Why Bobby Rainey is the Buccaneers' best running back

In this article, I want to review the production of the Tampa Bay Buccaneers' running backs in respect to median statistic, as opposed to the rushing average usually seen everywhere on every sports' statistic web site. There is a difference between the two statistics.

But what does this mean in real life? Average informs you of what is being produced equally per entry. Median informs where the middle of the production of that entry set exists.

What if I told you that sometimes the average could be wrong about dictating repetitive production?

Rainey averaged 4.3 yards per game, but did you know that 35% of his total rushing yards came in one game?

Average, or mean, adds up all of the entries and divides that result by the total number of entries. For example, we have five entries of 1, 2, 2, 10, and 10. Add them all together and the result will be 25. Since there are five entries, then divide the result by the number of entries.  In this case, 25 divided by 5 is 5. The average of those five entries is 5.  Without anyone giving you the entries and simply gave you the average of 5, then you would think every entry should be 5. But that is not the case.

Median is the middle of an ordered set.  Since our example above uses five entries, it is easy to spot the median.  The median is 2. This means you can expect more results near 2. That result is far different from the average as well as what one would believe most of the results should be, which is to average 5 per entry.

The median alone does not describe much, though. Surprisingly, you can break down an ordered set into two smaller sets, the lower half and upper half of an entry set where the median is the halfway junction. Find the median of the lower and upper half, then you will have created a range of where production occurs more often. This creates the box range of production for a box-and-whiskers plot.

Sometimes, averages could be deceiving like the example I present above.  A Box-and-Whiskers plot, or diagram, helps to paint a truer picture of production. And that is what I will be doing here with our running backs' productions.

Tampa Bay Buccaneers
2014 RB Game by Game Breakdown
Game	Team	Rush Defensive Rank (Yds/A)	RB	AVG	RB	AVG	RB	AVG
1	Car	27th	Martin	1.0	Rainey	3.0
2	StL	15th			Rainey	6.5
3	Atl	16th			Rainey	3.7
4	Pit	25th	Martin	3.1	Rainey	0.5
5	NO	31st	Martin	3.2	Rainey	3.5
6	Bal	3rd	Martin	4.1	Rainey	6.0
7	Min	24th	Martin	2.7	Rainey	3.1
8	Cle	28th			Rainey	4.6
9	Atl	16th			Rainey	2.3	Sims	2.9
10	Was	13th			Rainey	0.8	Sims	2.8
11	Chi	22nd	Martin	2.5	Rainey	3.0	Sims	3.7
12	Cin	18th	Martin	3.2	Rainey	11.0	Sims	1.2
13	Det	1st	Martin	4.4			Sims	-0.8
14	Car	27th	Martin	6.9			Sims	4.9
15	GB	20th	Martin	1.7			Sims	-0.3
16	NO	31st	Martin	5.7			Sims	3.8

Here is a snapshot of the season's production:

Tampa Bay Buccaneers
2014 Running Back Production
Player	Att	Yds	Avg	Long	TD
Martin	134	494	3.7	63	2
Rainey	94	406	4.3	31	1
Sims	66	185	2.8	20	1

Doug Martin

2014 Doug Martin Rush Stats
Median, Mode, Variance, and Difference
Per Game YPC, in order	1.0, 1.7, 2.5, 2.7, 3.1, 3.2, 3.2, 4.1, 4.4, 5.7, 6.9
Lower Quartile	2.5
Median	3.2	Mean (Avg)	3.7
Upper Quartile	4.4
Variance of the Box (UQ - LQ)	1.9	Median - Mean difference	-0.5

Bobby Rainey

2014 Bobby Rainey Rush Stats
Median, Mode, Variance, and Difference
Per Game YPC, in order	0.5, 0.8, 2.3, 3.0, 3.0, 3.1, 3.5, 3.7, 4.6, 6.0, 6.5, 11.0
Lower Quartile	(2.3 + 3.0)/ 2 =       2.65
Median	(3.1 + 3.5)/ 2 =          3.3	Mean (Avg)	4.3
Upper Quartile	(4.6 + 6.0)/ 2 =                 5.3
Variance of the Box (UQ - LQ)	2.65	Median - Mean difference	-1.0

Charles Sims

2014 Charles Sims Rush Stats
Median, Mode, Variance, and Difference
Per Game YPC, in order	-0.8, -0.3, 1.2, 2.8, 2.9, 3.7, 3.8, 4.9
Lower Quartile	(-0.3 + 1.2)/ 2 =     0.45
Median	(2.8 + 2.9 )/ 2=      2.85	Mean (Avg)	2.8
Upper Quartile	(3.7 + 3.8)/ 2 =       3.75
Variance of the Box (UQ - LQ)	3.3	Median - Mean difference	0.05

Median Comparison

Utilizing the median statistic of where the center of the entries are as well as where a large frequency of production revolves around, we have in order of most productive with Rainey (3.3 yards), Martin (3.2 yards), and Sims (2.85 yards). Rainey and Martin have similar Median statistics.  Sims is about half a yard behind.

Most of the production revolve around 3.3 yards per rush. To give perspective, 3.3 yards would rank 40+ out of all of the qualified rush leaders on ESPN.com. Already, our running backs are at the bottom rung of production in the league.

Box Comparison (UQ - LQ)

The box range represents the inner frequency of production.  It is within this range that you can find a player's production reproducibility. The smaller the range, the higher rate of reproducibility is found. In other words, the smaller the box, then the more predictable the production of the running back will become. Within that box range, the median informs us where the center of that production can be found. Which means more of that production can be found by the Median.

Box Differential: Martin: 1.9 yards; Rainey: 2.65 yards; Sims: 3.3 yards

Doug Martin possesses the smallest box range, informing us that we know what to expect from Martin game in and game out. Unfortunately, the median is to the low side.

Rainey has a larger box range than Martin, but his median is also on the low side.  Although Rainey does have the highest upper quartile point (5.3 yards), you can rest assured he is not likely to repeat that production as often as he would like as his median point is 3.3 yards. That two yard difference is a huge gap of inconsistency.

Sims has the widest box range.  Yet, his upper quartile happens to be the Median of both Rainey and Martin.  That statistic alone should speak volumes of Sims' production as a running back, or there lack of.

Whiskers Comparison (Extremes)

The Whiskers represents the extremes, the lowest production and the highest production.  These productions are not the norm, but they do help paint the overall picture of production.  Factor in the Box and the Median, then you begin to gauge where the most production occurs for each running back.

Bobby Rainey has the widest Whisker.  Yet most of his productions are on the very low side of the Whisker.  That means Rainey had some exceptional games, but many more mediocre games that pulled the frequency of reproduction much, much lower in respect of his Whisker (extremes).

Starting the Whiskers in the negative area has posted a false result in my excel chart for Charles Sims.  In the two years I have tracked Tampa Bay running backs, I have never seen a negative production before, let alone two negative productions. This extreme identification should put up a huge flag about Sims' running prowess.

Similar to Rainey's pattern of wide whisker with the box on the low side, Martin possesses that pattern, but the whisker is shorter than Rainey's on the high side.

Median - Mean difference Comparison

Sometimes the mean, or average, does not differentiate one game production that is an outrageously high result.  One game can skew the overall production.  Median and mean can be very similar. When that occurs, then the production of the running back is consistent in producing the same outcome more often. When the Median and mean differ greatly then the Box-and-Whiskers diagram helps to explain such inconsistency in the two statistics.

Martin's differential:  3.2 - 3.7 = 0.5

Rainey's differential:  3.3 - 4.3 = - 1.0

Sims' differential: 2.85 - 2.8 = 0.05

Tampa Bay Buccaneers
2014 Highest % Game Production v Total Production
RB	Higest game run production	Total run production	% of highest game prod vs total production
Martin	108	494	21.9%
Rainey	144	406	35.5%
Sims	69	185	37.3%

As you can see from the aforementioned chart, 35% of Rainey's total production came in one game.  Similarly, Sims also had a high percentage rate in one game.  This is where sometimes Median is a better review tool than averages, or at least should be used in conjunction to averages.  Medians may be a tool that could be helpful in fantasy football such that it can predict consistent production better than averages.

Recall, Rainey’s 2014 average, or mean, was 4.3 yards per game.  So as a fantasy football participant, you are expecting Rainey to produce 4.3 yards per game or around there for every outing.  The Box-and-Whiskers reveals a majority of his production was about a full yard less than the average.

Conclusion

Bobby Rainey is our best running back on the team in respect to Median statistics, but not by much.  The most reliable is Doug Martin.  Sims should not be a running back.  Mike James produced better in his rookie season than Sims did in his rookie season.  All together, the Bucs' running backs' productions were quite abysmal.

What is missing in the Box and Whiskers diagrams are fumbles and pass catching out of the backfield.  Fumbles as a runner and pass catcher were the fatal mistakes that Rainey made to fall out of favor with head coach Lovie Smith.  If Martin or Sims were available, then Rainey would not receive the same opportunities as if he were the only viable option. That lack of opportunities reveals the lack of trust the coaches have on Rainey.

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Added statistical reflection

Tampa Bay Buccaneers
Box and Whiskers History, Martin and Rainey
Year	Player	Avg		Low	LQ	Median	UQ	Highest
2012	Martin	4.6		1.8	3.2	4.05	5.2	10
2013	Martin	3.6		1.7	2.7	4.25	4.4	5
2014	Martin	3.7		1	2.5	3.2	4.4	6.9
2013	Rainey	3.9		1.9	2.2	3.45	5.5	5.8
2014	Rainey	4.3		0.5	2.65	3.3	5.3	11
Stats from ESPN.com

Martin's median stat fell by a whole yard between the two seasons. Rainey's median is pulling further away from his average production. The difference can be attributed to the new offense and new offensive linemen. Two seasons ago we had one of the worst offensive lines. This past season, the total rush yards for the team was 1,375 yards.  Two seasons ago, the total was 1,612.

Here is the first table introduced in this article, but re-ordered the list in respect to opposing defenses' rush defensive rank, from highest to lowest.

Tampa Bay Buccaneers
2014 Rush vs Def Rank
Game	Team	Rush Defensive Rank (Yds/A)	RB	AVG	RB	AVG	RB	AVG
13	Det	1	Martin	4.4			Sims	-0.8
6	Bal	3	Martin	4.1	Rainey	6.0
10	Was	13			Rainey	0.8	Sims	2.8
2	StL	15			Rainey	6.5
3	Atl	16			Rainey	3.7
9	Atl	16			Rainey	2.3	Sims	2.9
12	Cin	18	Martin	3.2	Rainey	11.0	Sims	1.2
15	GB	20	Martin	1.7			Sims	-0.3
11	Chi	22	Martin	2.5	Rainey	3.0	Sims	3.7
7	Min	24	Martin	2.7	Rainey	3.1
4	Pit	25	Martin	3.1	Rainey	0.5
1	Car	27	Martin	1.0	Rainey	3.0
14	Car	27	Martin	6.9			Sims	4.9
8	Cle	28			Rainey	4.6
5	NO	31	Martin	3.2	Rainey	3.5
16	NO	31	Martin	5.7			Sims	3.8

If you wish to copy and paste this table into your Excel program in order to utilize the ‘Sort & Filter' function, then only copy the table starting from categories. As it is set up, the top heading cells creates an error to sort because it does not share the same cell breakdown. The top heading is one long cell that merged nine cells horizontally. Differences in cell amounts are what cause the conflict in the program.

After the re-sorting, I then added the top two heading cells and renamed the Excel tab.