Doug Martin was far more consistent than Charles Sims

Another name for average is called mean. Don't run away just yet with the introduction of the actual mathematical term of average because you're having flashbacks of junior high or high school math. I promise to make this not so convoluted and simultaneously, literally and figuratively, paint a fuller picture in describing what has transpired over the past season in respect to the Tampa Bay Buccaneers dynamic duo of running backs in Doug Martin and Charles Sims.

The mean, or average, can be very deceiving on what it represents because one may believe that the production of average is a reproducible statistic. Allow me to present three scenarios before I delve into reviewing our running back situation in Tampa for the 2015 season.

Scenario 1

Entries:  5, 5, 5, 5, 5

Sum:  25

Mean (Avg):  5.0

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Scenario 2

Entries:  1, 2, 2, 10, 10

Sum:  25

Mean (Avg):  5.0

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Scenario 3

Entries:  0, 2, 7, 8, 8

Sum:  25

Mean (Avg):  5.0

With averages, we assume that most of the time the production would be that result. Yet with the three scenarios presented above, that does not necessarily happen. Averages are more precise when there are much more entries available because the outliers will not affect the final result as much. Football has 16 games. Basketball has 82 games. Hockey has 82 games. Baseball has 162 games.

While averages are affected greatly with fewer entries, we can introduce other metrics to help in giving better depth. In this case, I will utilize the median stat along with averages, or mean. Median is the middle of an ordered set of entries, and is best used with smaller entries or where there is a vast difference in entries, which is the reason for using the housing median as opposed to housing average. From the median, we can find the medians for the upper half and lower half.  We do this find a range where we can identify the range of reproducibility. The picture we are constructing is called a Box and Whiskers diagram.

Scenario 1

Entries:  5, 5, 5, 5, 5

Sum:  25

Mean (Avg):  5       -->       Median:  5

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Scenario 2

Entries:  2, 2, 2, 9, 10

Sum:  25

Mean (Avg):  5        -->      Median:  2

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Scenario 3

Entries:  0, 2, 7, 8, 8

Sum:  25

Mean (Avg):  5       -->       Median:  7

2015 is the third iteration of using rushing medians.  Here are the previous rushing median articles:

2013 Tampa Bay RB Rushing Median Review

2014 Tampa Bay RB Rushing Median Review

Run Production

Tampa Bay Bucs
2015 Run Production of Martin and Sims
RB	att	yards	avg	long	20+	TD	Yds/G	Fumble Lost
Martin	288	1402	4.9	84	14	6	87.6	4
Sims	107	529	4.9	59	4	0	33.1	1
Total	395	1931	4.9		18	6	120.7	5
http://espn.go.com/nfl/team/stats/_/name/tb

The Bucs run production boasted the best RB tandem in Martin and Sims. Martin finished second overall in rushing and lead the league in most years after contact, which all result into Martin's second Pro Bowl appearance. The 20+ yards runs ranks Martin first in the league and Sims contributed to that stat as well.

Both Martin and Sims have identical rushing averages of 4.9 yards per rush. With the possibility of Martin testing out free agency, from the average production alone would simply suggest that Sims can reproduce what Martin does.  Would we fans be mistaken?

2015 Medians

Tampa Bay Buccaneers
2014 RB Game by Game Breakdown, Total Yards Rushing
Game	Team	Rush Defensive Rank (Yds/A)	Yds/A		RB	Avg	RB	Avg
1	Ten	8	3.9		Martin	4.7	Sims	2.4
2	No	32	4.9		Martin	3.7	Sims	4.8
3	Hou	17	4.1		Martin	3.3	Sims	1.8
4	Car	7	3.9		Martin	5.3	Sims	3.8
5	Jax	5	3.7		Martin	5.1	Sims	4.3
6	Was	31	4.8		Martin	7.2	Sims	4.9
7	Atl	15	4		Martin	3.7	Sims	3.7
8	NYG	24	4.4		Martin	2.8	Sims	9.8
9	Dal	19	4.2		Martin	3.5	Sims	3.6
10	Phi	28	4.5		Martin	8.7	Sims	4.3
11	Indy	23	4.3		Martin	6.9	Sims	2
12	Atl	15	4		Martin	3.8	Sims	8
13	NO	32	4.9		Martin	7.4	Sims	2
14	StL	13	4		Martin	5.1	Sims	7.1
15	Chi	26	4.5		Martin	2.9	Sims	11.3
16	Car	7	3.9		Martin	3.2	Sims	3.8

To find the medians, we first have to identify the entries and then break them down. The list above shows the production in schedule order. We will have to put them into numerical order of production first. Then find the median, the middle most number. Afterwards, we can extrapolate more by finding the upper and lower medians to help create the range for the Box and Whisker diagram. In discovering the upper and lower medians, we have four quadrants, or quartiles. We are going to literally paint a picture of the run productions of each running back.

Doug Martin

Doug Martin
2015 Rushing Medians
Entries	Avg		Medians
1	2.8
2	2.9
3	3.1
4	3.2	6.50	3.25	Lower Quartile
5	3.3
6	3.5
7	3.7
8	3.8	8.50	4.25	Median
9	4.7
10	5.1
11	5.1
12	5.3	12.20	6.1	Upper Quartile
13	6.9
14	7.2
15	7.4
16	8.7

Doug's median of 4.25 yards per game is lower than his average of 4.9 yards per game, -0.65 yard difference. That is a huge difference in production. This can only mean Doug had a couple of great games to lift his average production higher than the median.

Although we have the numbers, we don't see the true perspective of what we found just by looking at the numbers.  So here is where we introduce the Box and Whiskers diagram.

Here we can see that Martin's box range from 3.25 to 6.1 yards. The blue dots are his entry productions. Inside of this box is where you can expect most of this production to be around. You can easily identify this with the numerous blue dots inside the box range. Within that box, we see the median line closer to the lower quartile. The highest extreme for Doug is 8.7 yards per rush for one game.

The red line running horizontal, from left to right, under the black number line is range of production that identifies the lowest production point to the highest production point, also known as the Whiskers portion of the Box and Whiskers diagram. Viewing one Box and Whiskers diagram does not mean much, but it will when there is another diagram to compare and contrast with. Please notice the length of the Whiskers for Martin's production.  We will revisit it again under Sims' section below.

Charles Sims

Charles Sims
2015 Rushing Medians
Entries	Avg		Medians
1	1.80
2	2.00
3	2.00
4	2.40	6.00	3.00	Lower Quartile
5	3.60
6	3.70
7	3.80
8	3.80	8.10	4.05	Median
9	4.30
10	4.30
11	4.80
12	4.90	12.00	6.00	Upper Quartile
13	7.10
14	8.00
15	9.80
16	11.30

For Charles, his median of 4.05 is nearly a yard below his average of 4.9 yards per rush average per game, -0.85 yards difference. That is much more stark than Doug Martin's differential, but at 4 yards per rush is still good production.

With Sims' Box and Whiskers diagram, we can now compare and contrast with Doug Martin's Box and Whiskers diagram. Both boxes are very similar and the medians are both on the lower side of the box. But the biggest differences are the scatter plots of average entries. Sims' scatter plot compared to Martin's are wildly spread out away from the box. The Whiskers extremes on Sims' diagram reveal how skewed his average is, but also how inconsistent and erratic Sims' production is: low of 1.80 yards for one game and 11.30 yards for another game.

The point of medians with Box and Whiskers diagram is to reveal a range of reproducibility.  Martin's median represents a higher base than Sims. Doug's Box and Whiskers diagram shows a lot of his productions on the lower end are much closer to the box, thus making Doug a more reliable runner to produce at a higher rate from game to game.

Although both runners produced very well at a 4.9 yards per average rush per game mean, or average, the median with Box and Whiskers diagram opens your eyes to the differences between the runners.

Volume and Context

Doug Martin had 288 rushing attempts. Charles Sims had 107 rushing attempts. Martin ran the ball 2.69 times more than Sims. Whether the number you use is 4.9 yards average or 4.25 yards median, Martin producing those numbers at such a high volume of attempts reveals he is a bell cow and does it well.

Pro Football Focus did an article on how running backs fared against base defenses as well as running backs who were fortunate enough not to face a lot base defenses in the article called "How Defensive Packages Impacted Yards Per Carry in 2015". Base defenses usually have more personal on the field to stop the run.  Nickel and Dime take away run stoppers for secondary help.

Pro Football Focus
2015 Tampa RBs vs Base, Nickel, and Dime
	Att	Base	Nickel	Dime
Martin	288	76%	22%	0%
Att %		218.8	63.3	0
Sims	106	35%	61%	1%
Att %		37.1	64.6	1.06
https://www.profootballfocus.com/blog/2016/02/15/fantasy-how-defensive-packages-impacted-yards-per-carry-in-2015/

Look at the volume that Doug faces against base defenses, this is from Pro Football Focus and not some made up farce of a stat that some people would like to pretend it is. But Martin should be facing more base defenses because he is utilized mostly on first and second downs.  Sims was used in a complementary role, spelling Martin in third and long situations at times or given a few series to give Martin a rest.

PFF also gave both running backs great reviews:

Doug Martin enjoyed a resurgence in 2015 and this study suggests that he was even better than his raw numbers suggest. Of Martin's 288 carries, 78 percent came when the defense had fewer than five defensive backs on the field. That's the league's fourth-highest mark. Martin averaged 4.8 YPC vs base defenses (10^thbest) and 5.6 YPC vs. nickel (fourth best).

And

If Martin moves on, the Buccaneers won't have trouble finding his replacement. Charles Sims is far from a household name, but he was one of the league's most-effective backs in 2015. Unlike Martin, Sims benefited from handling most of his carries against nickel and dime defenses (62 percent - 10^th highest). Like Martin, he easily outperformed his expected YPC. Sims averaged a solid 4.4 YPC vs base defenses and 5.8 YPC vs nickel (third best in the league).

Conclusion

2015 produced one of the best rushing tandems in the NFL. The rushing averages of both Martin and Sims of 4.9 yards per rush would imply that the Bucs have running backs that are interchangeable. Rushing medians depict a different picture of production. Volume also adds a different dimension to the thought that the running backs are interchangeable. In the set role designated this past year of one being a bell cow and the other a complimentary back, the Bucs were able to enjoy the fruits of their labor.

It would be best if Martin would be re-signed to keep the roles set. Even though Sims has production to have an average of 4.9 yards per game, the volume and wide extreme of production allude that making Sims the feature back may have a higher gamble than some do not see on the surface.