Jeff Zimmerman posted an interesting article on Friday. It prompted me to try to analyze the relationship between (i) an outfielder’s ability to make plays, and (ii) an outfielder’s ability to save runs. From my analysis below, the relationship is not as hand-in-glove as I initially would have thought.

From what I understood about Jeff’s article, he advanced a new defensive metric called “PMR,” which stands for Plays Made Ratio. Jeff calculated this ratio using data from Inside Edge, which categorizes every ball in play into one of six buckets. Jeff explains:

Most of the fielding data falls into two categories. The zero percentage plays are just that, impossible plays, and make up 23.2% of all the balls in play. Balls in this bucket are never caught and always have a 0% value. The other major range is the Routine Plays or the 90% to 100% bin. Defenders make outs on 97.9% of these plays, which make up 64.0% of all the plays in the field; the 2.1% which aren’t made are mostly errors. In total, 87.2% of all plays are graded out as either automatic hits or outs; it is the final ~13% which really determine if a defender is above or below average.

Between almost always and never, four categories remain. Even though each category has a defined range, like 40% to 60%, the average amount of plays made is not exactly in the middle of each range. Here are the actual percentage of plays made in each of the four ranges.

With these league average values and each individual player’s values, a ratio of number of plays made compared to the league average value can be calculated. To have the same output of stats like FIP- and wRC+, I put Plays Made Ratio on a 100 scale where a value like 125 is 25% better than the league average. Here is the long form formula and Jason Heyward’s value determined for an example.

Plays Made Ratio = ((Plays made from 1% to 90%)/((1% to 10% chances * .063%)+( 10% to 40% chances * .289)+ (40% to 60% chances * .576) + (60% to 90% chances * .805))) * 100

Heyward’s Plays Made Ratio = ((1+10+9+26)/((14*.063)+(16*.289)+(9*.576)+(27*.805)))*100

Heyward’s Plays Made Ratio = (46/32.4)*100

Heyward’s Plays Made Ratio = 142

Heyward had a heck of a season. Of the 66 playable balls hit to him, normally only 32 of them would have been caught for an out. Heyward was able to get to 46 of them, or 42% better than the league average. He has consistently had above league average values with a 133 value in 2012 and 125 in 2013.

Jeff posits that the new PFM metric gives us new insight that FanGraphs current go-to defensive metric (Ultimate Zone Rating) does not:

Now remember this stat [PMR] only looks at how often a fielder would have made the play considering their position on the field. The team could be playing its outfielders back to prevent a double or their infielders in for a bunt which could put the defender out of position. Additionally, it doesn’t look at the final results of the play (at least for now). If Sir Dive Alot is playing in the outfield and he loves to try to catch every ball hit his way, then he will get to a few extra flyballs by diving all the time, but those he doesn’t get to will pass him by for more doubles and triples. Also, an outfielder could be good at making plays while coming in versus going deep; balls which fall in over his head would be more damaging than those which fall for shallow singles. While his Plays Made Ratio may be high, the number of runs he saves, as seen by UZR or Defensive Runs Saved, may be lower by comparison.

This got me thinking about the relationship between a player’s PMR and his UZR, and, more specifically, his RngR. As I understand RngR, it is the component of UZR that estimates the number of runs a player saves, or surrenders, due to his range. RngR isolates the contribution a player’s range makes to his Ultimate Zone Rating by ignoring the contributions from his arm and his ability to limit errors.

Intuitively, it would make sense that a player’s PMR and his RngR would be strongly correlated. In other words, a player whose range allows him to make more plays than average would also be the same type of player whose range would allow him to save more runs than average. A simple two-by-two matrix, with RngR along the left side and PMR along the top would show the following quadrants:

My intuition is that players would fall in either quadrant (2) or quadrant (3). The interesting questions arise with players that would fall in quadrant (1) (those who exhibit poor range, but whose range saves runs), and in quadrant (4) (those who exhibit good range, but whose range does not save runs). There are several explanations for why a player may fall into quadrant (1) or (4).

Jeff noted three possible explanations.  First, a player may be overly aggressive, which would may lead to more outs (a higher PMR) but also more misplays resulting in doubles and triples (a lower RngR). Second, “an outfielder could be good at making plays while coming in versus going deep; balls which fall in over his head would be more damaging than those which fall for shallow singles. While his Plays Made Ratio may be high, the number of runs he saves, as seen by UZR or Defensive Runs Saved, may be lower by comparison.” Third, a player (or his team) may be particularly well adept at positioning himself, which would amplify his RngR rating, but not necessarily his PMR (as Jeff noted when discussing Nick Markakis).

How does the relationship between PMR and RngR look if it is applied to actual players? To find out, I looked at all center fielders who between 2012 and 2014 had at least 70 “total chances” (defined by Inside Edge as balls hit to that fielder where there is between a 1% and 90% likelihood that the ball is caught). That provided me a list of 18 center fielders. Next, I calculated each player’s rate-based RngR/150 (calculated by his total RngR divided by the innings he played in center field, multiplied by nine, multiplied by 150). That revealed the following table:

A scatter chart of this information looks like this. I also added a best-fit line to the scatter plot. My intuition that a player’s RngR/150 would be strongly correlated with his PMR is contradicted by this data. In fact, according to this data, (and based on my very limited skillset at statistical analysis, which may be completely incorrect), only 15% of the runs saved due to these 18 center fielders’ range can be explained by their Plays Made Ratio.

Even more interesting than the two-by-two matrix characterization introduced above, are the points on the scatter plot that are either way above (Juan Lagares and Lorenzo Cain) and way below (Dexter Fowler) the linear trendline.

The data suggest that Lagares/Cain and Fowler have similar range in center field, but that the former use their range to save more runs than the latter. One possible implication of this information is that Fowler is not optimizing his ability and that through better decision-making (such as being more aggressive or less aggressive on fly balls) or better positioning he could save more runs. As discussed earlier, it could also mean that Fowler is not (relatively) adept at playing balls hit over his head or in the gap, which leads to more doubles and triples.

On a larger scale, a possible implication of this data is that teams could significantly improve the amount of runs their center fielders save by (i) coaching their center fielders to make optimal decisions regarding their aggressiveness and (ii) properly positioning their center fielders. I would be curious to analyze what is the optimal amount of aggression a center fielder would have in going after balls hit to the outfield, the optimal way to position himself. For example, is it better to play shallow and be aggressive in cutting off singles (which Lagares has a reputation of doing) or to play deep? Those questions are best answered in a follow-up post/article.

A common refrain during this point in baseball’s calendar is that the free agent market isn’t what it used to be. The underlying premise is that more and more teams place more and more focus on locking up their young, talented players to long-term contract extensions.  In turn, fewer and fewer young and talented players are reaching free agency. With the free agent market drying up, teams must pay a significant premium for the few players that do reach free agency that are both relatively young and relatively talented. Ken Rosenthal highlighted this line of thinking in an article last year:

One of the game’s rising young stars recently told me he was concerned about the flurry of contract extensions in baseball. The player didn’t want to be identified, but his thoughts intrigued me, in no small part because he is a candidate for an extension himself. The player’s point was this: Free agency helped make the players union into a powerhouse. But now, with fewer top players reaching free agency, who is going to drive the top of the market? Shouldn’t players feel a sense of responsibility to those who came before them and those who will follow? Fair questions, particularly if you look at the next two free-agent classes, which are almost devoid of stars. But when I expressed the player’s concerns to the head of the union, Michael Weiner, and a prominent agent, Scott Boras, I didn’t get the answers I expected. Neither views the trend as necessarily a problem.

But is this really a trend at all? Let’s look at that question more closely. Let’s begin by looking at the 2014-2015 crop of free agents.  Baseball Reference has a list that is published here. As of this writing, that list contains 306 players. These 306 players have an average age of 31.6 and a median age of 31.0. The average WAR is at 5.54, which reflects outliers at the high end (like Ichiro and Jason Giambi); the median WAR for these 306 players is only 1.90. Of these 306, there are only six players that both (a) are 30 years old or younger (using Baseball Reference’s midpoint method to calculate ages, this is the age the player will be on July 1 of the next season), and (b) have achieved 12 wins above replacement in their career. These six players, in order of descending career WAR, are (i) Pablo Sandoval, (ii) Billy Butler, (iii) Asdrubal Cabrera, (iv) Melky Cabrera, (v) Colby Rasmus, and (vi) Max Scherzer.

If you are general manager looking to fill multiple holes in your roster, this is not the most inspiring group, especially when considering the cost of doing so. This group does reflect the current narrative — there does appear to be a dearth of high-end talent available on the free agent market. But how does this group compare to prior free agent cohorts? Has the free agent market really dried up, or has it always been dry?

Again, Baseball Reference is helpful. On its site, it lists the free agent signings for each year. For example, its list of 2013-2014 free agents is published here. Using the same criteria as before (30 or younger, and 12 career WAR or better), the 2013-2014 free agent crop had seven relatively young and relatively talented players: (i) Josh Johnson, (ii) Brian McCann, (iii) Jacoby Ellsbury, (iv) Ubaldo Jimenez, (v) Scott Kazmir, (vi) Chris Young (the hitter), and (vii) Matt Garza. Perhaps a bit better than 2014-2015, in general, but not markedly different. Looking back further, in summary fashion, here is a look at the free agent market during the ten seasons leading up to this one:

As for a list of the remaining names of the relatively young and relatively talented players appearing in the table above, they are:

2012-13:  Zack Greinke, Russell Martin, Michael Bourn, B.J. Upton, Melky Cabrera, Anibal Sanchez, Edwin Jackson, Stephen Drew

2011-12:  Jose Reyes, Grady Seizemore, Dontrelle Willis, Francisco Rodriguez, Aaron Hill, Prince Fielder, Kelly Johnson

2010-11:  Carl Crawford, Dontrelle Willis, Mark Prior, Jhonny Peralta

2009-10:Matt Holliday, Jon Garland, Rich Harden, Coco Crisp, Hank Blalock, Austin Kearns

2008-09:  CC Sabathia, Mark Teixeira, Jon Garland, Mark Prior, Francisco Rodriguez, Adam Dunn

2007-08:  Aaron Rowand

2006-07:  Barry Zito, Kerry Wood, Mark Mulder, Marcus Giles, Jeff Weaver, Wade Miller, Randy Wolf, Juan Pierre, Aramis Ramirez, Aubrey Huff

2005-06:  Rafael Furcal, Jeff Weaver, Wade Miller, Ramon Hernandez, Paul Konerko, A.J. Burnett

2004-05:  Carlos Beltran, J.D. Drew, Adrian Beltre, Troy Glaus, Edgar Renteria, Matt Morris, Richard Hidalgo, Eric Milton, Kevin Milwood, Placido Polanco, Wade Miller, Richie Sexson

What can we learn from looking at information from the ten free agent classes before this year’s free agent class?

1. The free agent classes have looked very similar, on average, for the past ten years.
2. Over the past ten years, free agency has not yielded the bumper crop of talent that has been suggested.  The locking up of young talent prior to free agency does not appear to be a recent trend.
3. The appearance of high-end talent, particularly high-end talent in the fat part of an aging curve, is at best sporadic (occasionally yielding a young high-end bat, such as Carlos Beltran, Adrian Beltre, Matt Holliday, or Prince Fielder, but almost never a pitcher with his best years ahead).

Based on this look, it has always been difficult to find players in their prime on the free-agent market. They exist, but they are rare. This does not appear to be a new trend.* The number of free agents in 2014 does not include the players that have not been tendered a contract for arbitration. Once this group of non-tendered players become free agents this winter, it will both inflate the number of available free agents and depress the average and median WAR figures shown in the table.