ABSTRACT 

Purpose. We investigated whether players drafted higher in the National Football League (NFL) over a ten-year period performed better in their first four years in the league, consistent with the trade value charts and rookie wage scale the NFL uses to value players. The purpose was to see whether how the NFL intuits draft values is connected to player performance.

Methods. In Study 1, we collected draft position data for each of the seven rounds of the draft over a ten-year period as well as the values for each of two different trade charts and the salaries in the rookie wage scale. We then coded data by round, third of round (top, middle, bottom), years in the league, and Pro Football Focus (PFF) grades.

Results. We found no correlation between performance and the way the NFL values draft positions and no difference in player performance and years in the league between draft positions in rounds 4 and 5. There were also no differences in player performance or years played in the among top, middle, or bottom thirds of rounds. We also found a distinct advantage in player performance for teams trading down for draft picks compared to those trading up for draft picks, contrary to the way the NFL values draft positions.

Conclusions. Our work shows several player performance-based results that contradict well-established beliefs concerning the value of draft picks in the NFL.

Applications in Sport. Trade values and rookie wage salaries are used as baselines by the NFL. The importance of drafting better players higher in the draft order have important implications for greater success for teams, executives, and players. Our work may inform strategies that might be best to use in drafting prospective players in the National Football League.

Key Words: NFL draft, trade value, intuitive beliefs, player performance.

INTRODUCTION 

The work here tested whether draft position predicts player performance once they are drafted into the National Football League (NFL). The NFL draft is set up so the team with the worst regular season record picks first, followed by the team with the second worst regular season record picking second, and so on. Picking first, though it means you finished with the worst record in the league the previous year, is an enviable position to be in at draft time as you have your pick of ~250-~275 players. The NFL draft consists of seven rounds(since 1994) of draft picks where, at least originally, every team has one pick in every round. Prevailing wisdom in this field and even if you are picking teams for any game whether athletic or not is that higher picks should be valued more than lower picks and that over time the data should bear this out.

The intuitive beliefs that the NFL, individual teams, and executives have about draft order or draft pick position can be measured in two ways. First, this may be measured by what are called ‘trade value charts,’ that define values for each one of the draft picks (3). There are a few different types of trade value charts, but most teams follow one of these versions if they want to trade draft picks with any other team. The classic version of a trade value chart is the Jimmy Johnson (JJ) chart. A more recent chart is the Rich Hill (RH) trade value chart. These charts basically provide teams with a framework or baseline from which to trade draft picks (14). The trade value charts are similar in several ways—(1) values increase exponentially in the first round from about pick 4 to pick 1 and (2) values for picks decrease for each subsequent pick. For instance, Pick #10 in the JJ chart this year was given a value that was 46.3% of Pick#1 (RH chart = 36.9%); Pick #20 was given a value that was 28.33% of Pick #1 (RH chart = 26.9%), and Pick #30 was given a value that was 20.67% of Pick #1 (RH chart = 19.6%). Consistent with this, the ratio of values in the top third : middle third of the first round is 1.824 in the JJ chart, (RH chart = 2); middle third : bottom third is ~1.49 (RH = 1.55); top third : bottom third is ~2.71 (RH = 3.13), and bottom third of 1^st : top third of 2^nd is 1.3 (RH = 1.5).

The second way the NFL’s intuitive beliefs about draft order may be measured is by the ‘rookie wage scale’ put forth by the player’s labor union and the NFL in 2011, which defines the parameters for what every drafted player will earn in his first four years in the league (3). For instance, this year, the number one overall draft pick will earn $48,757,500 in total value over his first 4 years; the number 10 pick will earn a little less than 55% of that (a difference of over $22M over the first four years); the number 20 pick will earn about 37% of that (a difference of almost $30M), while the number 30 pick will earn about 31.25% of that (a difference of ~$33.5M). While the percentage and salary difference is less in subsequent rounds among those picks (picks 1, 10, 20, and 30 in rounds 2-7), the importance of drafting better players higher in the draft order have important implications for building the best team, paying players the proper amount for their performance, the amount of money that is charged to a team’s salary cap, and the livelihood of the NFL executives who have a hand in drafting these players.

Previous work has investigated several avenues regarding characteristics that affect draft value, that are related to performance once in the NFL (5, 9, 15, 17, 20). The results of some of this work show how draft value does very little to affect probabilities of teams making the playoffs (9, 15), Other work has shown that college performance is a better predictor of performance once in the NFL than tests measuring physical ability (11, 20-21). While other work has shown that total yards gained by running backs in college and overall speed has been shown to be a primary predictor of both draft status and higher salaries once in the NFL over tests of physical ability and combine tests (6, 11, 16-17, 20). Additionally, predicting success based on results of athletic testing including the NFL Combine can yield complicated and somewhat mixed results (16).

The primary focus of this paper was to investigate whether what teams intuit of draft value based on grades in these trade value charts and rookie wage scales matches actual performance data for the players chosen in those spots. More specifically, our primary investigative foci in Study 1 were to: (1) analyze whether differences in player value (as given by trade value charts and the rookie wage scale) from pick-to-subsequent-pick were correlated with differences in player performance from pick-to-subsequent-pick, (2) analyze whether player performance, as measured by Pro Football Focus (PFF) grades and years spent in the league, was different among and within rounds (14), (3) analyze whether PFF grades and years in the league were different among thirds of rounds across and within rounds, (4) and analyze how the NFL valuation and PFF grades for last twelve picks of the first round compared to the first twelve picks of the second round.

STUDY 1

METHODS

Data Sets

We first used the Pro Football Reference site (20) to gather and download data for every player drafted from 2011-2020. We then used the Pro Football Focus (14) site to gather the overall season grades for each player across their first four years in the NFL. This resulted in 2,544 drafted players across 10 years. This study was approved by The Ohio State University Behavioral and Social Sciences Institutional Review Board (Study Number: 2023B0282).

Procedure

Evaluating a Player’s First Four Years in the NFL

Since we were interested in evaluating the success of teams in drafting, we evaluated player performance over the player’s first four years. This is because four years is the length of all rookie (1^st year player) contracts. Additionally, the first four years provides a very good indicator of what the teams think the player can do for their team in terms of performance.

Understanding the Pro Football Focus Grading System

PFF analyzes every player on every snap, with each play receiving a grade on a scale from -2 to +2. A score of 0 represents an average or the expected execution of the player’s responsibilities, while a +2 denotes an outstanding play and a -2 indicates a critical error. These assessments are adjusted for factors such as difficulty of assignment and game context. PFF’s system includes tracking over 200 data points per play using the All-22 coaches’ film, including such aspects as player alignment, assignment, and outcome of the play from every aspect of the field (1, 14). PFF then converts these evaluations into a normalized score on a 0–100 scale.

Calculation and Coding of PFF Grades and Years in the League

While PFF normalizes plays to values ranging from 0-100, the overall grades across an entire season of plays are far more restricted, ranging from ~high 40’s-low 90’s (for the requirement of at least 10 games played per season as described below). For every player, we calculated a mean for their overall PFF grade across their first four years after being drafted. For players with a missing grade, we found which of the four years there was a missing grade for and why. If the player was injured and missed the entire year (for any year), we did not count that year for their average and averaged across their other years. For players at most positions, we used the offense or defense overall grade for the given year. Only for punters and kickers did we use the special team grade. Our threshold for counting a PFF grade for the year, was at least ten games played. Additionally, if the drafting team waived the player they drafted, we assigned that player a value of 35, as that is below the lowest grade anyone on a team who played earned across an entire year of play (with a minimum of 10 games played). If they played on a team after they were waived, we filled in the four years with the grade(s) they earned in the remaining year(s) on the subsequent team. We wanted to penalize the drafting team, but we also did not want to assign a 0 as waiving the player was an act but does not represent their PFF grade over an entire year. Additionally, this happened far less often in earlier rounds and since we were calculating means, we did not want these outliers to dramatically influence the results. We assigned a value of 45 for a player who was on an NFL roster, but not active for the minimum number of games (or did not have enough snaps to be graded by PFF). This is a lower grade than any player we graded who played during the season for at least ten games and gave us a baseline for someone who is good enough to be on the team but may not be good enough/needed to dress on game day(s). We did not gather PFF data for rounds 6 and 7 as fewer players in these rounds were active for enough games (i.e., played enough snaps) for which PFF could assign grades.

Finally, we also analyzed the number of years players were in the league. Again, in the interests of evaluating how well teams draft, we were really focused on years in the league of these players over their first four to five years. Therefore, we coded years played in the league in categories of less than two years, two to three years, four years, five years, and more than five years, and then analyzed this coded data.

Availability of Data and Material

Data may be accessed at: https://osf.io/pf5hq/?view_only=28f7350c720f430b92270c76e5b48080

RESULTS

We performed Bayesian analyses throughout the Results sections for all experiments to properly identify and balance the same evidence in favor of as we did evidence opposed to differences, in line with the recommendations of both Dienes (4) and Kruschke (7). The primary independent variables were draft round and position within the round (top, middle, or bottom third), while the primary dependent variables were years in the league and PFF mean overall grade for players’ first four years in the league. We outline each set of analyses below.

Testing for Correlations Between Differences in PFF Grades and Differences in Jimmy Johnson and Rich Hill Trade Chart Values and Rookie Salaries for Each Subsequent Pick

 If players drafted with picks 1-10 are better than players drafted with picks 10-20, and so on, then both the difference in trade chart values and rookie wage scale salaries from pick #1 to pick #2 and pick #2 to #3 and so on through the first five rounds of the draft should be highly correlated with PFF grades. Bayesian correlational analyses showed substantial to strong evidence that there was close to zero correlation between PFF grades and trade chart values, RH trade value chart: Bayes Factor in favor of the null hypothesis (BF₀₁)= 5.594, r = .086, JJ trade value chart: BF₀₁= 10.485, r = .014, and PFF grades and rookie wage scale salaries: BF₀₁= 9.047, r = .043. The Bayes factors may be interpreted that it is 5.594, 10.485, and 9.047 times as likely that there is no correlation between PFF grades and RH trade chart values, JJ trade chart values, and rookie wage scale salaries, respectively, than there is a correlation (12, 24). Values of BF₀₁ or BF₁₀ of 0-1 = no evidence, 1-3 = anecdotal evidence, 3-10 = substantial evidence, 10-30 = strong evidence, 30-100 = very strong evidence, and >100 = decisive evidence in favor of whatever hypothesis is being tested (null (BF₀₁) or alternative (BF₁₀) (12, 24).

Analyzing How the NFL Values Draft Positions Based on the Rookie Wage Scale

We first established how the NFL values draft position across rounds and thirds of rounds. We used the rookie wage scale salaries for the first five rounds of the draft (the same rounds for which we calculated PFF grades for players—picks 1-165). Bayesian analyses showed decisive evidence of differences in salaries across rounds, BF₁₀= 2.806 x 10⁺³⁷, F(4, 150) = 448.83, p < .001, h² = 0.71, Cauchy Prior with a scale of .707. Post hoc tests also indicated decisive evidence for differences among all rounds. Bayesian analysis showed substantial evidence of differences in salaries across thirds of rounds, BF₁₀= 4.99, F(2, 150) = 88.19, p < .001, h² = 0.07, Cauchy Prior with a scale of .707. Post hoc tests confirmed between anecdotal to substantial evidence for differences among all thirds of rounds (top, middle, and bottom). Virtually identical results were found when performing these same analyses using each trade value chart in lieu of the rookie wage scale.

Analyzing Differences in Rounds for Coded Years in League and PFF Overall Mean Grade

 Coded Years in League

 A Bayesian one-way ANOVA analyzing whether there were differences in years played in the league showed that there were: BF₁₀= 2.806 x 10⁺¹¹¹ (decisive evidence), > Test value F(6, 2536) = 101.93, p < .001, h² = 0.19, Cauchy Prior with a scale of .707. Post hoc tests indicated that there was moderate to strong evidence that players drafted in round 1 remained in the league somewhat longer than players drafted in round 2, BF₁₀= 4.312 (moderate to substantial). Players in almost all subsequent rounds remained in the league for less time than the previous round. One exception was that there was no difference in years played in the league between rounds 4 and 5, BF₀₁ = 3.83 in favor of no difference, indicating moderate to substantial evidence in favor of no difference in years played in the league for 4^th and 5^th round draft picks.

 PFF Overall Mean Grade

A Bayesian one-way ANOVA analyzing whether there were differences in PFF overall mean grade showed that there were: BF₁₀= 2.673 x 10⁺⁵⁹ (decisive evidence), > Test value F(6, 2536) = 80.95, p < .001, h² = 0.16, Cauchy Prior with a scale of .707. Additionally, again almost all post hoc test BF₁₀ evidence showed decisive evidence for differences among all five rounds with values ranging from BF₁₀ = 188.192 to 2.724 x 10⁺³⁸. The one exception was that there was no difference in PFF overall mean grade between rounds 4 and 5, BF₀₁ = 4.51 in favor of no difference, indicating moderate to substantial evidence in favor of no difference. Figure 1 shows a graph of pick position (x-axis) by PFF grade (y-axis) for picks across all ten years.

Figure 1.

Shown is a plot of the pick number by overall mean PFF grade for the first 4 years. Each symbol represents the average PFF grade across 10 years for a particular position in the draft (picks1-179).

Differences in Thirds of Rounds for Coded Years in League and PFF Overall Mean Grade

A Bayesian one-way ANOVA analyzing whether there were differences in years played in the league in terms of whether a player was chosen at the top, in the middle, or at the bottom third of the round showed decisive evidence that there is no difference: BF₀₁= 20.998, Cauchy Prior with a scale of .707.

PFF Overall Mean Grade

A Bayesian one-way ANOVA analyzing whether there were differences in PFF overall mean grade showed decisive evidence that there also is no difference: BF₀₁= 30.292, Cauchy Prior with a scale of .707.

Differences Among Top, Middle, and Bottom of Rounds for Coded Years in League and PFF Overall Mean Grade Round-by-Round

While our previous analyses show no differences among player longevity and PFF overall mean grade across the top, middle, and bottom of rounds, it could be that any potential differences were washed out by combining rounds for the analysis. For instance, later rounds that have lesser talented players overall may see no differences, or have more talented players at the middle and bottom of rounds than the tops of rounds, whereas earlier rounds may have more talented players at the tops of rounds than at the middle and bottom of rounds. These effects or patterns may cancel each other out by combining all rounds. Therefore, we again tested for differences among the top, middle, and bottom third of rounds, but this time did so within each round. Table 1 shows the results of these analyses.

Table 1.

Shown are Bayes factor in favor of the null hypothesis (BF₀₁) for one-way ANOVAs testing for differences in coded years in the league and PFF overall mean grades for draft picks in rounds 1-7 (for years) and round 1-5 (for PFF grades) from 2011-2020. Values of BF₀₁ of 1-3 = anecdotal evidence, 3-10 = substantial evidence, 10-30 = strong evidence, 30-100 = very strong evidence, and >100 = decisive evidence in favor of the null hypothesis) (12, 23).

Predicting PFF Grades from Trade Value Charts and Evaluating Whether Trading Up into the First Round from the Second Round Warranted

Many times, draft experts will argue that some teams may “trade up” into the bottom third of the first round—that is, the last ~twelve to fifteen (~picks 18-32 or so)–from the top of the second round in order to draft a second player for whom they will have the 5^th year option (1^st round pick). Many teams have done this in the past. In fact, according to the values themselves, the NFL views the bottom 10-15 picks in round 1 as over 7008 times greater in value than the top 10-15 picks in round 2 , BF₁₀= 7008.114, Cauchy Prior with a scale of .707). When we analyzed PFF grades across ten years for the “bottom third” of the first round (12 picks—21-32) and compared them to PFF grades across ten years for the “top third” of the second round (12 picks—33-44), a Bayesian one-way ANOVA showed substantial evidence that there is no difference: BF₀₁= 6.854, Cauchy Prior with a scale of .707 (M_{Bottom10of1st} = 63.835; SD_{Bottom10of1st} = 10.642, M_Top10of2nd= 64.387, SD_Top10of2nd = 9.975).

STUDY 2

In Study 1 we found that the NFL values draft positions in the top of a round far more than those in the middle or bottom of a round and those in the middle of the round far more than those in the bottom of a round. However, there was substantial to decisive evidence of no differences in PFF grades across and within rounds, respectively, for top, middle, and bottom thirds of draft positions in rounds. We also found that there was no difference in PFF grades for draft positions in the top third of the 2^nd round compared to the bottom third of the 1^st round. This predicts that teams should not move up in a draft for players as the player performance will not be better for players drafted even 20-30 picks higher. When teams move up in the draft, they give up more draft capital for at least two reasons. First, while the values in the trade value chart might be even, typically the team moving back must give up more than one pick to do that in order to even out the trade value. Second, the team trading down must be incentivized in some ways to trade down. Sometimes, that team simply needs more players for the values to be even. Other times, the team trading down will ask for more as they are giving up an attractive draft pick. In Study 2, we sought to investigate whether the findings from the ten year period we investigated in Study 1 would predict the outcome of pick-for-pick trades in the 2021 NFL draft.

METHODS

We identified each of the draft pick-for-draft pick trades in the draft immediately after the last season for which we analyzed draft picks (the 2021 NFL draft). We evaluated each of the twenty-nine trades that are listed by the NFL that occurred during the 2021 draft (15). We did this because the 2021 draft was the first draft after the last year for which player performance data was collected so it allowed us to test whether our findings predicted future patterns and because it was the last year that would still allow us to analyze player performance in the first four years of the player’s career. We only looked at trades involving draft picks for draft picks.

Raters

We had two high school football players (M_Age = 18 years, M_{ExperiencePlayingCompetitiveFootball} = 6 years) who have a strong knowledge of not only the workings of football but also a strong knowledge of the NFL, the NFL draft, and grading players.

Procedure     

We gave raters the series of trades with round(s), pick number(s), and PFF grades across years played listed for each pick. We removed the draft year and team and player names from the list. Raters were also blind to which part of the trade was the “trade up” and which part was the “trade down.” Our list consisted of Team A on one side and Team B on the other. We randomly assigned which team (“trade up” or “trade down”) was Team A and which team was Team B. We instructed raters on how PFF grades are set up and general cutoffs for what PFF grades are generally considered elite, good, above average, average, and poor. We also instructed them to decide which team “won” each trade. While they were instructed that they should use all the information available in making their decisions, they were told that the performance of the players (i.e. PFF grades) should be paramount in making their decisions.

Raters made their judgments independently from one another. They were initially seated in two different areas at the same time while they made their judgments. They then came together, compared their judgments, and went over the judgments that were different to see whether they could come to a consensus on the judgments that were different.

RESULTS

The raters initially agreed on 20/29 trades. After discussing the trades they had originally disagreed on, they came to a consensus on all 29. Of the 9 on which they initially had different answers, neither rater favored the “trade up” team; each of the 9 consisted of one rater deciding on the “trade down” team and the other deciding on “neither.” For 6/9 of the trades they eventually decided on “neither,” and in the other 3 trades they decided on “trade down.” Finally agreed-upon frequencies for each group were: Trade Up: 4, Trade Down: 19, and Neither: 6.

Since we were only interested in testing whether trading up resulted in better player performance, we were most interested in a comparison where we split the categories into the following two groups: Group 1: Trade Up and Group 2: Trade Down and Neither. We performed a Bayesian binomial test on frequencies of what the raters judged as “wins” in each category. Raters judged that there were significantly more wins in terms of better performing players for teams who traded down than for teams who traded up, BF₁₀  = 753.471, Proportion = .832, Prior Distribution with α and β = 1. This is decisive evidence that trading down led to better performing players than trading up and may be interpreted that it is more than 753 times more likely that trading down led to better performing players than trading up. In a second analysis, we compared only trade downs versus trade ups and removed any trade that resulted in a judgement of “neither.” Raters again judged that there were significantly more wins in terms of better performing players for teams who traded down than for teams who traded up, BF₁₀  = 39.472 , Proportion = .826, Prior Distribution with α and β = 1. This indicates very strong evidence that trading down led to better performing players than trading up. Therefore, even when solely comparing trade ups versus trade downs, it is still over thirty nine more times likely that trading down led to better performing players than trading up.

DISCUSSION 

The way the NFL values draft positions in terms of trade values and rookie salaries is not correlated at all with player performance consistent with previous work (14). While time spent in the league and overall PFF grade during their rookie contracts did, for the most part, gradually decline in subsequent rounds as trade value charts, fans, and NFL executives would all predict, this pattern was not straightforward. One large deviation from this gradual decline between rounds was between the  4^th and 5^th rounds, where there was moderate to substantial evidence in favor of no difference in both years played and overall PFF grades between those rounds, contradicting how the NFL values draft position. In fact, if we use trade values as a representation of people’s intuitions then we should expect far greater value out of 4^th round picks than we do from 5^th round picks, as a Bayesian independent-samples t-test analyzing trade values in round 4 versus round 5 found decisive evidence that round 4 values are significantly greater than round 5 values, BF₁₀= 7.294 x 10⁺¹¹, Cauchy Prior with a scale of .707. According to the values themselves, the NFL views round 4 picks as 7.294 x 10⁺¹¹ greater in value than 5^th round picks.

There were several other counterintuitive findings. First, there was decisive evidence of no difference among the top, middle, and bottom thirds of rounds across all rounds for both years in the league and PFF grades. Second, this evidence of no difference for both years in the league and PFF grades among the top, middle, and bottom thirds of rounds was a regularity for every round when evaluating each round individually. Third, we found that the performance of players taken in the top third of the second round was no different from the performance of players taken in the bottom third of the first round across all ten years, contradicting what the trade values tell us—that there is decisive evidence in favor of differences in those respective trade values.

When we looked at trades that occurred in 2021, we found that, in terms of quality of player(s), the large majority—over 82%–and significant number of trades did not favor the team who traded higher up in the draft where that pick had greater value. This result is consistent with what was found with the analyses finding no differences across thirds of rounds across and within rounds across our data. This has important implications for not only player performance, but also because it has been recently shown that teams getting the better end of trades increase their probability of making the playoffs (9).

There were limitations to this study. First, while PFF grades are used by NFL teams, NFL analytics sites, and content creators to assess player performance and are seen as the best tool for doing this, they are not perfect. However, while there may be an argument as to what goes into creating the absolute grades, we analyzed the grades relatively for players so the shortcomings of the grades themselves would apply to all players. A second limitation is that we used trade values and rookie wage salaries to as a measure of how general managers (GMs) of teams and the NFL as a whole assess player quality without directly asking them about how they value draft positions. However, there was a collective bargaining agreement between the NFL and player’s union that put in place the rookie wage scale in 2011 (3), and owners, GMs, and players all had their input into how this would be created. Additionally, every team in the NFL uses these trade values as the standard way to barter before, during, and after the draft. Thus, we feel this was a fair way to assess the way the NFL values draft positions.

Further research should be conducted to see how the player performance grades in the first four years connect with second contracts of players in their next 2-5 years. It may be that it takes certain players four years to blossom in the league. However, the average tenure of a player who makes the opening-day roster is ~6 years (about half of that if you include drafted players who do not make the opening day roster). Other work should focus on directly assessing the executives in charge of the teams who draft players and the intuitions they have regarding trading up or down in the draft and what goes into these decisions. It may be that player performance is not the only factor that drives this decision making.

CONCLUSION 

Differences in the way the NFL values draft positions are not associated with player performance in those respective draft positions. This occurs whether you analyze differences in values assigned to draft positions, different positions within a round, or adjacent positions across rounds. These patterns from our findings also predict the outcomes of future drafts in terms of the assets a team trading up gets compared to a team trading down.

APPLICATIONS IN SPORT

Trade values and trade value charts in the NFL are used as the baselines by which to trade draft picks. These charts serve at least two purposes. First, they give general managers a common mechanism that they generally agree on to trade draft picks. Second, it prevents desperate teams from trading away too much and prevents overly greedy teams from demanding too much. These values assign an assumed or perceived worth of the player picked in that position. The idea is that, while picks that are very close together may result in players that are of equal talent, picks that are several positions away from one another should result in better players for those picks that are higher in the draft order. This is reflected in the draft assets that teams are willing to give up to move up in the draft order. Our work shows that there are several performance-based patterns that contradict these naïve beliefs stemming from values given to players. While some teams might argue that they needed a player at a specific position over the best available player, one would expect that if teams stayed with their original pick, that across a general manager’s tenure they would be better off picking someone who provides better performance and not positional need. One should also expect that over one’s tenure the player performance is more valuable as a better player is more valuable as a trade asset. Our work may inform strategies that might be best to use in drafting prospective players in the National Football League.

ACKNOWLEDGEMENTS

Dennis M. Shaffer conceptualized the studies. For Study 1, the author oversaw investigation, methodology, and data curation. Formal analysis in the paper was conducted by this author. 

Ryanne E. Shaffer contributed to both studies, assisting with data curation for Study 1, and conducting Study 2. Dennis M. Shaffer supervised Study 2. 

The paper was drafted by Dennis M. Shaffer; the paper was reviewed and edited by Ryanne E. Shaffer. 

The authors would like to thank JD Okuma and Gavin Davis for their work as raters.

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