Y’ALL NEED A RUNNINBACK?By: Chris Torgalski & Jin Lee

WHAT IS A RUNNING BACK? A running back (RB) is a position on a

football team. He usually lines up behind the linemen

and the quarterback. His job is to take handoffs and pitches,

occasionally go out for passes, and to block for the quarterback.

He is also referred to as a tailback or halfback.

WHAT WE WANT TO FIND Is there a relationship between loss of

production and turning 30 years old for NFL running backs? Rushing Yards Rushing Touchdowns

What is the average amount of Pro Bowls a running back makes?

HOW WE COLLECTED DATA List of running drafted between 1995

and 2004 Assign each player a number Randomly generate a number until we

had a list of 50 running backs that met our criteria without any repeats

1 SAMPLE T-TEST:RUSHING YARDS DIFFERENCE (YARDS AT 25-YARDS AT 30)

Ho: µrushing difference = 0Ha: µrushing difference > 0

= 3.457

State Check1)SRS 1) Stated random2) Pop ≥ 10n 2) All RB in history ≥ 5003)Normal pop or n ≥ 30 3) n = 50

xtsn

P(T > 3.457 l df = 49)

= .00057

We reject the HO because our P-value of .00057 < alpha = .05.We have sufficient evidence that the rushing difference between age 25 and 30 for running backs is greater than 0. This means running rush for more yards at age 25 than they do at age 30.

Conditions met -> t distribution -> 1 sample t-test

1 SAMPLE T-INTERVAL:RUSHING YARDS DIFFERENCE (YARDS AT 25-YARDS AT 30)

df= 49= (123.384 , 465.976)

State Check1)SRS 1) Stated random2) Pop ≥ 10n 2) All RB in history ≥ 5003)Normal pop or n ≥ 30 3) n = 50

We are 95% confident that the true difference in rushing yards between ages 25 and 30 is 123.384 and 465.976 yards.

Conditions met -> t distribution -> 1 sample t-interval

* sx tn

RUSHING DIFFERENCE GRAPHS

Shape: unimodal, symmetric Center: mean - 295.413 Spread: (-869,1566) Most running backs rush for about 295.413 more

yards when they are 25 than when they are 30.

Rushing_Difference-1000 -500 0 500 1000 1500

Collection 1 Box Plot

1

2

3

4

5

6

7

8

9

Rushing_Difference-1000 -500 0 500 1000 1500 2000

Collection 1 Histogram

Collection 1

Rushing_Difference

295.413-869-128

224.5745

1566601.333

S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = s

1 SAMPLE T-TEST:RUSHING TOUCHDOWN DIFFERENCE (TOUCHDOWNS AT 25- TOUCHDOWNS AT 30)

Ho: µtouchdown difference = 0Ha: µtouchdown difference > 0

= 2.485

State Check1)SRS 1) Stated random2) Pop ≥ 10n 2) All RB in history ≥ 5003)Normal pop or n ≥ 30 3) n = 50

xtsn

P(T > 2.485 l df = 49)

= .0082

We reject the HO because our P-value of .0082 < alpha = .05.We have sufficient evidence that the touchdown difference between age 25 and 30 for running backs is greater than 0. This means running rush for more touchdowns at age 25 than they do at age 30.

Conditions met -> t distribution -> 1 sample t-test

1 SAMPLE T-INTERVAL:RUSHING YARDS DIFFERENCE (YARDS AT 25-YARDS AT 30)

df= 49= (.447338 , 4.23266)

State Check1)SRS 1) Stated random2) Pop ≥ 10n 2) All RB in history ≥ 5003)Normal pop or n ≥ 30 3) n = 50

We are 95% confident that the true difference in rushing touchdowns between ages 25 and 30 is .447338 and 4.23266 touchdowns.

Conditions met -> t distribution -> 1 sample t-interval

* sx tn

TOUCHDOWN DIFFERENCE GRAPHS

Shape: unimodal, roughly symmetric Center: mean - 2.34 Spread: (-20,20) Most running backs score about 2.34 touchdowns

more when they are 25 then when they are 30.

2

4

6

8

10

12

TD_Difference-20 -10 0 10 20

Collection 1 Histogram

TD_Difference-20 -10 0 10 20

Collection 1

TD_Difference

2.34-20

016

206.65969

S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = s

1 SAMPLE T-TEST:PRO BOWLS MADE

Ho: µpro bowls made = 1Ha: µpro bowls made > 1

= 1.275

State Check1)SRS 1) Stated random2) Pop ≥ 10n 2) All RB in history ≥ 5003)Normal pop or n ≥ 30 3) n = 50

xtsn

P(T > 1.275 l df = 49) = .1

We fail to reject the HO because our P-value of .1 > alpha = .05.We have sufficient evidence that running backs make 1 Pro Bowl during their career in the NFL.

Conditions met -> t distribution -> 1 sample t-test

1 SAMPLE T-INTERVAL:PRO BOWLS MADE

df= 49= (.838827 , 1.72117)

State Check1)SRS 1) Stated random2) Pop ≥ 10n 2) All RB in history ≥ 5003)Normal pop or n ≥ 30 3) n = 50

We are 95% confident that the true number of Pro Bowls that a running back makes during his career in the NFL is between .838827 and 1.72117 Pro Bowls.

Conditions met -> t distribution -> 1 sample t-intevral

* sx tn

PRO BOWLS MADE GRAPHS

Shape: unimodal, right-skewed Center: median - 1 Spread: (0,5) Most running backs make about 1 Pro Bowl.

Pro_Bowl0 1 2 3 4 5 6

Collection 1 Box Plot

5

10

15

20

25

Pro_Bowl-1 0 1 2 3 4 5 6 7

Collection 1 Histogram

Collection 1

Pro_Bowl

1.2800125

1.55235S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = s

RUSHING YARDS SCATTERPLOT

Formula: RY@30 = .286(RY@25) + 300

Interpretation: rushing yards at 25 times .286 plus 300 = rushing yards at 30

0200400600800

100012001400160018002000

0 400 800 1200 1600 2000Rushing_Yards_at_25

Rushing_Yards_at_30 = 0.286Rushing_Yards_at_25 + 3e+02; r2 = 0.12

Collection 1 Scatter Plot

TOUCHDOWN SCATTERPLOT

Formula: TD@30 = .116(TD@25) + 2.8

Interpretation: touchdowns at 25 times .116 plus 2.8 = touchdowns at 30

0

5

10

15

20

25

30

TD_at_250 2 4 6 8 10 12 14 16 18 20 22

TD_at_30 = 0.116TD_at_25 + 2.8; r2 = 0.016

Collection 1 Scatter Plot

WHO IS THIS RUNNING BACK? Age 25 Stats

Yards: 1298 Touchdowns:

12 Age 30

prediction Yards: 671.228 Touchdowns:

4.192ADRIAN PETERSON

WHO IS THIS RUNNING BACK? Age 25 Stats

Yards: 1364 Touchdowns:

11 Age 30

prediction Yards: 690.104 Touchdowns:

4.076CHRIS JOHNSON

WHO IS THIS RUNNING BACK? Age 25 Stats

Yards: 1008 Touchdowns:

13 Age 30

prediction Yards: 588.288 Touchdowns:

4.308BENJARVIUS GREEN-ELLIS

WHO IS THIS RUNNING BACK? Age 25 Stats

Yards: 1515 Touchdowns:

18 Age 30

prediction Yards: 733.29 Touchdowns:

4.888DEANGELO WILLIAMS

WHO IS THIS RUNNING BACK? Age 25 Stats

Yards: 1324 Touchdowns: 5

Age 30 prediction Yards: 678.664 Touchdowns:

3.38

MAURICE JONES DREW

WHO IS THIS RUNNING BACK? Age 25 Stats

Yards: 1042 Touchdowns: 7

Age 30 prediction Yards: 598.012 Touchdowns:

3.612

STEVEN JACKSON

APPLICATION Running backs are better statistically at

age 25 than they are at age 30. This means running backs should work

to become productive earlier in their careers in order to obtain a large contract early.

The player might want to work harder than planned at age 30 so that they can improve their production.

BIAS/ERROR The running back got hurt during their

season for being 25 or 30 The running back could have been a

starter for one season and a backup for the other

The offensive line could have been better one year than it is the other.

CONCLUSION/OPINION We would choose to have a running back

age 25 on our team instead of a running back age 30

Running backs that are 25 score more touchdowns and gain more yards

They will also be in the league longer due to younger age

We found out running backs will make around one Pro Bowl in their career