values (because of the possibility of negative values, the sum of all second-level EqPt values is only about 82 percent of the sum of first-level EqPts), but looking at second-level Points Per Play (or 2ndPPP) adds a factor of timely play-making to the equation -- because in football, as in comedy and sniper-fire, it's all about timing -- while further subtracting empty gains on second- or third-and-long.

Secondary point values add context where little existed before.  The general EqPts figure correlates more closely to overall quality, and that's why it gets used as part of S&P+ (for a while, I experimented with using a combination of PPP and 2nd PPP, but it just dragged the correlations down), but there is a lot of value here regardless.  If we are to look at a given drive like Run Expectancy looks at a given baseball inning, then this extra context comes in handy.

Yard-per-yard table and an example drive after the jump.

YdLine
1st Down
2nd Down
3rd Down
4th Down
1 0.9450 0.5791 0.3391 0.0022
2 0.9752 0.7180 0.3404 0.0043
3 1.0578 0.7923 0.3415 0.0065
4 1.1528 0.8590 0.3426 0.0086
5 1.1663 0.8671 0.3530 0.0108
6 1.1864 0.8713 0.3640 0.0130
7 1.2057 0.8722 0.4069 0.0151
8 1.2154 0.8741 0.4247 0.0173
9 1.2166 0.8753 0.5421 0.0194
10 1.2254 0.8787 0.5457 0.0219
11 1.2288 0.8929 0.5541 0.0243
12 1.2434 0.9461 0.5557 0.0267
13 1.2673 0.9916 0.5658 0.0291
14 1.3050 0.9984 0.5691 0.0316
15 1.3358 1.0123 0.5745 0.0340
16 1.3762 1.0564 0.5919 0.0342
17 1.4531 1.1089 0.6235 0.0381
18 1.4698 1.1257 0.6883 0.0420
19 1.4746 1.1425 0.7884 0.0459
20 1.4875 1.1692 0.8081 0.0632
21 1.4960 1.2069 0.8085 0.0661
22 1.5090 1.2348 0.8498 0.0689
23 1.5276 1.2603 0.8593 0.0790
24 1.5528 1.2986 0.8688 0.0891
25 1.5828 1.3369 0.8895 0.0993
26 1.6040 1.3845 0.9104 0.0998
27 1.6383 1.4168 0.9678 0.1003
28 1.6992 1.4508 0.9927 0.1019
29 1.7625 1.4990 1.0004 0.1037
30 1.8132 1.5119 1.0077 0.1054
31 1.8866 1.5189 1.0126 0.1070
32 1.9335 1.5402 1.0174 0.1085
33 1.9774 1.5694 1.0223 0.1136
34 2.0063 1.6229 1.0272 0.1186
35 2.0206 1.6284 1.0334 0.1237
36 2.0452 1.7073 1.1117 0.1287
37 2.0698 1.7462 1.1944 0.1338
38 2.0850 1.8098 1.2037 0.1387
39 2.1108 1.8486 1.2881 0.1798
40 2.1425 1.8848 1.3154 0.1851
41 2.1776 1.8897 1.3168 0.2028
42 2.2464 1.8946 1.3289 0.2183
43 2.3038 1.9206 1.3497 0.2338
44 2.3050 1.9485 1.3520 0.2391
45 2.4235 2.0000 1.3543 0.2492
46 2.4529 2.0449 1.3567 0.2593
47 2.4976 2.0927 1.3867 0.2695
48 2.5295 2.1163 1.4387 0.2797
49 2.5764 2.1807 1.4894 0.2835
50 2.5929 2.2074 1.5695 0.2873
51 2.6854 2.2664 1.6005 0.2911
52 2.7368 2.3332 1.6187 0.3013
53 2.8279 2.3711 1.6225 0.3115
54 2.8727 2.3845 1.6352 0.3219
55 2.9033 2.4711 1.6643 0.3321
56 2.9262 2.5128 1.7152 0.3856
57 2.9949 2.5253 1.7425 0.4346
58 3.0477 2.5691 1.8542 0.4925
59 3.1160 2.6903 1.9836 0.5807
60 3.2059 2.7175 2.0067 0.5942
61 3.2926 2.7756 2.1486 0.6443
62 3.3818 2.8884 2.2449 0.7834
63 3.4063 3.0035 2.3019 0.8476
64 3.5002 3.0904 2.3158 0.9797
65 3.5418 3.1773 2.4009 1.1454
66 3.5583 3.2453 2.4859 1.2270
67 3.5875 3.3109 2.5494 1.3710
68 3.6741 3.3575 2.6044 1.4931
69 3.6773 3.4709 2.6316 1.7021
70 3.7547 3.4772 2.6589 1.7523
71 3.8032 3.5182 2.7811 1.8772
72 3.8580 3.5846 2.9264 1.9467
73 3.9346 3.6266 3.0300 1.9584
74 4.0220 3.7253 3.1082 1.9700
75 4.0728 3.7779 3.1590 1.9818
76 4.1758 3.8556 3.2071 2.0508
77 4.2855 3.8568 3.2227 2.0643
78 4.2859 3.9478 3.2414 2.0777
79 4.3273 3.9498 3.3895 2.1176
80 4.3618 3.9517 3.4394 2.1580
81 4.3808 4.0312 3.5298 2.2289
82 4.3917 4.1271 3.5960 2.2867
83 4.4567 4.1803 3.6453 2.3911
84 4.5161 4.2335 3.6564 2.4464
85 4.6265 4.3289 3.6815 2.5017
86 4.6768 4.3994 3.7065 2.5050
87 4.7455 4.4467 3.7233 2.5083
88 4.7817 4.4498 3.7511 2.5137
89 4.8061 4.4570 3.7744 2.5862
90 4.8813 4.4771 3.8180 2.6146
91 4.9041 4.4995 3.9344 2.6942
92 4.9714 4.6353 4.0957 2.7847
93 5.1909 4.7989 4.2520 2.8160
94 5.2686 4.9634 4.3634 2.8609
95 5.4047 5.1794 4.4570 2.8914
96 5.6264 5.3287 4.6920 2.9766
97 5.8424 5.5478 4.8670 3.0618
98 6.0943 5.8578 5.3222 3.8831
99 6.2531 5.9992 5.5141 4.1119
100 6.9630 6.9630 6.9630 6.9630

To understand how this can work from a Point Expectancy standpoint, let's see it in action.  Here is TCU's first touchdown drive from the 2011 Rose Bowl:

 

Down/
Distance
Yard
Line
Play Starting
Exp. Pts.
Ending
Exp. Pts.
PLAY
VALUE
1st-and-10 TCU 23 Dalton, Andy pass complete to Young, Jimmy for 9 yards to the TC32 (FENELUS, Antoni) 1.53 1.54 +0.01
2nd-and-1 TCU 32 Dalton, Andy rush for 11 yards to the TC43 (HENRY, Aaron) 1.54 2.30 +0.76
1st-and-10 TCU 43 PENALTY WIS pass interference (SMITH, Devin) 6 yards to the TC49 2.30 2.58 +0.28
1st-and-10 TCU 49 Dalton, Andy rush for no gain to the TC49 (NZEGWU, Louis) 2.58 2.18 -0.40
2nd-and-10 TCU 49 Dalton, Andy pass incomplete to Shivers, Luke (WATT, J.J.) 2.18 1.49 -0.69
3rd-and-10 TCU 49 Dalton, Andy pass complete to Young, Jimmy for 14 yards to the WIS37 (FENELUS, Antoni) 1.49 3.40 +1.91
1st-and-10 UW 37 Dalton, Andy pass incomplete to Clay, Curtis 3.40 3.00 -0.40
2nd-and-10 UW 37 Dalton, Andy rush for 5 yards to the WIS32 (ALLEN, Beau) 3.00 2.60 -0.40
3rd-and-5 UW 32 PENALTY TC false start (Roth, Zach) 5 yards to the WIS37 2.60 2.30 -0.30
3rd-and-10 UW 37 Dalton, Andy pass complete to Young, Jimmy for 11 yards to the WIS26 (TAYLOR, Mike) 2.30 4.02 +1.72
1st-and-10 UW 26 Dalton, Andy rush for 3 yards to the WIS23 (WATT, J.J.) 4.02 3.86 -0.16
2nd-and-7 UW 23 Dalton, Andy pass complete to Johnson, Bart for 23 yards to the WIS0, TOUCHDOWN 3.86 6.96 +3.10

Of course, there is still a little bit missing.  Third-and-10 is treated the same as third-and-1.  If you want to see some crazy ups and downs in expected points, wait until we start talking about (and trying to draw tables for) the third-level (tertiary) point values that take yard line, down and distance into account.

Tomorrow we'll look at offenses based on 2nd PPP, and the teams whose PPP and 2nd PPP rankings varied the most significantly.

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