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My Own Statistical Analysis (Part 2) Defense

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It's time to examine the Offense, Defense, and Pitching of the Arizona Diamondbacks.

Jack Nicholson reads a stat sheet.
Jack Nicholson reads a stat sheet.
Jayne Kamin-Oncea-USA TODAY Spor

In Part one of this series I uncovered what I thought to be a useful tool in gauging the potency of the offense as a whole.  It was simply RBI/H.  I was hoping to measure the efficiency of an offense to produce runs where there was opportunity.  Rightly so many people put this statistic under the microscope and deemed it a good try, but needed more scrutiny.  Mostly the logic behind using the RBI was the major suspect.  After all, any team with a large RBI total would have a large RBI/H conversion rate.  Rare is the case where a team would have a low RBI total and a high conversion rate.

There were also calls for me to come up with a statistic that was better suited to be used at the player level, not the team level.  Most of us are looking to assess player abilities individually, not a team which we can clearly see is winning or losing games.

So this time around I hope to satisfy both sets of critics with my defensive metric.  I call it Weighted Fielding Rate, or WFR for short.  It is indented to assess the players fielding aptitude and weigh it with the importance of the player to the teams overall defense.  We can also compare WFR positionally to see how that player stacks up against the rest of the league.  I call that particular metric PWFR or Positional Weighted Fielding Rate.  You will see by the results, the metrics sure do fit the eyeball.

Formula

I had to make one other metric which probably already exists but I could not find it.  If you know of it's existence already, please feel free to let me in on it.  Otherwise DIBS!  For my purposes I call it the Fielding Weight, or FW.  If this metric doesn't already exist, it should.  It's simple:

FW = (PO + A + E) / Inn * 3

This simply gives us a percentage of how many times a player gets their hands on a ball defensively in the field.  Clearly there are positions which will have a higher weight.  1st base, SS, and 2nd.  The LF, RF, and C positions all have very low weighted defense.  Due to the unique nature of the Catching position, the FW and WFR are not really intended to value a catcher for their overall defensive abilities behind the plate but can be used to assess their fielding prowess.  After all a catcher can jump on a bunt and get the out, but a mishandled ball will result in an Error just like everyone else.

Now that we know the weight of the position we can use an already known statistic of Fielding Percentage or (PO + A)/(PO + A + E) to determine that players aptitude for a throwing or catching error.

By simply multiplying FW with FP we get the WFR.

Here are some numbers I worked up from this year.

MLB CF Avg = 0.096

Ender Inciarte (CF) = .105 WFR (PWFR +0.009)

AJ Pollock (CF) = .092 WFR (PWFR -0.004)

MLB RF Avg = 0.077

David Peralta = .063 WFR (PWFR -.014)

MLB 1B League Avg = .338

Mark Trumbo (1B) = .337 WFR (PWFR -.001)

Paul Goldschmidt = .350 WFR (PWFR +.012)

Nick Swisher (CLE) = .325 WFR (PWFR -.013)

As you can see just from a few players most everything lines up to how they performed this year.  AJ might be the one guy that sticks out because we know him to be a good defensive player.  However he did not perform at quite the same level this year.  Even Baseball-Reference.com has his Rtot at -7.  Despite what we think of his defensive abilities, he had a down year.

Goldie also is a stand out while Trumbo is just average at first base.  We know Goldie gets to far more balls at 1st base than most of his peers.  He also make good digs on poor throws.  If it weren't for injury, he would have been a shoe in for another gold glove.  I threw Nick Swisher in there just for comparison as to how bad it can get.

PWFR helps when comparing different positions defensively since it helps take the sting out of being a weighted value.  However it doesn't take it out completely.  We do need to factor into the defensive capabilities of the player the amount of times he/she is relied upon to perform the job.  Ender does a great job patrolling center field and that puts him only a handful of points below the defensive capability of Goldie at 1st.

Hopefully WFR and PWFR are a bit more to everyone's liking.  It may not be the next break out stat that all the Sabermatricians use to asses players, but I think it fairly accurately points out the defensive value of the player to their position as well as being comparable to other position players.

Added:  Here are all of our fielders in their positions this year.

Name Pos WFR MLB PWFR
Eric Chavez 3B 0.060976 0.094054094 -0.033
Bronson Arroyo P 0.093023 0.0589424 0.034
Oliver Perez P 0.034364 0.0589424 -0.025
Cody Ross LF 0.045494 0.070842467 -0.025
Cody Ross RF 0.073122 0.07650589 -0.003
J.J. Putz P 0.050505 0.0589424 -0.008
David Peralta CF 0.06422 0.095880758 -0.032
David Peralta LF 0.047418 0.070842467 -0.023
David Peralta RF 0.074697 0.07650589 -0.002
Joe Paterson P 0 0.0589424 -0.059
Jordan Pacheco 1B 0.280899 0.338253862 -0.057
Jordan Pacheco 2B 0.041667 0.171813427 -0.130
Jordan Pacheco 3B 0.01328 0.094054094 -0.081
Will Harris P 0.022989 0.0589424 -0.036
Andy Marte 3B 0.091954 0.094054094 -0.002
Ryan Rowland-Smith P 0 0.0589424 -0.059
Martin Prado 2B 0.190476 0.171813427 0.019
Martin Prado 3B 0.095107 0.094054094 0.001
Miguel Montero C 0.318866 0.308308799 0.011
Cliff Pennington 2B 0.199368 0.171813427 0.028
Cliff Pennington 3B 0.114123 0.094054094 0.020
Cliff Pennington SS 0.144364 0.15340157 -0.009
Nolan Reimold LF 0.075269 0.070842467 0.004
Zeke Spruill P 0.03003 0.0589424 -0.029
Eury De la Rosa P 0.055249 0.0589424 -0.004
Joe Thatcher P 0 0.0589424 -0.059
Brandon McCarthy P 0.057998 0.0589424 -0.001
Ender Inciarte CF 0.105788 0.095880758 0.010
Ender Inciarte LF 0.091561 0.070842467 0.021
Ender Inciarte RF 0.041667 0.07650589 -0.035
Tony Campana CF 0.108772 0.095880758 0.013
Tony Campana LF 0.055556 0.070842467 -0.015
Bo Schultz P 0.125 0.0589424 0.066
Alfredo Marte LF 0.070922 0.070842467 0.000
Alfredo Marte RF 0.046041 0.07650589 -0.030
Roger Kieschnick LF 0.051852 0.070842467 -0.019
Roger Kieschnick RF 0.069808 0.07650589 -0.007
Tuffy Gosewisch C 0.306038 0.308308799 -0.002
Xavier Paul LF 0.035587 0.070842467 -0.035
Randall Delgado P 0.064767 0.0589424 0.006
Didi Gregorius 2B 0.164141 0.171813427 -0.008
Didi Gregorius 3B 0.1 0.094054094 0.006
Didi Gregorius SS 0.16546 0.15340157 0.012
Aaron Hill 2B 0.183624 0.171813427 0.012
Aaron Hill 3B 0.081699 0.094054094 -0.012
Trevor Cahill P 0.051422 0.0589424 -0.008
Bobby Wilson C 0.366667 0.308308799 0.058
Mark Trumbo 1B 0.33687 0.338253862 -0.001
Mark Trumbo LF 0.065141 0.070842467 -0.006
Chase Anderson P 0.073035 0.0589424 0.014
Daniel Hudson P 0 0.0589424 -0.059
Brad Ziegler P 0.109453 0.0589424 0.051
Josh Collmenter P 0.067002 0.0589424 0.008
Bradin Hagens P 0.151515 0.0589424 0.093
Nick Evans 1B 0.305556 0.338253862 -0.033
Nick Evans 3B 0.142857 0.094054094 0.049
Nick Evans LF 0 0.070842467 -0.071
Gerardo Parra CF 0.119048 0.095880758 0.023
Gerardo Parra RF 0.071918 0.07650589 -0.005
Wade Miley P 0.056357 0.0589424 -0.003
Paul Goldschmidt 1B 0.34986 0.338253862 0.012
A.J. Pollock CF 0.092014 0.095880758 -0.004
A.J. Pollock LF 0 0.070842467 -0.071
Brett Jackson CF 0.666667 0.095880758 0.571
Brett Jackson RF 0.117371 0.07650589 0.041
Vidal Nuno P 0.052083 0.0589424 -0.007
Chris Owings 2B 0.173018 0.171813427 0.001
Chris Owings SS 0.153068 0.15340157 0.000
Addison Reed P 0.01692 0.0589424 -0.042
Mike Bolsinger P 0.102367 0.0589424 0.043
Nick Ahmed 2B 0.212121 0.171813427 0.040
Nick Ahmed SS 0.1388 0.15340157 -0.015
Matt Stites P 0.060606 0.0589424 0.002
Evan Marshall P 0.067889 0.0589424 0.009
Andrew Chafin P 0.047619 0.0589424 -0.011
Jacob Lamb 3B 0.086475 0.094054094 -0.008