DATA606 - Final Project
Data Preparation
Data for project was derived from Ron Graf’s data work on NFL Football Draft Outcomes (Graf, 2016). The data is consolidated draft data from website: http://www.pro-football-reference.com
#load packages and csv file
library(ggplot2)
library(psych)##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha#Load data from local machine.
#main
nfl_draft<-read.csv('./nfl_draft.csv',sep=',',stringsAsFactors=F)
nfl_draft2005 <- subset(nfl_draft, Year < 2006)
nfl_draft2005$totalyears <- nfl_draft2005$To - nfl_draft2005$Year
# Reduce unneeded columns from nfl_draft2005 (Balla, 2015)
nfl_draft2005Rev2 <- subset(nfl_draft2005, select = c(Rnd,Pos,G))
nflplayersQB <- subset(nfl_draft2005Rev2, Pos == "QB", select=c(Rnd,G))
nflplayersWR <- subset(nfl_draft2005Rev2, Pos == "WR", select=c(Rnd,G))
nflplayersRB <- subset(nfl_draft2005Rev2, Pos == "RB", select=c(Rnd,G))
nflplayersTE <- subset(nfl_draft2005Rev2, Pos == "TE", select=c(Rnd,G))
nflplayersT <- subset(nfl_draft2005Rev2, Pos == "T", select=c(Rnd,G))
nflplayersC <- subset(nfl_draft2005Rev2, Pos == "C", select=c(Rnd,G))
nflplayersDT <- subset(nfl_draft2005Rev2, Pos == "DT", select=c(Rnd,G))
nflplayersLB <- subset(nfl_draft2005Rev2, Pos == "LB", select=c(Rnd,G))
nflplayersDB <- subset(nfl_draft2005Rev2, Pos == "DB", select=c(Rnd,G))
nflplayersDE <- subset(nfl_draft2005Rev2, Pos == "DE", select=c(Rnd,G))
nflplayersK <- subset(nfl_draft2005Rev2, Pos == "K", select=c(Rnd,G))
nflplayersP <- subset(nfl_draft2005Rev2, Pos == "P", select=c(Rnd,G))
# Elminate missing data from data frame
nflplayersQB <- na.omit(nflplayersQB)
nflplayersWR <- na.omit(nflplayersWR)
nflplayersRB <- na.omit(nflplayersRB)
nflplayersTE <- na.omit(nflplayersTE)
nflplayersT <- na.omit(nflplayersT)
nflplayersC <- na.omit(nflplayersC)
nflplayersDT <- na.omit(nflplayersDT)
nflplayersLB <- na.omit(nflplayersLB)
nflplayersDB <- na.omit(nflplayersDB)
nflplayersDE <- na.omit(nflplayersDE)
nflplayersK <- na.omit(nflplayersK)
nflplayersP <- na.omit(nflplayersP)
str(nflplayersQB)## 'data.frame': 197 obs. of 2 variables:
## $ Rnd: int 1 1 1 3 3 4 5 6 7 7 ...
## $ G : int 135 136 90 26 15 87 27 71 102 122 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:85] 6 8 10 12 23 25 28 30 53 56 ...
## .. ..- attr(*, "names")= chr [1:85] "2631" "2667" "2698" "2775" ...str(nflplayersWR)## 'data.frame': 540 obs. of 2 variables:
## $ Rnd: int 1 1 1 1 1 1 2 2 2 2 ...
## $ G : int 112 49 56 54 83 171 72 57 90 3 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:186] 17 18 21 26 31 56 62 80 82 88 ...
## .. ..- attr(*, "names")= chr [1:186] "2664" "2677" "2701" "2741" ...str(nflplayersRB)## 'data.frame': 461 obs. of 2 variables:
## $ Rnd: int 1 1 1 2 2 3 3 3 4 4 ...
## $ G : int 132 96 81 58 9 175 39 38 99 109 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:136] 9 13 19 21 50 51 52 53 72 73 ...
## .. ..- attr(*, "names")= chr [1:136] "2647" "2666" "2767" "2789" ...str(nflplayersTE)## 'data.frame': 275 obs. of 2 variables:
## $ Rnd: int 1 3 3 5 6 6 7 7 1 1 ...
## $ G : int 168 124 17 3 90 120 8 120 105 163 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:68] 6 10 25 58 60 70 73 76 86 90 ...
## .. ..- attr(*, "names")= chr [1:68] "2742" "2801" "3038" "3529" ...str(nflplayersT)## 'data.frame': 297 obs. of 2 variables:
## $ Rnd: int 1 1 2 2 2 3 3 3 4 4 ...
## $ G : int 85 87 148 151 50 76 141 68 44 116 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:112] 6 14 21 22 23 24 35 38 39 41 ...
## .. ..- attr(*, "names")= chr [1:112] "2637" "2699" "2757" "2760" ...str(nflplayersC)## 'data.frame': 127 obs. of 2 variables:
## $ Rnd: int 1 4 4 4 5 5 7 2 3 4 ...
## $ G : int 137 48 59 100 14 118 83 66 136 46 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:34] 6 13 14 17 23 24 31 41 43 53 ...
## .. ..- attr(*, "names")= chr [1:34] "2711" "2991" "2998" "3044" ...str(nflplayersDT)## 'data.frame': 281 obs. of 2 variables:
## $ Rnd: int 1 1 2 3 3 5 6 6 6 6 ...
## $ G : int 76 147 112 106 15 87 18 15 58 140 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:104] 12 24 36 56 66 71 75 93 113 115 ...
## .. ..- attr(*, "names")= chr [1:104] "2749" "2873" "3027" "3270" ...str(nflplayersLB)## 'data.frame': 629 obs. of 2 variables:
## $ Rnd: int 1 1 1 1 1 2 2 2 2 2 ...
## $ G : int 173 75 143 164 16 116 136 84 16 65 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:176] 21 25 28 32 66 115 124 145 152 153 ...
## .. ..- attr(*, "names")= chr [1:176] "2705" "2716" "2729" "2798" ...str(nflplayersDB)## 'data.frame': 853 obs. of 2 variables:
## $ Rnd: int 1 1 1 1 1 2 2 2 2 2 ...
## $ G : int 124 155 133 81 56 100 119 90 121 96 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:210] 34 37 43 46 50 85 89 98 141 146 ...
## .. ..- attr(*, "names")= chr [1:210] "2693" "2707" "2754" "2765" ...str(nflplayersDE)## 'data.frame': 403 obs. of 2 variables:
## $ Rnd: int 1 1 1 2 2 2 3 4 4 5 ...
## $ G : int 28 124 82 96 2 179 147 102 148 29 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:91] 8 22 38 39 40 43 56 65 67 86 ...
## .. ..- attr(*, "names")= chr [1:91] "2638" "2774" "2946" "2948" ...str(nflplayersK)## 'data.frame': 36 obs. of 2 variables:
## $ Rnd: int 2 6 7 3 5 7 4 7 4 7 ...
## $ G : int 150 59 22 115 172 201 13 15 34 16 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:22] 6 11 23 24 25 26 27 30 32 33 ...
## .. ..- attr(*, "names")= chr [1:22] "3030" "3739" "5608" "5651" ...str(nflplayersP)## 'data.frame': 38 obs. of 2 variables:
## $ Rnd: int 3 6 3 6 7 5 6 4 4 6 ...
## $ G : int 184 64 14 201 192 195 14 1 162 4 ...
## - attr(*, "na.action")=Class 'omit' Named int [1:22] 12 19 21 24 25 26 27 28 31 32 ...
## .. ..- attr(*, "names")= chr [1:22] "3721" "5049" "5292" "5605" ...plot_ss <- function(x, y, maintitle, showSquares = FALSE, leastSquares = FALSE){
plot(x,y,xlab="Draft Round", ylab = "Average Number of Games Played", main = maintitle)
#plot(y~x, asp = 1)# xlab = paste(substitute(x)), ylab = paste(substitute(y)))
if(leastSquares){
m1 <- lm(y~x)
y.hat <- m1$fit
} else{
pt1 <- locator(1)
points(pt1$x, pt1$y, pch = 4)
pt2 <- locator(1)
points(pt2$x, pt2$y, pch = 4)
pts <- data.frame("x" = c(pt1$x, pt2$x),"y" = c(pt1$y, pt2$y))
m1 <- lm(y ~ x, data = pts)
y.hat <- predict(m1, newdata = data.frame(x))
}
r <- y - y.hat
abline(m1)
oSide <- x - r
LLim <- par()$usr[1]
RLim <- par()$usr[2]
oSide[oSide < LLim | oSide > RLim] <- c(x + r)[oSide < LLim | oSide > RLim] # move boxes to avoid margins
n <- length(y.hat)
for(i in 1:n){
lines(rep(x[i], 2), c(y[i], y.hat[i]), lty = 2, col = "blue")
if(showSquares){
lines(rep(oSide[i], 2), c(y[i], y.hat[i]), lty = 3, col = "orange")
lines(c(oSide[i], x[i]), rep(y.hat[i],2), lty = 3, col = "orange")
lines(c(oSide[i], x[i]), rep(y[i],2), lty = 3, col = "orange")
}
}
}
summaryTable <- function(currentPlayerPosition,maintitle = ""){
draftRound <- currentPlayerPosition$Rnd
gamesPlayed <- currentPlayerPosition$G
meanTable <- tapply(gamesPlayed,draftRound,mean)
show(nrow(currentPlayerPosition))
show(describeBy(gamesPlayed, group = draftRound, mat=TRUE))
barplot(meanTable,beside=T,col=c("#ee7700","#3333ff")
,main=maintitle,xlab="Round",ylab="Average Games Played")
#show(meanTable)
}
inferenceTests <- function(currentPlayerPosition, player, maintitle = "") {
draftRound <- currentPlayerPosition$Rnd
gamesPlayed <- currentPlayerPosition$G
plot_ss(x = draftRound, y = gamesPlayed, maintitle, showSquares = FALSE)
m2 <- lm(G ~ Rnd, data = currentPlayerPosition)
summary(m2)
}
inferenceTest0 <- function(currentPlayerPosition) {
m2 <- lm(G ~ Rnd, data = currentPlayerPosition)
hist(m2$residuals)
qqnorm(m2$residuals)
qqline(m2$residuals)
}Part 1 - Introduction
Research Question
Does a National Football League (NFL) player’s draft round placement affect his longevity in the NFL based on his position?
Applicability
I am a big NFL fan. I enjoy observing football games and the excitement they bring. I enjoy watching particular players and how they perform on the field. The NFL recruits its players from an annual event called the NFL Draft. The NFL Draft occurs in mid Spring before the start of the NFL season which begins at the end of the Summer. During the NFL Draft, college-level players who have excelled at their level perform a battery of tests to make themselves attractive to the NFL teams that are seeking players to fill their rosters. The NFL teams with the worst winning record of the previous season get to pick the players they need in the first round. The NFL teams with the best winning record of the previous season including the Super Bowl champions pick players in subsequent rounds based on the immediate needs of the teams. According to NFL regulations, this helps to promote parity between all the teams. It is hoped for the individual NFL team that the best quarterbacks or wide receivers at the college-level will improve their winning record in the next season.
Based on personal observations and watching various media, I see that many of the star players in the NFL were not 1st Round Draft Picks. Some notable examples are: Tom Brady of the New England Patriots, 6th round; Russell Wilson of the Seattle Seahawks, 3rd round; Joe Montana of the San Francisco 49ers, 3rd round; and Roger Stauback of the Dallas Cowboys, 10th round (Vergara, 2017). These players are/were Super Bowl-winning quarterbacks. Other notable examples are Stephen Gostkowski, kicker, 4th round; Julian Edelman, wide receiver, 7th round; Trent Cole, defensive end, 5th round; Josh Sitton, offensive lineman, 4th round; etc. (Brandt, 2016).
The problem fascinates me. The players listed above are star players who were not even selected in the 1st round of the NFL Draft. Because of this, I find it hard to believe that NFL team owners will spend millions of dollars on 1st Round players who may amount to nothing. Why don’t NFL team owners go after players in the subsequent rounds instead? Regardless of players’ names and their individual statistics, is there a statistical correlation between a player’s longevity in the NFL (number of games played) based on his position and his round placement in the NFL Draft? Using all other variables are beyond the scope of this project.
The investigation will be beneficial to other NFL fans who love to study the statistics related to football. Based on personal obversation, other NFL fans could use this information for their own NFL games, arguing over football semantics with their friends, and apply this methodology to predict future draft choices.
Part 2 - Data
Data Collection
The data was collected by IBM Data Scientist Ron Graf for his own personal experimentation on NFL Draft Data. For this project, the data will only cover players drafted between 1985 and 2005 even though the original data covers players drafted from 1985 to 2015.
Cases
Each case represents an NFL player in the United States drafted 2005 or earlier. There are 4524 observations in the given data set.
Variables
The response variable is total games played and is numerical.
The explanatory variable is draft round and is numerical.
Type of Study
This is an observational study. I arrived at this conclusion because the data extrapolated already contains information on individual player statistics for their active years in the NFL.
Scope of Inference - Generalizability
The population of interest for this project will be all players drafted from 1985 to 2005. That are 4524 observations. I could have acquired a random sample from these observations, but I am using a targeted analysis of players based on their position. This data represents a sample of the population of all NFL draftees since the NFL’s inception. Therefore, the findings from this analysis can be generalized to the entire population of all NFL draftees. I specifically chose 2005 as the end point because I wanted to make sure that selected players had a good chance in completing at least 10 seasons in the NFL. Players selected in the 2017 NFL Draft, for example, were not included in this study because the limited number of games played would represent outliers in this study.
There are some potential sources of bias, but I believe these sources of bias could be quite small that they would not affect the generalizability of the data. The study does not account for trends in the NFL Draft over a period of years. Since the study only focuses on players drafted between 1985 to 2005, player performance statistics, game longevity, and draft placement may be different for other years.
Scope of Inference - Causality
Based on the large number of variables for each player, the data could be used to establish causal links between the number of games played and draft round placement. The usage of multi-regression on various individual player statistics based on position can make more powerful correlations of how draft placement affects player longevity. However, this is beyond the scope of this project and could be investigated by other students at a future date.
Part 3 - Exploratory Data Analysis
In this section, we will explore my initial statistical findings that I submitted in my Project Proposal. I show Summary Statistics for All Players and the 12 positions represented in the data. The 12 positions are: quarterback, running back, wide receiver, tight end, offensive tackle, center, defensive tackle, defensive back, defensive end, kicker, and punter. Each position will highlight the average number of games vs. draft rounds for each player position. There will be a short discussion about each position.
A. All Positions Statistics
## [1] 4524
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 590 116.72542 58.70211 116.5 115.61017 64.4931 3
## X12 2 2 1 597 95.65494 54.85840 96.0 94.06472 62.2692 0
## X13 3 3 1 603 77.97015 55.47394 72.0 72.79503 60.7866 1
## X14 4 4 1 588 68.47959 54.52950 56.5 63.12076 60.0453 1
## X15 5 5 1 533 58.28705 52.33056 43.0 51.33021 47.4432 1
## X16 6 6 1 516 53.53682 51.66536 34.0 46.31159 44.4780 1
## X17 7 7 1 529 46.72023 50.79174 25.0 38.22118 32.6172 1
## X18 8 8 1 146 55.30137 57.73619 32.0 46.43220 40.0302 1
## X19 9 9 1 120 44.68333 55.80684 18.0 34.43750 23.7216 1
## X110 10 10 1 106 47.23585 54.98356 18.5 39.06977 24.4629 1
## X111 11 11 1 98 43.63265 51.78831 19.5 34.95000 24.4629 1
## X112 12 12 1 98 39.74490 55.51954 14.0 28.60000 17.7912 1
## max range skew kurtosis se
## X11 303 300 0.1883973 -0.527211611 2.416728
## X12 327 327 0.3268150 -0.091076096 2.245205
## X13 244 243 0.7154554 -0.096660360 2.259073
## X14 301 300 0.7766416 0.006003296 2.248759
## X15 264 263 1.0917869 0.700738044 2.266688
## X16 245 244 1.1082406 0.645404688 2.274441
## X17 220 219 1.2835396 0.808147093 2.208336
## X18 262 261 1.2001727 0.647753710 4.778281
## X19 236 235 1.3701304 0.852451453 5.094444
## X110 231 230 1.1332936 0.371242751 5.340475
## X111 234 233 1.5029849 1.949866714 5.231409
## X112 297 296 2.0404254 4.524217431 5.608320
Observations
The study encompasses 4524 players. All Draft Rounds are covered in the data set and the average number of games played is 117 for 1st Round players and slowly decreases to 40 games played for 12th Round players. The bars on the chart slowy descend in number of games from 1st to 12th Rounds. There is a slight uptick for the 8th round. From this observation alone, the higher the draft placement (lowest draft round number), the average number of games a player plays goes up. There are no apparent outliers or anomalies in this chart.
B. Quarterback Statistics
## [1] 197
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 41 100.41463 69.483802 92.0 96.48485 96.3690 6
## X12 2 2 1 17 85.05882 84.446337 67.0 76.20000 80.0604 1
## X13 3 3 1 24 59.37500 59.549623 29.5 50.75000 22.2390 2
## X14 4 4 1 33 38.30303 41.596638 25.0 31.74074 29.6520 1
## X15 5 5 1 11 15.18182 16.406207 7.0 12.66667 5.9304 1
## X16 6 6 1 27 52.85185 61.753046 21.0 42.82609 29.6520 1
## X17 7 7 1 28 23.78571 41.275369 5.0 16.45833 5.9304 1
## X18 8 8 1 3 33.00000 42.154478 16.0 33.00000 20.7564 2
## X19 9 9 1 3 80.33333 86.558266 54.0 80.33333 65.2344 10
## X110 10 10 1 1 90.00000 NA 90.0 90.00000 0.0000 90
## X111 11 11 1 6 20.50000 35.702941 3.0 20.50000 0.7413 2
## X112 12 12 1 3 6.00000 8.660254 1.0 6.00000 0.0000 1
## max range skew kurtosis se
## X11 266 260 0.3640747 -0.9615647 10.851547
## X12 302 301 1.0900514 0.3140173 20.481245
## X13 220 218 1.2008846 0.3300035 12.155516
## X14 157 156 1.2994677 0.9410191 7.241045
## X15 52 51 0.9587090 -0.4442819 4.946658
## X16 231 230 1.4001553 1.3342005 11.884379
## X17 147 146 1.8510965 1.9974155 7.800312
## X18 81 79 0.3376920 -2.3333333 24.337899
## X19 177 167 0.2760693 -2.3333333 49.974438
## X110 90 0 NA NA NA
## X111 92 90 1.2565441 -0.2783706 14.575665
## X112 16 15 0.3849002 -2.3333333 5.000000
Observations
The study encompasses 197 quarterbacks. All Draft Rounds are covered in the data set and the average number of games played is 100 for 1st Round players and slowly decreases to 6 games played for 12th Round players. The bars on the chart varies in number of games played from 1st to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. For example, the average number of games for the 2nd and 10th draft rounds are 85 and 90 respectively. The data on the quarterbacks warrants further investigation.
C. Wide Receiver Statistics
## [1] 540
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 75 114.53333 60.94311 112 113.34426 57.8214 8
## X12 2 2 1 77 91.90909 54.88533 86 90.23810 63.7518 3
## X13 3 3 1 72 71.56944 60.19425 49 63.53448 48.9258 2
## X14 4 4 1 64 66.54688 54.72469 53 59.98077 49.6671 2
## X15 5 5 1 59 48.03390 42.83487 34 43.34694 37.0650 1
## X16 6 6 1 69 34.91304 43.13581 14 27.87719 19.2738 1
## X17 7 7 1 56 42.28571 50.34886 18 33.86957 19.2738 1
## X18 8 8 1 12 37.08333 38.10860 16 32.80000 15.5673 3
## X19 9 9 1 18 41.05556 61.39503 13 33.93750 17.0499 1
## X110 10 10 1 14 31.14286 32.95185 21 27.75000 29.6520 1
## X111 11 11 1 12 35.91667 35.34109 29 30.10000 30.3933 2
## X112 12 12 1 12 25.83333 58.08745 8 9.90000 7.4130 2
## max range skew kurtosis se
## X11 303 295 0.3529274 0.03037733 7.037105
## X12 223 220 0.2663593 -0.90570341 6.254764
## X13 244 242 1.0439895 0.26329079 7.093960
## X14 234 232 1.0774279 0.76052859 6.840586
## X15 177 176 1.0027200 0.31670673 5.576626
## X16 206 205 1.6619899 2.46698468 5.192941
## X17 205 204 1.4198620 0.99197963 6.728150
## X18 114 111 0.8583488 -0.93921841 11.001004
## X19 195 194 1.4825125 0.67769872 14.470947
## X110 102 101 0.5908750 -1.00304104 8.806751
## X111 128 126 1.3084314 1.08537702 10.202093
## X112 209 207 2.5820053 5.25015127 16.768402
Observations
The study encompasses 540 wide receivers. All Draft Rounds are covered in the data set and the average number of games played is 115 for 1st Round players and slowly decreases to 26 games played for 12th Round players. The bars on the chart slowy descend in number of games played from 1st to 12th Rounds. There are some slight upticks for some of the rounds. From this observation alone, the higher the draft placement (lowest draft round number), the average number of games a player plays goes up. There are no apparent outliers or anomalies in this chart. However, an inference test will be conducted in the next section to remove any bias in the author’s observations.
D. Running Back Statistics
## [1] 461
## item group1 vars n mean sd median trimmed mad min max
## X11 1 1 1 72 94.98611 48.52631 89.5 91.34483 60.0453 28 226
## X12 2 2 1 57 83.87719 49.72462 87.0 83.34043 74.1300 3 182
## X13 3 3 1 58 68.93103 39.77474 61.5 65.89583 35.5824 11 175
## X14 4 4 1 54 52.88889 45.96745 39.0 47.22727 40.0302 1 163
## X15 5 5 1 48 59.02083 52.95140 43.0 53.10000 42.2541 1 223
## X16 6 6 1 44 46.00000 45.35391 32.5 39.55556 43.7367 1 194
## X17 7 7 1 46 28.86957 31.24783 15.5 23.55263 17.7912 1 141
## X18 8 8 1 20 36.70000 36.67654 28.5 31.75000 31.8759 3 121
## X19 9 9 1 17 34.47059 44.01721 7.0 30.33333 8.8956 1 130
## X110 10 10 1 11 65.00000 49.56813 56.0 65.77778 78.5778 2 121
## X111 11 11 1 12 34.33333 33.84546 26.0 31.20000 26.6868 2 98
## X112 12 12 1 22 19.54545 30.23358 9.5 12.44444 9.6369 2 135
## range skew kurtosis se
## X11 198 0.53988556 -0.6486614 5.718880
## X12 179 0.08981597 -1.2828612 6.586187
## X13 164 0.72452576 -0.2207932 5.222680
## X14 162 0.90273019 -0.2723466 6.255377
## X15 222 1.11167905 0.5657363 7.642876
## X16 193 1.25205219 1.2053847 6.837359
## X17 140 1.64423121 2.3819082 4.607242
## X18 118 0.95240051 -0.4883366 8.201123
## X19 129 1.05388182 -0.4622521 10.675741
## X110 119 -0.04668137 -1.8978827 14.945355
## X111 96 0.81161582 -0.8956462 9.770343
## X112 133 2.65259069 6.9947697 6.445821
Observations
The study encompasses 461 running backs. All Draft Rounds are covered in the data set and the average number of games played is 95 for 1st Round players and decreases to 20 games played for 12th Round players. The bars on the chart varies in number of games played from 1st to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. For example, the average number of games for the 2nd and 10th draft rounds are 84 and 65 respectively. The data on the running backs warrants further investigation.
E. Tight End Statistics
## [1] 275
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 20 138.40000 47.62949 132.5 136.50000 38.5476 57
## X12 2 2 1 27 110.03704 53.67529 98.0 110.82609 60.7866 16
## X13 3 3 1 31 78.67742 50.39933 82.0 75.80000 57.8214 3
## X14 4 4 1 33 76.24242 48.39101 75.0 74.25926 59.3040 6
## X15 5 5 1 39 54.28205 42.05507 48.0 50.81818 34.0998 1
## X16 6 6 1 39 60.97436 56.61852 30.0 56.00000 42.9954 1
## X17 7 7 1 48 61.25000 55.82819 42.0 53.72500 44.4780 1
## X18 8 8 1 14 41.64286 36.88987 35.0 38.25000 34.0998 3
## X19 9 9 1 6 41.50000 46.75789 26.0 41.50000 36.3237 1
## X110 10 10 1 5 56.60000 69.03840 18.0 56.60000 22.2390 3
## X111 11 11 1 8 19.50000 22.60847 13.5 19.50000 15.5673 2
## X112 12 12 1 5 106.60000 67.95440 118.0 106.60000 65.2344 12
## max range skew kurtosis se
## X11 270 213 0.70152740 0.9362986 10.650278
## X12 196 180 0.02519248 -1.1508672 10.329815
## X13 218 215 0.49562408 -0.1403793 9.051987
## X14 167 161 0.39486009 -0.9978056 8.423793
## X15 158 157 0.83809271 -0.2619044 6.734201
## X16 207 206 0.72755207 -0.6824275 9.066220
## X17 220 219 1.18273219 0.7412983 8.058106
## X18 121 118 0.83142383 -0.6252168 9.859233
## X19 114 113 0.45459228 -1.7470264 19.088827
## X110 154 151 0.40837613 -1.9944897 30.874909
## X111 68 66 1.11784564 -0.1975737 7.993301
## X112 193 181 -0.13344192 -1.7084406 30.390130
Observations
The study encompasses 275 tight ends. All Draft Rounds are covered in the data set and the average number of games played is 138 for 1st Round players and decreases to 20 games played for 11th Round players. The bars on the chart varies in number of games played from 1st to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. For example, the average number of games for the 2nd and 12th draft rounds are 110 and 106 respectively. The data on the tight ends warrants further investigation.
F. Offensive Tackle Statistics
## [1] 297
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 64 118.31250 61.454041 115.0 118.65385 65.2344 3
## X12 2 2 1 35 100.02857 54.772517 106.0 100.17241 62.2692 2
## X13 3 3 1 39 69.05128 50.195905 62.0 67.66667 68.1996 2
## X14 4 4 1 35 65.31429 62.402287 46.0 58.41379 60.7866 1
## X15 5 5 1 31 45.80645 47.509592 25.0 38.36000 29.6520 1
## X16 6 6 1 31 56.48387 55.206202 30.0 48.44000 37.0650 1
## X17 7 7 1 30 51.30000 58.259319 17.0 42.45833 22.9803 1
## X18 8 8 1 9 27.55556 41.179822 7.0 27.55556 5.9304 3
## X19 9 9 1 6 28.66667 40.361698 14.5 28.66667 8.8956 3
## X110 10 10 1 3 69.66667 115.470054 3.0 69.66667 0.0000 3
## X111 11 11 1 10 43.30000 61.166530 6.0 32.75000 5.9304 1
## X112 12 12 1 4 7.25000 9.878428 3.0 7.25000 1.4826 1
## max range skew kurtosis se
## X11 263 260 -0.02460856 -0.7562645 7.681755
## X12 198 196 -0.21418775 -0.9894433 9.258245
## X13 161 159 0.31317007 -1.3646834 8.037778
## X14 207 206 0.80439635 -0.5930619 10.547912
## X15 192 191 1.34255371 1.2522349 8.532975
## X16 245 244 1.45484021 2.1177759 9.915327
## X17 186 185 0.90807053 -0.5612952 10.636648
## X18 125 122 1.38122482 0.5677501 13.726607
## X19 110 107 1.28344981 -0.2080213 16.477594
## X110 203 200 0.38490018 -2.3333333 66.666667
## X111 170 169 1.04293090 -0.5910933 19.342555
## X112 22 21 0.72911379 -1.7001367 4.939214
Observations
The study encompasses 297 offensive tackles. All Draft Rounds are covered in the data set and the average number of games played is 118 for 1st Round players and decreases to 10 games played for 12th Round players. The bars on the chart varies in number of games played from 1st to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. For example, the average number of games for the 2nd and 10th draft rounds are 100 and 70 respectively. The data on the offensive tackles warrants further investigation.
G. Center Statistics
## [1] 127
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 7 139.85714 23.15476 137.0 139.85714 17.7912 105
## X12 2 2 1 18 119.61111 72.15273 119.0 119.37500 81.5430 2
## X13 3 3 1 21 100.52381 69.96901 93.0 98.17647 78.5778 2
## X14 4 4 1 18 98.66667 65.31192 96.0 96.93750 76.3539 7
## X15 5 5 1 18 83.05556 49.82496 88.0 84.06250 63.7518 1
## X16 6 6 1 12 60.08333 56.82582 57.5 51.00000 42.2541 1
## X17 7 7 1 18 71.05556 61.98716 61.0 67.50000 57.0801 1
## X18 8 8 1 6 51.16667 54.51391 38.5 51.16667 49.6671 4
## X19 9 10 1 4 78.25000 104.59884 37.0 78.25000 39.2889 8
## X110 10 11 1 4 86.75000 109.11576 55.5 86.75000 76.3539 2
## X111 11 12 1 1 5.00000 NA 5.0 5.00000 0.0000 5
## max range skew kurtosis se
## X11 173 68 0.009984757 -1.5138506 8.751676
## X12 241 239 0.053268784 -1.3235259 17.006561
## X13 239 237 0.178211110 -1.1833115 15.268489
## X14 218 211 0.298231938 -1.2648757 15.394167
## X15 149 148 -0.315860825 -1.5134563 11.743855
## X16 210 209 1.297609987 1.3085206 16.404202
## X17 198 197 0.798233384 -0.6067782 14.610515
## X18 147 143 0.685309412 -1.2163396 22.255212
## X19 231 223 0.641035373 -1.7741003 52.299418
## X110 234 232 0.397098666 -2.0047330 54.557882
## X111 5 0 NA NA NA
Observations
The study encompasses 127 Centers. All Draft Rounds are covered in the data set and the average number of games played is 140 for 1st Round players and decreases to 5 games played for 12th Round players. The bars on the chart varies in number of games played from 1st to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. The data on the centers warrants further investigation.
H. Defensive Tackle Statistics
## [1] 281
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 48 125.31250 54.64008 136.0 127.12500 62.2692 19
## X12 2 2 1 25 97.80000 50.50330 99.0 99.04762 62.2692 0
## X13 3 3 1 40 79.85000 60.49817 76.0 74.28125 72.6474 3
## X14 4 4 1 41 62.36585 47.08437 64.0 59.30303 65.2344 1
## X15 5 5 1 32 76.71875 56.48821 79.5 73.96154 76.3539 3
## X16 6 6 1 39 62.46154 53.00290 50.0 57.90909 50.4084 3
## X17 7 7 1 40 44.90000 51.83198 27.0 35.78125 37.8063 1
## X18 8 8 1 6 10.66667 10.17186 9.5 10.66667 9.6369 1
## X19 9 9 1 1 2.00000 NA 2.0 2.00000 0.0000 2
## X110 10 10 1 6 56.50000 53.32823 35.0 56.50000 34.8411 3
## X111 11 11 1 1 119.00000 NA 119.0 119.00000 0.0000 119
## X112 12 12 1 2 51.00000 52.32590 51.0 51.00000 54.8562 14
## max range skew kurtosis se
## X11 208 189 -0.2794264 -0.9535537 7.886617
## X12 180 180 -0.2254590 -1.0407170 10.100660
## X13 229 226 0.5757565 -0.5682028 9.565600
## X14 173 172 0.3824850 -1.0676492 7.353343
## X15 193 190 0.2908056 -1.2829710 9.985800
## X16 185 182 0.7708587 -0.5907335 8.487257
## X17 182 181 1.2020488 0.4253849 8.195355
## X18 27 26 0.4227533 -1.6264744 4.152643
## X19 2 0 NA NA NA
## X110 131 128 0.4217819 -1.9021489 21.771158
## X111 119 0 NA NA NA
## X112 88 74 0.0000000 -2.7500000 37.000000
Observations
The study encompasses 281 defensive tackles. All Draft Rounds are covered in the data set and the average number of games played is 125 for 1st Round players and decreases to 2 games played for 9th Round players. The bars on the chart varies in number of games played from 1st to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. For example, the average number of games for the 2nd and 11th draft rounds are 98 and 120 respectively. The data on the defensive tackles warrants further investigation.
I. Linebacker Statistics
## [1] 629
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 64 121.64062 60.15308 125 120.67308 57.0801 14
## X12 2 2 1 89 94.10112 49.85275 90 92.13699 51.8910 2
## X13 3 3 1 90 81.48889 56.56601 76 76.76389 58.5627 3
## X14 4 4 1 80 74.33750 52.53304 79 70.90625 63.7518 1
## X15 5 5 1 73 62.61644 55.92372 50 55.37288 54.8562 1
## X16 6 6 1 73 56.02740 47.65005 43 51.32203 51.8910 1
## X17 7 7 1 67 43.68657 46.74632 24 36.81818 29.6520 1
## X18 8 8 1 21 69.66667 67.29364 44 61.94118 41.5128 3
## X19 9 9 1 21 31.90476 45.50924 16 21.70588 19.2738 3
## X110 10 10 1 19 28.15789 39.30121 10 24.17647 11.8608 1
## X111 11 11 1 17 47.35294 52.34494 17 44.06667 22.2390 1
## X112 12 12 1 15 40.06667 43.97315 22 37.23077 28.1694 1
## max range skew kurtosis se
## X11 268 254 0.06861843 -0.5087968 7.519135
## X12 212 210 0.34463321 -0.6047797 5.284381
## X13 243 240 0.62048451 -0.3416904 5.962581
## X14 203 202 0.39079139 -0.7714685 5.873372
## X15 228 227 1.02982663 0.4062170 6.545376
## X16 167 166 0.65781393 -0.8083509 5.577016
## X17 197 196 1.24246993 0.7895766 5.710972
## X18 208 205 0.86879563 -0.7927357 14.684675
## X19 153 150 1.71036522 1.5199620 9.930929
## X110 123 122 1.38721468 0.4689007 9.016315
## X111 143 142 0.74417978 -1.1766695 12.695513
## X112 116 115 0.66611249 -1.3525340 11.353819
Observations
The study encompasses 629 linebackers. All Draft Rounds are covered in the data set and the average number of games played is 122 for 1st Round players and slowly decreases to 40 games played for 12th Round players. The bars on the chart slowy descend in number of games played from 1st to 12th Rounds. There are some slight upticks for some of the rounds. From this observation alone, the higher the draft placement (lowest draft round number), the average number of games a player plays goes up. There are no apparent outliers or anomalies in this chart. However, an inference test will be conducted in the next section to remove any bias in the author’s observations.
J. Defensive Back Statistics
## [1] 853
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 87 124.21839 50.85191 124.0 122.52113 60.7866 27
## X12 2 2 1 139 101.79137 52.03893 98.0 101.22124 56.3388 1
## X13 3 3 1 113 74.26549 51.48943 74.0 69.38462 60.7866 1
## X14 4 4 1 121 67.86777 51.62266 61.0 63.25773 56.3388 1
## X15 5 5 1 116 52.51724 44.81255 41.0 47.25532 42.9954 1
## X16 6 6 1 90 52.38889 43.47896 46.5 47.41667 45.9606 1
## X17 7 7 1 89 45.78652 43.24441 35.0 40.34247 38.5476 1
## X18 8 8 1 29 81.20690 55.20376 87.0 80.00000 77.0952 2
## X19 9 9 1 24 39.00000 48.69068 18.0 31.65000 25.2042 1
## X110 10 10 1 20 42.40000 49.29119 12.0 37.12500 14.8260 1
## X111 11 11 1 12 47.33333 50.27259 29.0 41.70000 37.8063 3
## X112 12 12 1 13 59.15385 67.28032 29.0 53.36364 41.5128 1
## max range skew kurtosis se
## X11 254 227 0.2298194 -0.6784093 5.451897
## X12 234 233 0.1335407 -0.5607330 4.413885
## X13 241 240 0.7573194 0.1530722 4.843718
## X14 214 213 0.6350780 -0.5434657 4.692969
## X15 199 198 1.0446193 0.5964777 4.160741
## X16 194 193 0.8980874 0.2628261 4.583085
## X17 198 197 1.1115839 0.6294046 4.583898
## X18 177 175 0.1275203 -1.3258484 10.251082
## X19 185 184 1.3362062 1.0936073 9.938944
## X110 127 126 0.6537198 -1.4522625 11.021844
## X111 148 145 0.7325539 -1.0477267 14.512447
## X112 181 180 0.7024190 -1.2544535 18.660202
Observations
The study encompasses 853 defensive backs. All Draft Rounds are covered in the data set and the average number of games played is 124 for 1st Round players and decreases to 39 games played for 9th Round players. The bars on the chart varies in number of games played from 1st to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. For example, the average number of games for the 2nd and 8th draft rounds are 102 and 82 respectively. The data on the defensive backs warrants further investigation.
K. Defensive End Statistics
## [1] 403
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 81 119.92593 62.74089 120.0 118.29231 75.6126 15
## X12 2 2 1 62 86.16129 49.88583 94.0 87.08000 60.0453 1
## X13 3 3 1 48 85.72917 55.32755 84.5 82.55000 64.4931 6
## X14 4 4 1 46 78.13043 61.10669 80.0 74.89474 91.9212 1
## X15 5 5 1 39 65.58974 63.05917 37.0 59.87879 48.9258 2
## X16 6 6 1 41 50.34146 51.88719 31.0 42.93939 37.0650 1
## X17 7 7 1 47 44.02128 52.46178 15.0 36.82051 20.7564 1
## X18 8 8 1 8 25.75000 24.11135 19.5 25.75000 19.2738 1
## X19 9 9 1 8 75.37500 83.86203 44.5 75.37500 60.7866 2
## X110 10 10 1 8 15.87500 26.92549 5.0 15.87500 5.1891 1
## X111 11 11 1 7 28.57143 28.35993 17.0 28.57143 22.2390 2
## X112 12 12 1 8 41.50000 44.21700 29.5 41.50000 26.6868 2
## max range skew kurtosis se
## X11 279 264 0.1987050 -0.8516630 6.971210
## X12 179 178 -0.1970252 -1.1142683 6.335507
## X13 233 227 0.4932224 -0.4085609 7.985844
## X14 201 200 0.3069736 -1.2317174 9.009689
## X15 202 200 0.6884779 -0.9575130 10.097548
## X16 198 197 1.1030872 0.1117564 8.103418
## X17 173 172 1.0798279 -0.2124354 7.652338
## X18 71 70 0.6928066 -1.0832455 8.524649
## X19 236 234 0.7209794 -1.0658827 29.649703
## X110 81 80 1.6985994 1.3130746 9.519599
## X111 68 66 0.3087314 -1.9405131 10.719047
## X112 131 129 0.9766856 -0.6432127 15.633069
Observations
The study encompasses 403 defensive ends. All Draft Rounds are covered in the data set and the average number of games played is 129 for 1st Round players and decreases to 26 games played for 8th Round players. The bars on the chart varies in number of games played from 1st to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. For example, the average number of games for the 2nd and 9th draft rounds are 86 and 75 respectively. The data on the defensive ends warrants further investigation.
L. Kicker Statistics
## [1] 36
## item group1 vars n mean sd median trimmed mad min
## X11 1 1 1 1 262.00000 NA 262.0 262.00000 0.0000 262
## X12 2 2 1 4 155.75000 130.05480 142.5 155.75000 103.0407 11
## X13 3 3 1 6 100.33333 60.51666 112.0 100.33333 70.4235 8
## X14 4 4 1 6 97.83333 118.20900 31.0 97.83333 16.3086 13
## X15 5 5 1 1 172.00000 NA 172.0 172.00000 0.0000 172
## X16 6 6 1 5 97.00000 70.12489 96.0 97.00000 75.6126 3
## X17 7 7 1 8 78.25000 82.40969 30.0 78.25000 27.4281 8
## X18 8 8 1 1 182.00000 NA 182.0 182.00000 0.0000 182
## X19 9 9 1 1 169.00000 NA 169.0 169.00000 0.0000 169
## X110 10 10 1 1 80.00000 NA 80.0 80.00000 0.0000 80
## X111 11 12 1 2 150.50000 207.18229 150.5 150.50000 217.2009 4
## max range skew kurtosis se
## X11 262 0 NA NA NA
## X12 327 316 0.2250414 -1.864662 65.02740
## X13 165 157 -0.3598035 -1.702168 24.70582
## X14 301 288 0.7526474 -1.398467 48.25862
## X15 172 0 NA NA NA
## X16 180 177 -0.1094249 -1.892818 31.36080
## X17 201 193 0.4719338 -1.860597 29.13623
## X18 182 0 NA NA NA
## X19 169 0 NA NA NA
## X110 80 0 NA NA NA
## X111 297 293 0.0000000 -2.750000 146.50000
Observations
The study encompasses 36 kickers. All Draft Rounds EXCEPT the 11th round are covered in the data set and the average number of games played is 262 for 1st Round players and decreases to 78 games played for 7th Round players. The bars on the chart varies in number of games played from 1st to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. For example, the average number of games for the 5th and 8th draft rounds are 172 and 182 respectively. The data on the kickers warrants further investigation.
M. Punter Statistics
## [1] 38
## item group1 vars n mean sd median trimmed mad min max
## X11 1 2 1 1 178.0000 NA 178.0 178.0000 0.0000 178 178
## X12 2 3 1 6 153.5000 88.11754 163.0 153.5000 103.0407 14 244
## X13 3 4 1 6 106.1667 70.93495 120.5 106.1667 77.0952 1 183
## X14 4 5 1 8 105.3750 113.64096 39.0 105.3750 41.5128 3 264
## X15 5 6 1 8 90.2500 101.23205 39.0 90.2500 51.8910 4 239
## X16 6 7 1 3 129.6667 99.43004 182.0 129.6667 14.8260 15 192
## X17 7 8 1 2 80.0000 84.85281 80.0 80.0000 88.9560 20 140
## X18 8 9 1 2 120.0000 93.33810 120.0 120.0000 97.8516 54 186
## X19 9 12 1 2 61.5000 45.96194 61.5 61.5000 48.1845 29 94
## range skew kurtosis se
## X11 0 NA NA NA
## X12 230 -0.3666446 -1.599919 35.97383
## X13 182 -0.2996777 -1.815521 28.95907
## X14 261 0.4631208 -1.867411 40.17815
## X15 235 0.3945304 -1.909509 35.79094
## X16 177 -0.3805249 -2.333333 57.40596
## X17 120 0.0000000 -2.750000 60.00000
## X18 132 0.0000000 -2.750000 66.00000
## X19 65 0.0000000 -2.750000 32.50000
Observations
The study encompasses 38 punters. All Draft Rounds EXCEPT the 1st, 10th, and 11th round are covered in the data set and the average number of games played is 178 for 2nd Round players and decreases to 45 games played for 12th Round players. The bars on the chart varies in number of games played from 2nd to 12th Rounds. From this observation alone, the average number of games a player plays varies for each round. For example, the average number of games for the 3rd and 7th draft rounds are 154 and 99 respectively. The data on the punters warrants further investigation.
Exploratory Data Analysis Summary
Based on the exploratory data analysis, in the next section we will focus on inference tests on the player positions that exhibit interesting anomalies in draft round placement and average number of games played. The Player positions that meet this criteria are quarterback, running back, tight end, offensive tackle, center, defensive tackle, defensive back defensive end, kickers, and punters. However, inference tests will be conducted in all other positions in the next section to remove any bias in the author’s observations.
Part 4 - Inference
Despite what the Exploratory Data Analysis exposed on the interesting anomalies in draft round placement and average number of games played, inference tests will need to be conducted to verify that All positions and each of the positions show cause for more analyses in future investigations.
Prior to conducting the inference tests for each position, I inspected the data by using a plot to help me understand the data visually. Despite the fact that average number of games fluctuates for each rounds based on player position, the anomalies do not seem out of the ordinary when you take into account the visual inspection of the plot. I did not consider the number of players for each of the draft rounds and they could certainly affect the anomalies presented in the previous section.
I chose Linear Regression as my algorithm for inference calculations. By conducting the linear regression tests, it clearly shows the data trends of each position and shows whether if draft round placement clearly affects the number of games a player plays in.
Prior to executing all inference tests, I will conduct a test to verify that the data meets the criteria for inference. After each linear regression run, I will propose a Hypothesis Test and indicate at each of the player positions whether they meet the Hypothesis Test’s parameters. The sample Hypothesis test used for each position is highlighted below.
H0: There IS NO evidence that draft round placement determines a player’s average number of games he plays.
H1: There IS evidence that draft round placement determines a player’s average number of games he plays.
Preliminary - Does the Data Meet Criteria for Inference?
Prior to conducting inference tests for the data, we will have to determine if the data meets the criteria for inference.
Linearity. The data does not show a clear residual trend. However, using the residuals in the Histogram graph, we see that the residuals are between -100 and 220. This is a good indication of linearity in the data. CONDITION ACCEPTED.
Nearly normal residuals. The residuals graph indicated by the Historgram show a pattern of near normal distribution. There is some skew on the right of the chart. CONDITION ACCEPTED.
Constant variability. The variability of points around the least squares line remains roughly constant as evidenced by the QQ-Plot. There is skew in both the top-right and bottom-left part of the chart, but there is a clearly a large black line of data converging on the center of the least squares line. CONDITION ACCEPTED.
Independent observations. The data was not independently collected. It was collected for all players drafted between 1985 and 2005. However, 4524 observations were collected which increases the likelihood of data independence. The data used is greater than 10% of all NLF drafts. CONDITION ACCEPTED.
The Football Player data has satisfied all conditions for linear regression.
A. All Positions Inference Test
inferenceTests(nfl_draft2005Rev3, "All Players", "All Players - Inference Analysis")
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -96.49 -44.23 -11.68 36.01 282.32
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 107.1960 1.6156 66.35 <2e-16 ***
## Rnd -7.7096 0.2999 -25.71 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 55.35 on 4522 degrees of freedom
## Multiple R-squared: 0.1275, Adjusted R-squared: 0.1273
## F-statistic: 660.8 on 1 and 4522 DF, p-value: < 2.2e-16H0: There is no evidence that draft round placement determines All Players’ average number of games they play.
H1: There is evidence that draft round placement determines All Players’ average number of games they play.
The inference test for All Positions shows that the p-value for the linear regression is 2.2 * 10-16 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines All Players’ average number of games they play. For the purposes of the comparison, I will use the R2 value of 0.1275 as a comparison to the rest of the positions.
According to the linear regression test, a player at the 1st Draft Round on average plays 99 games in his tenure. For each subsequent Draft Round, the average number of games a player plays goes down by 8. However, the plot chart clearly indicates that a large number of players play at games in the 150 and 200 range as evidenced by the dark lines on Rounds 2, 3, 4, 5, 6, and 7 rounds.
B. Quarterback Inference Test
inferenceTests(nflplayersQB, "Quarterback", "Quarterback - Inference Analysis")
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -78.45 -42.13 -22.69 28.75 225.99
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 92.886 7.967 11.659 < 2e-16 ***
## Rnd -8.439 1.556 -5.424 1.72e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 59.34 on 195 degrees of freedom
## Multiple R-squared: 0.1311, Adjusted R-squared: 0.1266
## F-statistic: 29.42 on 1 and 195 DF, p-value: 1.716e-07H0: There is no evidence that draft round placement determines a Quarterback’s average number of games he plays.
H1: There is evidence that draft round placement determines a Quarterback’s average number of games he plays.
The inference test for Quarterbacks shows that the p-value for the linear regression is 1.72 * 10-7 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Quarterbacks’ average number of games they play. The R2 value is 0.1311 which seems to indicate the linear regression strength against variability is better than that of All Players.
According to the linear regression test, a quarterback at the 1st Draft Round on average plays 85 games in his tenure. For each subsequent Draft Round, the average number of games a quarterback plays goes down by 8. The plot chart clearly indicates some anomalies, but definitely supports the linear regression test. I have indicated in the previous section that the player(s) at the 10th round had a very high average number of games. However, the plot clearly shows that only 1 player occupies the 10th draft round and clearly represents a lone outlier.
C. Wide Receiver Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -88.62 -40.66 -14.02 35.49 209.67
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 105.462 4.445 23.72 <2e-16 ***
## Rnd -8.844 0.828 -10.68 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 53.73 on 538 degrees of freedom
## Multiple R-squared: 0.175, Adjusted R-squared: 0.1734
## F-statistic: 114.1 on 1 and 538 DF, p-value: < 2.2e-16H0: There is no evidence that draft round placement determines a Wide Receiver’s average number of games he plays.
H1: There is evidence that draft round placement determines a Wide Receiver’s average number of games he plays.
The inference test for Wide Receivers shows that the p-value for the linear regression is 2.2 * 10-16 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Wide Receivers’ average number of games they play. The R2 value is 0.175 which seems to indicate the linear regression strength against variability is better than that of All Players.
According to the linear regression test, a wide receiver at the 1st Draft Round on average plays 96 games in his tenure. For each subsequent Draft Round, the average number of games a wide receiver plays goes down by 9. The plot chart clearly indicates some numerous anomalies, especially in the next 5 rounds. I have indicated in the previous section that the wide receiver follows a similar pattern of number of games played goes down at each round. The visual data indicates that there are more numerous anomalies than normal to warrant an investigation in the future.
D. Running Back Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -75.460 -35.579 -8.992 26.774 164.480
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 91.7540 3.8998 23.528 <2e-16 ***
## Rnd -6.6468 0.6814 -9.755 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 45.2 on 459 degrees of freedom
## Multiple R-squared: 0.1717, Adjusted R-squared: 0.1699
## F-statistic: 95.16 on 1 and 459 DF, p-value: < 2.2e-16H0: There is no evidence that draft round placement determines a Running Back’s average number of games he plays.
H1: There is evidence that draft round placement determines a Running Back’s average number of games he plays.
The inference test for Running Backs shows that the p-value for the linear regression is 2.2 * 10-16 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Running Backs’ average number of games they play. The R2 value is 0.1717 which seems to indicate the linear regression strength against variability is better than that of All Players.
According to the linear regression test, a running back at the 1st Draft Round on average plays 84 games in his tenure. For each subsequent Draft Round, the average number of games a running back plays goes down by 7. The plot chart clearly indicates some anomalies, but definitely supports the linear regression test. I have indicated in the previous section that the player(s) at the 10th round had a very high average number of games. However, the plot clearly shows that only 11 players, 2.3% of all running backs, occupy the 10th draft round and clearly represents a small outlier.
E. Tight End Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -86.51 -41.81 -10.40 37.16 173.36
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 112.797 7.185 15.699 < 2e-16 ***
## Rnd -7.763 1.240 -6.262 1.47e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 52.9 on 273 degrees of freedom
## Multiple R-squared: 0.1256, Adjusted R-squared: 0.1224
## F-statistic: 39.21 on 1 and 273 DF, p-value: 1.471e-09H0: There is no evidence that draft round placement determines a Tight End’s average number of games he plays.
H1: There is evidence that draft round placement determines a Tight End’s average number of games he plays.
The inference test for Tight Ends shows that the p-value for the linear regression is 1.47 * 10-9 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Tight Ends’ average number of games they play. The R2 value is 0.1256 which seems to indicate the linear regression strength against variability is slight less than that of All Players.
According to the linear regression test, a tight end at the 1st Draft Round on average plays 105 games in his tenure. For each subsequent Draft Round, the average number of games a tight end plays goes down by 8. The plot chart clearly indicates some anomalies, but definitely supports the linear regression test. I have indicated in the previous section that the player(s) at the 12th round had a very high average number of games. However, the plot clearly shows that only 4 players occupy the 10th draft round and clearly represents a small outlier.
F. Offensive Tackle Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -100.609 -44.609 -9.606 37.391 187.892
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 112.910 6.040 18.693 < 2e-16 ***
## Rnd -9.300 1.192 -7.801 1.07e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 57.33 on 295 degrees of freedom
## Multiple R-squared: 0.171, Adjusted R-squared: 0.1682
## F-statistic: 60.86 on 1 and 295 DF, p-value: 1.069e-13H0: There is no evidence that draft round placement determines an Offensive Tackle’s average number of games he plays.
H1: There is evidence that draft round placement determines a Offensive Tackle’s average number of games he plays.
The inference test for Offensive Tackles shows that the p-value for the linear regression is 1.069 * 10-13 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Offensive Tackles’ average number of games they play. The R2 value is 0.171 which seems to indicate the linear regression strength against variability is higher than that of All Players.
According to the linear regression test, an offensive tackle at the 1st Draft Round on average plays 104 games in his tenure. For each subsequent Draft Round, the average number of games a offensive tackle plays goes down by 9. The plot chart clearly indicates some anomalies, but definitely supports the linear regression test. I have indicated in the previous section that the player(s) at the 2nd and 10th rounds had a very high average number of games. The 2nd round seems to be justified as the majority of players listed are above the regression line. The plot clearly shows that only 2 players occupy the 10th draft round: one player has a low game value and the other player has a high game value above 200. The average of the 2 clearly puts it in competition with the 1st round average and thus is clearly an anomaly.
G. Center Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -110.21 -49.80 -10.38 42.09 191.69
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 127.748 12.250 10.429 < 2e-16 ***
## Rnd -7.767 2.260 -3.437 0.000799 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 64 on 125 degrees of freedom
## Multiple R-squared: 0.08635, Adjusted R-squared: 0.07905
## F-statistic: 11.81 on 1 and 125 DF, p-value: 0.0007987H0: There is no evidence that draft round placement determines a Center’s average number of games he plays.
H1: There is evidence that draft round placement determines a Center’s average number of games he plays.
The inference test for Centers shows that the p-value for the linear regression is 7.9 * 10-4 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Centers’ average number of games they play. The R2 value is 0.086 which seems to indicate the linear regression strength against variability is less than that of All Players.
According to the linear regression test, a center at the 1st Draft Round on average plays 120 games in his tenure. For each subsequent Draft Round, the average number of games a center plays goes down by 8. The plot chart clearly indicates some anomalies, but definitely supports the linear regression test. There are outliers in all draft rounds. The low R2 value clearly supports this.
H. Defensive Tackle Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -99.316 -44.906 -7.316 37.448 139.566
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 119.080 6.661 17.877 < 2e-16 ***
## Rnd -9.882 1.354 -7.299 3.03e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 54.31 on 279 degrees of freedom
## Multiple R-squared: 0.1603, Adjusted R-squared: 0.1573
## F-statistic: 53.28 on 1 and 279 DF, p-value: 3.027e-12H0: There is no evidence that draft round placement determines a Defensive Tackle’s average number of games he plays.
H1: There is evidence that draft round placement determines a Defensive Tackle’s average number of games he plays.
The inference test for Defensive Tackles shows that the p-value for the linear regression is 3.03 * 10-12 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Defensive Tackles’ average number of games they play. The R2 value is 0.1603 which seems to indicate the linear regression strength against variability is more than that of All Players.
According to the linear regression test, a defensive tackle at the 1st Draft Round on average plays 109 games in his tenure. For each subsequent Draft Round, the average number of games a defensive tackle plays goes down by 10. The plot chart clearly indicates some anomalies, but definitely supports the linear regression test. I have indicated in the previous section that the player(s) at the 11th round had a very high average number of games. However, the plot clearly shows that only 1 player occupies the 11th draft round and clearly represents an outlier.
I. Linebacker Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -91.880 -42.331 -9.955 32.819 166.195
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 109.7298 4.2258 25.97 <2e-16 ***
## Rnd -7.9248 0.7608 -10.42 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 53.4 on 627 degrees of freedom
## Multiple R-squared: 0.1475, Adjusted R-squared: 0.1462
## F-statistic: 108.5 on 1 and 627 DF, p-value: < 2.2e-16H0: There is no evidence that draft round placement determines a Linebacker’s average number of games he plays.
H1: There is evidence that draft round placement determines a Linebacker’s average number of games he plays.
The inference test for Linebackers shows that the p-value for the linear regression is 2.2 * 10-16 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Linebackers’ average number of games they play. The R2 value is 0.1475 which seems to indicate the linear regression strength against variability is better than that of All Players.
According to the linear regression test, a linebacker at the 1st Draft Round on average plays 102 games in his tenure. For each subsequent Draft Round, the average number of games a linebacker plays goes down by 8. The plot chart clearly indicates some anomalies, but definitely supports the linear regression test. I have indicated in the previous section that the player(s) at the 8th round had a very high average number of games. However, the plot clearly shows that only 21 players, 3.3% of all linebackers, occupy the 8th draft round and clearly represents a small outlier.
J. Defensive Back Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -91.657 -41.971 -7.735 35.422 167.558
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 108.500 3.553 30.54 <2e-16 ***
## Rnd -7.921 0.681 -11.63 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 51.37 on 851 degrees of freedom
## Multiple R-squared: 0.1372, Adjusted R-squared: 0.1362
## F-statistic: 135.3 on 1 and 851 DF, p-value: < 2.2e-16H0: There is no evidence that draft round placement determines a Defensive Back’s average number of games he plays.
H1: There is evidence that draft round placement determines a Defensive Back’s average number of games he plays.
The inference test for Defensive Backs shows that the p-value for the linear regression is 2.2 * 10-16 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Defensive Backs’ average number of games they play. The R2 value is 0.1372 which seems to indicate the linear regression strength against variability is better than that of All Players.
According to the linear regression test, a defensive back at the 1st Draft Round on average plays 101 games in his tenure. For each subsequent Draft Round, the average number of games a defensive back plays goes down by 8. The plot chart clearly indicates some anomalies, but definitely supports the linear regression test. I have indicated in the previous section that the player(s) at the 8th round had a very high average number of games. However, the plot clearly shows that only 29 players, 3.3% of all defensive backs, occupy the 8th draft round and clearly represents a small outlier.
K. Defensive End Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -95.928 -48.003 -7.003 38.035 203.367
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 115.298 5.142 22.424 <2e-16 ***
## Rnd -9.185 1.022 -8.991 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 56.93 on 401 degrees of freedom
## Multiple R-squared: 0.1678, Adjusted R-squared: 0.1657
## F-statistic: 80.85 on 1 and 401 DF, p-value: < 2.2e-16H0: There is no evidence that draft round placement determines a Defensive End’s average number of games he plays.
H1: There is evidence that draft round placement determines a Defensive End’s average number of games he plays.
The inference test for Defensive Ends shows that the p-value for the linear regression is 2.2 * 10-16 which is less than 0.05. We have enough evidence to reject the Null Hypothesis and therefore, there is evidence that draft round placement determines Defensive Ends’ average number of games they play. The R2 value is 0.1678 which seems to indicate the linear regression strength against variability is better than that of All Players.
According to the linear regression test, a defensive end at the 1st Draft Round on average plays 106 games in his tenure. For each subsequent Draft Round, the average number of games a defensive end plays goes down by 9. The plot chart clearly indicates some anomalies, but definitely supports the linear regression test. I have indicated in the previous section that the player(s) at the 9th round had a very high average number of games. However, the plot clearly shows that only 8 players, 2% of all defensive ends, occupy the 9th draft round and clearly represents a small outlier.
L. Kicker Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -112.052 -89.562 -8.052 65.711 204.209
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 128.270 35.110 3.653 0.000864 ***
## Rnd -2.739 5.849 -0.468 0.642533
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 94.74 on 34 degrees of freedom
## Multiple R-squared: 0.00641, Adjusted R-squared: -0.02281
## F-statistic: 0.2193 on 1 and 34 DF, p-value: 0.6425H0: There is no evidence that draft round placement determines a Kicker’s average number of games he plays.
H1: There is evidence that draft round placement determines a Kicker’s average number of games he plays.
The inference test for Kickers shows that the p-value for the linear regression is 0.6425 which is greater than 0.05. We do not have enough evidence to reject the Null Hypothesis and therefore, there is NO evidence that draft round placement determines Kickers’ average number of games they play. The R2 value is 0.00641 which seems to indicate the linear regression strength against variability is a lot less than that of All Players.
According to the linear regression test, a kicker at the 1st Draft Round on average plays 125 games in his tenure. For each subsequent Draft Round, the average number of games a kicker plays goes down by 3. The residuals are all over the regression line thus supporting the very low R2 value. Only 1 player represents a first round choice. It appears that NFL teams do not place high value on obtaining a kicker in the first draft round.
M. Punter Inference Test
##
## Call:
## lm(formula = G ~ Rnd, data = currentPlayerPosition)
##
## Residuals:
## Min 1Q Median 3Q Max
## -122.107 -88.783 -9.342 79.746 148.775
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 154.638 37.771 4.094 0.000229 ***
## Rnd -7.883 6.298 -1.252 0.218746
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 88.03 on 36 degrees of freedom
## Multiple R-squared: 0.04171, Adjusted R-squared: 0.01509
## F-statistic: 1.567 on 1 and 36 DF, p-value: 0.2187H0: There is no evidence that draft round placement determines a Punter’s average number of games he plays.
H1: There is evidence that draft round placement determines a Punter’s average number of games he plays.
The inference test for Punters shows that the p-value for the linear regression is 0.2187 which is greater than 0.05. We do not have enough evidence to reject the Null Hypothesis and therefore, there is NO evidence that draft round placement determines Punters’ average number of games they play. The R2 value is 0.04171 which seems to indicate the linear regression strength against variability is a lot less than that of All Players.
According to the linear regression test, a punterer at the 2nd Draft Round on average plays 147 games in his tenure. For each subsequent Draft Round, the average number of games a punter plays goes down by 8. The residuals are all over the regression line thus supporting the very low R2 value. Only 1 player represents a second round choice and NO player represents the 1st, 10th and 11th rounds. It appears that NFL teams do not place high value on obtaining a punter in the first draft round.
Part 5 - Conclusion
The research question this study intended to address was if an NFL player’s draft round placement affected his longevity in the NFL based on his position in terms of games played throughout his career. Initially when I developed this project, I hoped that anomalies in individual players performing magnificent feats in the NFL would make this correlation negligible. In the Project Proposal, when I developed statistical graphs showing the average number of games played for all players of a specific position against their draft rounds, I found some interesting trends that led me to believe that draft round status does not really affect the number of games played by players of a particular position.
However, the inference tests indicated that the research question was affirmed for most positions that an NFL player’s draft round placement did affect his longevity in the NFL based on his position in terms of games played throughout his career. The higher a player’s draft round placement (1st being the highest), the more games he played in his career. From the inference tests, there is sufficient evidence to conclude that draft round placement of All Players in general and almost all positions influenced their total number of games played in their career. Positions that followed this trend include quarterbacks, wide receivers, running backs, tight ends, offensive tackles, centers, defensive tackles, linebackers, defensive backs, and defensive ends. It has been found according to the inference tests that the draft round placement of kickers and punters did not affect their total number of games played in their career. The number of kickers and punters in the NFL drafted from 1985 to 2005 is quite small, 1.6% of all players drafted in the same time period. Kickers are responsible for one-third of all points scored (Gilbert, 2018) and punters are a hard-to-fill team need (Yuille, 2013) and yet they are never top priorities for NFL teams in general.
The study only focused on the variables draft round placement and number of games played. It would be interesting to determine in other studies how the other variables affect the analysis. Moreover, it would be interesting to investigate the R2 value when other variables are included to help formulate a more concrete model that determines player longevity in the NFL based on his draft round placement. The variability of the players’ number of games played certainly comes into question as evidenced by the low R2 values less than 0.2 found in all positions in this study.
References
Balla, D. (2015). R: Keep/Drop Columns from Data Frame. Retrieved from https://www.listendata.com/2015/06/r-keep-drop-columns-from-data-frame.html
Brandt, G. (2016). Top 16 lat-round picks since the Tom Brady draft. Retrieved from http://www.nfl.com/photoessays/0ap3000000652507
Gilbert, J (2018). Why NFL teams don’t turn to the draft for kickers. Retrieved from https://www.fieldgulls.com/2018/4/14/17237560/why-nfl-teams-dont-draft-kickers-seattle-seahawks-janikowki-myers-aguayo-gay-walsh-succop-bosher
Graf, D. (2016). NFL Draft Outcomes: All players selected in the NFL Draft from 1985 to 2015. Retrieved from https://www.kaggle.com/ronaldjgrafjr/nfl-draft-outcomes
Kabacoff, R. (2017). Missing Data. Quick-R powered by DataCamp. Retrieved from https://www.statmethods.net/input/missingdata.html
Vergara, A. (2017). The 15 Super Bowl-winning quarterbakcs who weren’t first-round draft picks. Retrieved from https://www.foxsports.com/nfl/gallery/nfl-draft-15-super-bowl-winning-quarterbacks-not-first-round-picks-tom-brady-joe-montana-kurt-warner-brett-favre-042817
Yuille, S. (2013). A study on punters and the NFL Draft. Retreived from https://www.prideofdetroit.com/2013/2/21/4012156/nfl-draft-punters