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# My Own Statistical Analysis (Part 2) Defense

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

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