A Possible Relation between Offensive and Defensive Statistics

During my playing days, my father would always tell me that "Walks (defensively speaking) and Errors will kill you".  Of course, he said this in reference to the outcome of a game.  With consideration of his past advice and my forward statistical thinking, I decided to tamper with some current statistics in an attempt to correlate a players offensive and defensive abilities.  Keep in mind that none of my statistics are perfected, but are in beta (development) per say.  In my research, I constructed a statistic, which I refer to as Net Runs (NR).  Net Runs is based off of Bill James' statistic, Runs Created.  Runs Created is a statistic used to estimate the amount of runs a player or team created (http://sabr.org/sabermetrics/statistics).  The equation is as follows:

Runs Created= (((Total Bases) * (Hits + Walks))/(At-Bats + Walks))

Taking Runs Created into consideration, I sought to incorporate an additional concept factoring in the estimated amount of runs that a player costs his team on defense.  I figured that typically with a fielding error, the amount of bases the defense concedes is one.  Thus, four errors should equate to one run.  All of the proceeding aspects being taken in consideration, the equation for Net Runs is as follows:

Net Runs= Runs Created - (Errors/ 4)

Now, I am going to analyze this statistic with current players.  For my data set, I will use the top 50 offensive players in the MLB, as ranked by their Runs Created statistic, from this 2014 season.  The first column of the chart shows the players Runs Created rank.  The second column of the chart shows the players Net Runs rank.

RC Rank	NR Rank	Player	RC	Errors	Err./4	Net Runs
1	1	Troy Tulowitzki	70	2	0.5	69.5
2	2	Andrew McCutchen	63	4	1	62
3	3	Jose Bautista	61	2	0.5	60.5
4	4	Giancarlo Stanton	59	3	0.75	58.25
6	5	Yasiel Puig	56	0	0	56
5	6	Paul Goldschmidt	56	6	1.5	54.5
7	7	Mike Trout	55	2	0.5	54.5
8	8	Nelson Cruz	53	0	0	53
9	9	Carlos Gomez	52	2	0.5	51.5
10	10	Michael Brantley	50	1	0.25	49.75
13	11	Victor Martinez	49	3	0.75	48.25
11	12	Miguel Cabrera	49	4	1	48
12	13	Edwin Encarnacion	49	6	1.5	47.5
14	14	Jonathan Lucroy	48	2	0.5	47.5
15	15	Anthony Rizzo	48	4	1	47
17	16	Hunter Pence	47	3	0.75	46.25
18	17	Justin Upton	47	4	1	46
20	18	Melky Cabrera	46	0	0	46
19	19	Jose Altuve	46	2	0.5	45.5
16	20	Lonnie Chisenhall	47	9	2.25	44.75
23	21	Brandon Moss	45	2	0.5	44.5
22	22	Brian Dozier	45	4	1	44
24	23	Charlie Blackmon	44	2	0.5	43.5
26	24	Chase Utley	44	4	1	43
25	25	Todd Frazier	44	6	1.5	42.5
28	26	Freddie Freeman	43	3	0.75	42.25
30	27	Nick Markakis	42	0	0	42
31	28	David Ortiz	42	0	0	42
21	29	Josh Donaldson	45	13	3.25	41.75
29	30	Daniel Murphy	43	7	1.75	41.25
27	31	Matt Carpenter	43	8	2	41
32	32	Alex Gordon	41	0	0	41
33	33	Adam Jones	41	3	0.75	40.25
34	34	Jayson Werth	41	4	1	40
36	35	Jacoby Ellsbury	40	1	0.25	39.75
39	36	Mike Morse	40	1	0.25	39.75
35	37	Robinson Cano	40	3	0.75	39.25
37	38	Dexter Fowler	40	3	0.75	39.25
38	39	Justin Morneau	40	3	0.75	39.25
46	40	Neil Walker	39	1	0.25	38.75
47	41	Christian Yelich	39	2	0.5	38.5
40	42	Jose Abreu	39	3	0.75	38.25
42	43	Shin-Soo Choo	39	3	0.75	38.25
49	44	Seth Smith	38	0	0	38
41	45	Xander Bogaerts	39	6	1.5	37.5
43	46	Alexei Ramirez	39	6	1.5	37.5
45	47	Anthony Rendon	39	7	1.75	37.25
48	48	Adam LaRoche	38	3	0.75	37.25
50	49	Brett Gardner	37	0	0	37
44	50	Hanley Ramirez	39	9	2.25	36.75

I took the liberty of highlighting the players that have the largest gaps between their RC and NR ranks.  For the players with large positive changes (rank movement of at least 3 places), their names are highlighted in green.  Then for the players with large negative changes, their names are highlighted in red.  The greatest positive movement belongs to Christian Yelich, an outfielder for the Miami Marlins.  Yelich moved up a total of 6 spots.  Now, looking at the converse situation, Josh Donaldson, Third Baseman for the Oakland Athletics, owns the largest skid.  Donaldson descended a total of 8 spots.

I understand that the probability of committing errors varies with each position.  I also acknowledge that some of these players are designated hitters and have no risk of committing errors.  This statistic is just an attempt to try to combine the offensive and defensive statistics of a player.  I will work to try and refine this statistic for the future.  A factor which I wish to consider for Net Runs in the future is figuring out the exact amount of bases that a defensive players error actually yields.  I could even make the statistic more efficient through adjusting the equation so that the equation would produce the players net runs per game.

Net Runs Per Game= (Runs Created - (Errors/ 4)) / Games Played

*NOTE THAT ALL OF THE STATISTICS, WITH THE EXCLUSION OF NET RUNS, ARE NOT MINE.  THEY BELONG TO THEIR RIGHTFUL CREATORS.  ALL DATA I USED TO PERFORM MY CALCULATIONS IS COMPILED FROM BASEBALL-REFERENCE.COM.*