Cannons and Popguns — Rating Outfield Arms

To me, the most exciting play on a baseball field is a close play on a runner at home plate with a strong throw coming from the outfield. In my mind’s eye I see a low liner shooting out to right field and the runner, off from second on contact, already halfway to third base. The right fielder (I keep thinking of Dwight Evans, which betrays my age, I guess) charges and picks the ball up off his shoetops. In one sweet motion, and taking only one step, he rifles the ball on a line towards home where the runner is converging on the plate. The catcher has one foot firmly planted between the plate and the now-sliding runner as he takes the ball. He sweeps down with the glove to the left and behind him. The runner slides wide and reaches to touch the plate with this hand. The umpire is in perfect position to make the call…

So, who are the best at throwing out runners? Or, perhaps just as importantly, which outfielders have such fearsome arms that runners are afraid to challenge them, afraid to take the extra base? And which of these aspects is more important: throwing out runners or intimidating them enough to make them cautious? I’ve got a way of answering these questions using play-by-play data. But, before we go to the numbers, who do the fans, scouts and players consider to have the best outfield arms?

Scouting Reports

The analyst known as Tangotiger has created something known as the Fan’s Scouting Report, which is a defensive scouting report supplied by fans. (See the site for details.) This is an excellent project that deserves praise. It’s useful for me because it allows me to see who the fans consider to be the best throwing outfielders. Based on three separate categories (Release, Strength and Accuracy) here are the owners of the top outfield in 2005 according to the fans:

Top-Ranked Outfield Arms, Fans' Scouting Report
1. I Suzuki 
2. J Francoeur 
3. A Kearns 
4. M Kotsay 
5. T Hunter 
6. J Edmonds 
7. G Jenkins 
8. L Walker 
9. A Jones 
10. A Rios 

And because it’s just as much fun (or maybe more) to look at trailers, as it is leaders, here are the worst:

Lowest-Ranked Outfield Arms, Fans' Scouting Report
1. L Gonzalez 
2. B Williams 
3. S Stewart 
4. D Young 
5. J Damon 
6. R White 
7. C Everett 
8. C Crisp 
9. N Logan 
10. Q McCracken 

A player survey conducted by Sports Illustrated in 2003 came up with these top outfield arms:

Best Outfield Arms, SI Player Survey, 2003
1. Vladimir Guerrero        
2. Jose Guillen             
3. Ichiro Suzuki            
4. Raul Mondesi             
5. Larry Walker             
6. Jim Edmonds              
7. Torii Hunter             
8. Bobby Higginson          
9. Andruw Jones             
10. Shawn Green              

Suzuki, Hunter, Edmonds, Walker and A. Jones all appeared on the Fans’ Scouting Report mentioned above.

Last summer ran a couple of articles on the most powerful and most accurate outfield arms. Among the powerful arms, in addition to
guys already mentioned above, we find Richard Hidalgo and Bobby
. Hideki Matsui was mentioned in the “Accurate Arms” article, with a reference to his “quick release.” OK, this looks like a pretty good crop of outfield cannons based on scouting reports. Let’s have a look at the data to see what we find.

Method for Rating Outfield Arms

I think it’s safe to say that raw assists totals are not necessarily a good measure of throwing ability for an outfielder. The main problem with counting assists is that
runners will be cautious when a strong-armed outfielder is trying to gun them down; they will not try to take the extra base. The guy with the cannon will just not have as many chances to throw somebody out.

A better picture of outfield arms can be obtained by analyzing the play-by-play data. In many situations, you can tell if a base runner took an extra base or not, and you can keep track of assist opportunities as well as assists.

There are many different kinds of plays that require an outfielder to use his arm, and it probably isn’t possible to take all of them into account. To keep the analysis manageable, I’ve isolated five different outfield plays that I use to measure the prowess of outfield arms:

  1. S-1B: A single is hit to the OF with a runner on 1B and 2B unoccupied.
  2. S-2B: A single is hit to the OF with a runner on 2B.
  3. D-1B: A double is hit to the OF with a runner on 1B.
  4. F-3B: An OF fly is caught with a runner on 3B, fewer than 2

  5. F-2B: An OF fly is caught with a runner on 2B and 3B unoccupied, fewer than two outs.

For each play that falls into one of these categories, I classify the play into one of three possible outcomes:

  1. Kill: an assist was recorded by the outfielder
  2. Hold: the runner did not take the extra base
  3. Advance: the runner took the extra base

My original intention was to focus solely on the key runner, i.e. the runner mentioned in the definition of the five situations. My thinking was that this is the runner that can do the most damage, by scoring or reaching 3B, so that is the one who’d most likely draw a throw. The problem is that this reasoning turns out to be flawed. Almost half the kills in these situations (especially situations 1-3) eliminate either a trailing runner or the batter. As an example, consider Vlad Guerrero in 2004. He recorded 13 assists overall, and 10 of them occured in one of the five situations that we are considering. (The other three occured when Vlad threw out batters trying to stretch a single or a double for an extra base. I cannot consider such plays, since the data do not tell us how often a “stretch” is attempted.) But, of the 10 assists that occured in one of our five situations, only three times was the “key” runner put out. The other seven times a trailing runner (including the batter) was eliminated.

So, here is how I classify the plays into the three outcomes: if the outfielder records an assist on the play, on any runner, he gets a kill. If there is no assist, then I look at the “key” runner. If he takes the extra base, that is an “advance” charged to the fielder. Otherwise, the outcome is considered a “hold.” Note that we are still not considering “all” plays where an outfielder’s arm comes into play. Specifically, we don’t capture Guerrero throwing out batters attempting to stretch a single. Nor do we take into account those times when an OF forces a runner at 2B after a would-be single. Hardly ever happens, you say? Maybe, but three of Vlad’s eight assists in 2005 were of this variety. In any case, as we’ll see, quite a bit of an outfielder’s throwing work falls into one of the five situations that we are considering.

Average Rates for Kills and Holds

An ingredient necessary for this analysis is the league rate for Kills, Advances and Holds for each of the five situations. Actually, the rates differ markedly depending on the number of outs; in particular there is generally a large difference when there are two outs. The rates also depend on which outfielder fields the ball. Clearly, more runners will go first-to-third on a base hit to right field than they will if the ball is hit to left. The average rates for the different situations are shown in the following graphs:


A Hardball Times Update
Goodbye for now.

From the first graph you get an idea of how often a runner tries for the extra base depending on the type of play (Situation). The purple bars represent successful advances and one can see that runners really “go for it” in sacrifice fly situations (F-3B) and when trying to score from second base on a single (S-2B). Another feature that is observable in the first graph is the dependence of the advance rate on the location of the batted ball. When the advance would bring the runner to third base (first and fifth situations), we see that he’s more likely to try on a hit to right, as we expect, since a longer throw from right field is required. When the play is at the plate, however (Situations 2-4), the runner will go more often against the center fielder.

Comparing the bottom plot with the top one gives an idea of the effect of having two outs on the board: runners are much more inclined to take risks, in certain situations. In particular, almost all runners attempt to score from second base on a single when there are two outs (note the prominence of the purple bars in the middle of the lower plot).

In what follows, I will be comparing how an outfielder did in terms of Kills, Holds and Advances compared to league average. Based on what we’ve seen here, it’s
necessary to determine the averages separately for LF, RF and CF; for the particular situation (1-5) and for the number of outs (fewer than two or two outs).

A Couple of Noteworthy Performances

First, let’s have a look at a couple of example players, with the results broken down by the five situations I am considering. Let’s start with a rookie who made a big splash in 2005 by gunning down quite a few runners from right field. In fact, despite playing less than half a season, Jeff Francoeur led all major league right fielders in assists. In the table that follows, “K” means Kills and “H” means Holds.

Jeff Francoeur, RF
                             Actual         Expected
 Situatation  |   Opps  |    H    K  |      H      K 
        S-1B  |     24  |   15    0  |   13.3    0.4 
        S-2B  |     30  |    7    6  |    9.1    2.3 
        D-1B  |     14  |    9    1  |    8.8    0.6 
       OF-3B  |      7  |    3    1  |    1.6    0.3 
       OF-2B  |     11  |    5    1  |    6.2    0.2 
     Overall  |     86  |   39    9  |   39.0    3.9 

Francoeur really excelled at cutting down runners trying to score from second base on a single. The table above shows him nailing six of these guys, while the average right fielder would have nabbed just two and a half. Overall, he killed nine baserunners; the expectation was around four, so it’s quite a nice haul. On plays where he didn’t nail anybody, runners advanced slightly less often than average.

Across the way, in the other outfield corner, the major league assist leader was … Manny Ramirez! Who’d’ve ever thunk it? Let’s see how Manny did in our five situations in 2005:

Manny Ramirez, LF
                             Actual         Expected
 Situatation  |   Opps  |    H    K  |      H      K 
        S-1B  |     62  |   50    4  |   53.0    0.7 
        S-2B  |     49  |   21    6  |   15.6    3.8 
        D-1B  |     44  |   26    2  |   26.7    1.4 
       OF-3B  |     18  |    5    0  |    4.1    0.8 
       OF-2B  |     19  |   17    0  |   17.3    0.4 
     Overall  |    192  |  119   12  |  116.6    7.1 

Manny found himself in one of our five situations 192 times, which is the second-highest total among left fielders. So that explains part of his high assist total. However, he did throw out about five more runners than the average left fielder would have given Manny’s opportunities. And Manny did not allow an excessive number of runners to take the extra base. Two things to note here: these numbers are not park-adjusted, and if any park needs adjusting, Fenway probably does. The second thing to remember is that our five situations do not take into account all outfield throwing situations. Manny actually had 17 assists last season, while only 12 show up in the ledger above. Manny threw out five batters trying to take an extra base, a situation that I cannot handle in this analysis, as explained above.

How should we rank?

Ok, now that we have a method of evaluating how our outfielders did in throwing situations, how do we rank them overall? The first thing I did was to calculate two rate stats for each player: Hold Rate and Kill Rate. Kill rate is just the number of runners cut down divided by the number expected (times 100). So a Kill Rate of 110 means the fielder threw out 10% more than the expected number of runners. The Hold Rate is calculated in a similar fashion: the number of Holds divided by the number of expected Holds. Base runner Kills are removed from consideration when calculating the Hold Rate because you wouldn’t want to penalize a player for getting fewer holds, simply because he was throwing out more runners.

Here are the Top 10 right fielder arms for 2005, ranked by Kill Rate (KR), minimum of 75 opportunities:

Top Right Field Arms by Kill Rate
          Opps      KR    HldR
Francoeur   86     265    105
Hawpe      128     193	   97
Gibbons     97     181	   93
Jenkins    158     159	  103
Ordonenz   112     137	   89
Kearns     136     128	  100
Suzuki     221     124	   98
Nixon      143     123	   91
Guillen,J  176     121	   95
Abreu      154     117	   97

And here are the Top 10 ranked by Hold Rate (HldR), minimum 75 opps:

Top Right Field Arms by Hold Rate
            Opps     KR    HldR
Lane         137     84    124
Rios         145    115    117
Diaz,V        86     68    117
Guerrero     113     53    115
Jones,J      122    103    114
Sheffield    140     50    107
Cameron       78     90    107
Hidalgo      113     74    106
Lawton       137     90    105
Francoeur     86    265    105

Note that Francoeur is the only right fielder to make both lists.

Well, that’s fine, but it’d be nice to have a neat, tidy list of the top 10 right field arms for 2005. It’d be nice to be able to combine HldR and KR somehow to get a single number. One way to do this is to determine the value of each Hold and each Kill in terms of runs. This needs a little bit of explanation, so let’s start a new section.

The Value of a Kill (or a Hold)

The most direct way to assign a run value to a player’s performance would be to use the Run Expectancy Matrix (REM). If you’re not familiar with the REM, Dan Fox provides a concise (and painless) introduction to the subject here. Basically the REM tells you, given a combination of outs and runners on base, how many runs a team will score in the rest of the inning. These run values are averages. They assume average hitters coming to the plate: an average pitcher, average defenders, etc. By considering the run value before and after any given play, you can assign a run value to the play itself.

So, in principle, one could consider every single throwing opportunity and assign a run value to the outfielder based on the REM. I chose not to do things this way, because I’m not interested so much in what happened in specific situations, but rather just how good the outfielder’s arm is. For example, say a right fielder throws out a runner at home on a single with none out (the situation we are calling S-2B). Now consider the same play, but the second time it occurs with the bases loaded (it’s still S-2B). The run value on the two plays is quite different and the right fielder will get different amounts of “credit” for his kill in the two cases, although he performed equally well both times.

To avoid this kind of thing, and also to avoid splitting up the data into too many small sub-samples, I calculated average run values for the different outcomes (Kill, Hold, Advance) for the five situations. I also split the data up according to the number of outs: fewer than two outs or two outs.

OK, with the run values in hand (I didn’t show them to you, but I have them), we can determine which right fielder saved his team the most runs in 2005 (75 opps min):

Top Right Field Arms by Runs Saved
Name        Opps     KR   HldR   Runs
Francoeur     86    265    105    5.5
Jenkins      158    159    103    3.6
Rios         145    115    117    2.6
Lane         137     84    124    2.5
Jones,J      122    103    114    2.4

The five trailers in terms of total runs:

Worst Right Field Arms by Runs Saved
Name        Opps     KR   HldR   Runs
Brown,E      180    107     85   -5.1
Burnitz      163     72     84   -4.3
Green,S      126     22     99   -4.3
Blake        151     38     92   -3.6
Nixon        143    123     91   -1.7

Another thing to note is that the absolute run values are fairly modest, a subject I will come back to at some point.

Lastly, I wanted to rank the right fielders on a per-opportunity basis. So I calculated the run value per 200 opportunities, which corresponds to slightly more than a full season. I was going to list the top and bottom five, but since there are only 28 qualifiers, heck, here’s the whole list:

Top Right Field Arms by Runs Saved per 200 Opps
Name        Opps     KR   HldR   Runs  Runs/200 opss
Francoeur    86    265    105    5.5   12.8
Diaz         86     68    117    2.2    5.2
Jenkins     158    159    103    3.6    4.6
Jones,J     122    103    114    2.4    4.0
Rios        145    115    117    2.6    3.6
Lane        137     84    124    2.5    3.6
Cameron      78     90    107    1.3    3.4
Hawpe       128    193     97    1.9    3.0
Gibbons      97    181     93    1.4    2.8
Giles,B     184     86    100    2.2    2.4
Guillen,J   176    121     95    1.3    1.5
Abreu       154    117     97    1.2    1.5
Ordonez,M   112    137     89    0.5    0.9
Encarnacion 151     75    104    0.5    0.6
Kearns      136    128    100    0.3    0.4
Sheffield   140     50    107    0.2    0.3
Suzuki      221    124     98    0.1    0.1
Dye         160     89    102   -0.0   -0.0
Lawton      137     90    105   -0.1   -0.2
Huff        124     46     98   -0.1   -0.2
Hidalgo     113     74    106   -0.6   -1.1
Swisher     103     87     99   -1.0   -2.0
Guerrero    113     53    115   -1.2   -2.2
Nixon       143    123     91   -1.7   -2.4
Blake       151     38     92   -3.6   -4.8
Burnitz     163     72     84   -4.3   -5.2
Brown,E     180    107     85   -5.1   -5.7
Green,S     126     22     99   -4.3   -6.8

Francoeur is off the charts, but his is a smaller sample size than most and there is certainly some luck involved there. Geoff Jenkins, always considered a fine left fielder, moved to right field for 2005
when the Brewers acquired Carlos Lee, and he did a fine job throwing in the more demanding position.

I was surprised to see Guerrero below average, and his ranking actually points to one of the limitations of this analysis. The problem, already alluded to above, is that our five situations only capture a part of the throwing duties of an outfielder. Overall, Vlad recorded eight assists in 2005, but only two were made in our five situations. So, in some sense, he’s not getting credit for those other six assists. If a player specializes in situations that are not among the five, then he will be undervalued. I don’t know if that’s the case for Guerrero; I already mentioned that in 2004 10 of his 13 assists go into the analysis. In case you’re wondering how
Vlad got those other six assists, here is a breakdown:

  • Batter thrown out trying to stretch a double into a triple: one assist
  • Runner doubled off 1B after catching a fly ball in right field: two assists
  • Runner from 1B forced at 2B on a would-be hit to right field (this is your basic 9-2 force out): three assists

Ichiro also suprised me by placing near the middle of the pack. All nine of his assists entered into this analysis, so that’s not the problem. (I’m assuming Ichiro’s arm really is well above average.) The problem is very likely just an overall small sample size issue. Data from multiple years will likely be necessary to get a reasonable idea of throwing ability.

Final Thoughts and Future Plans

I don’t think there is anything groundbreaking in what I’ve done here. If I remember correctly, Mitchel Lichtman, when he published his UZR metric for defensive range in past years, also included an arm rating that was likely similar to what I’ve done here, in concept, at least. Mitchel certainly took into account more effects than I have been able to here. However, Mitchel has not been publishing those results lately, so I thought I might tackle the task of rating outfield arms.

My method identifies five critical situations that require a throw from the outfield. These five situations are not comprehensive, so I’m capturing only a part of outfield throwing, but I think it’s a substantial part. I consider how often the outfielder throws somebody out in the five situations and, in the case of nobody thrown out, how often the key base runner advances an extra base. I then compare each outfielder to the league average and come up with Hold and Kill Rates for each outfielder and, assigning average run values to the various plays, I also see how many runs each outfielder has saved with his arm (for the five situations considered, of course). One piece of the puzzle still not included is park effects. Maybe in the next version.

If you’ve read Dan Fox’s excellent series on base running, you’ll see a parallel with this analysis. Dan looks at the outcomes of the situations (he considers situations 1-3) depending on who the base runner is, while I do it in terms of who the throwing outfielder is.

Now that things are set up, oh, there are many things one could look at:

  • First off, we can rate the center fielders and left fielders, too. Was Manny Ramirez really the best throwing left fielder in 2005?
  • We can group together a few years’ worth of data to try to reduce the fluctuations and really see who has a cannon and who has a popgun.
  • Comparison to the scouting reports mentioned in passing above. Do the fans and players agree with Yours Truly?
  • What’s more important: throwing runners out or keeping them from advancing? We can study the relative importance of Hold Rate and Kill Rate in saving runs.
  • Conventional wisdom has it that once a player has established himself his assists go down, because nobody will run on him. We can look at Hold and Kill Rates over time for individual players to see if conventional wisdom has this right.
  • Roberto Clemente’s arm is often considered the best ever. Curious
    as to how Clemente ranks using this system? Well, we can do it! Retrosheet data goes back to 1960 in the NL, and we can use it to evaluate Clemente. (Frankly, I would consider this more an evaluation of the method than an evaluation of Clemente.) In fact, one could think of doing a historical retrospective of famous outfield arms in the period 1960-1992, years that are covered by the Retrosheet data. Dave Parker, Andre Dawson, Jesse Barfield, Ellis Valentine, Dave Winfield,
    Dwight Evans, …

Oh, the mind reels at the possiblities. Keep an eye out here at The Hardball Times for more on outfield arms in the near future.

References & Resources

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