1. H [Human Capital Engaged in Play-making (HY) + Human Capital Engaged in Play Design (HA)]
H=YPA - 6.692/6.692
2. HY [Human Capital Engaged in Play-making]
HY =[120(YPA/10)] - 100/100
The equation is consistent with the limit of the design space of a football field. A football field is 120 yards long with two scoring zones (end zones) separated by a 100-yard non-scoring zone (the field of competition). The calculation indicates that the value of NFL player human capital engaged in play-making is equal to the sum of the scoring zones and the field of competition times a team's efficiency (YPA/10) less the field of competition divided by the field of competition.
3. HA [Human Capital Engaged in Play Design]
HA=H - HY
It is important to note that, consistent with (Growth Theory (a/k/a Endogenous Technological Change), HA must be non-negative, i.e., HA must be greater than or equal to 0. In other words, a coaching staff cannot contribute any negative play design to a team. The worst a coaching staff can do is contribute nothing. Because coaches never physically enter the field of competition on the football field, it is impossible for coaches to contribute negative plays such as interceptions, fumbles, sacks, or penalties. Only players can contribute such negative plays. Thus, the lower limit floor on a coaching staff's contribution to the success is nothing or 0.
4. ðHY [Player Play-making Productivity]
ðHY =(.1YPA)/[(1-.1YPA-.01YRA)(.1YPA + .01 YRA)]
In this model, YPA (yards per pass attempt) and YRA (yards per rush attempt) constitute technology parameters. YPA is multiplied by 1/10 because the purpose of the technology is to make a first down, which in the first instance requires a 10-yard gain. YRA is multiplied by 1/100 because in the second instance, the purpose of the technology still is to make a first down, but the required yardage is unknown.
The model is consistent with both the limit of the design space (a first down is 10 yards and a football field of competition is 100 yards) and the findings of Baldwin and Clark who have found that "[i]n investigations of design structure, there is an emerging consensus that the fundamental units of design--the smallest building blocks--are decisions. Design decisions yield the instructions and parameters that determine the final form of the artifact. Design structure in turn is determined by dependencies that exist between (or among decisions). Speaking informally, decision B depends on decision A if a change in A might require a change in B. In this case, B's decision-maker needs to know what has been decided about A in order to choose B appropriately."
Implicitly, the player productivity calculation is constrained by the requirement that ðHY be non-negative and that the sum of [.1YPA + .01YRA] be less than 1. Super Bowl data demonstrates that this constraint has little effect on the reliability of the equation to describe NFL player productivity. In 43 years, Super Bowl teams whose player productivity has been greater than 1 [.1YPA + .01YRA > 1] are 13-1 and the one loss is explained by the "black swan" known as the Delhomme Exception (See 10th Commandment). Where [.1 YPA + .01YRA > 1], QC assumes that player productivity is infinite [$].
During the 2008
National Football League season, the team with the greater player productivity
(ðHY) won over 76 percent of
the games played.
5. ð [Productivity Parameter]
6. ðHA [Coaching Productivity]
Coaching productivity is a paradoxical mess. However, an honest mess is better than a a tidy lie. Here is QC's graph of coaching productivity. Some observations about the graph are below.
First, paradoxically, at YPA less than 8.333, coaching productivity decreases even as both the contribution that coaches are making (HA) and player productivity (ðHY) is increasing. From 0 YPA to approximately 7.5 YPA, coaching productivity decreases almost imperceptibly, but from 7.5 YPA to 8.333 YPA, coaching productivity decreases dramatically. In other words, in this YPA range, coaching productivity is inversely related to coaching contribution and player productivity.
Second, at YPA equal to 8.333, coaching productivity is undefinable (Ø) because the players' play-making contribution at 8.333 equals 0 and productivity divided by 0 is undefinable (See Equation Nos. 2 + 5 above). As advancednflstats.com has found, a run becomes a better choice than a pass only in situations requiring a gain less than 2 yards. In other words, a run becomes a better choice (or at least as good a choice) as a pass at approximately 8.333 YPA. Consequently, an offensive play designer's choices become balanced at 8.333 YPA.
Third, again paradoxically, at YPA greater than 8.333 and less than 9, coaching productivity decreases even as both the contribution that coaches are making (H A) and player productivity (ðHY) is increasing. In other words, in this YPA range, coaching productivity is inversely related to coaching contribution and player productivity.
Finally, for YPA greater than 9, coaching productivity increases as the contribution that coaches make (HA) and player play-making productivity (ðHY ) increases. Offensive play designers--Bill Walsh, Mike Martz, George Blanda, Peyton Manning, et al.--who create a design edge for their team are virtually unstoppable. At YPA greater than 9, the number of play designs available to a team is growing. Such an offensive team is changing and adapting so fast that a defense simply cannot keep up with the offense. THIS TEAM WILL DOMINATE if it also holds its opponent to 6.692 D-QCYPA (or less). As the Super Bowl statistics demonstrate, teams that have met these standards in the Super Bowl are 13-0.