## 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 YardLine Play StartingExp. Pts. EndingExp. Pts. PLAYVALUE 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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