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January 17, 2008

Schrodinger's Bat

For the Sake of Completeness

by Dan Fox

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"I don't really like to run, and that's why I didn't go out for track in high school. I ain't no fool, I see those dudes running around a track for a living. I wouldn't want to run against them. I wouldn't want to embarrass myself."
--Willie Wilson

Since this column started back in March of 2006, I've spent a good deal of time on the topic of baserunning. Those efforts have resulted in the creation of five metrics under a common methodology that, when combined, can give us a fairly complete picture of the contributions that runners make on the bases. For readers new to BP--or those simply wishing to get an overview of the framework as a whole--you'll be happy to know that an essay titled "The Tortoise, the Hare, and Juan Pierre: Translating Baserunning into Runs" describing the system, along with the totals for all major and minor league players from 2005 through 2007, will be included in Baseball Prospectus 2008 (so make sure and get yours pre-ordered today).

Besides preparing the essay for BP2K8, the topic has been on my mind recently because of the discussion surrounding Tim Raines' first year of eligibility for the Hall of Fame. Raines doesn't have gaudy statistical Hall credentials such as 3,000 hits, 500 home runs, or 1,500 RBI, nor was he ever that undefinable but apparently now oh-so-important "most feared hitter in the game." But there's no doubt that just below Ricky Henderson, Raines was at the very top of the list in terms of leadoff hitters in the history of baseball. As a result, some of the focus on Raines rightly centered on his baserunning exploits. Dan Rosenheck of the New York Times took up the topic last week and, using the numbers from my baserunning metrics, made the point that in the running 80s the top runners--like Raines--had the talent to contribute over ten runs per year, while those today are three or four runs short of that. In fact, the league leaders from 1982 through 1989 (which includes talent plus variance due to luck) averaged +13.2 total runs on the bases (EqBRR), while from 2000 through 2007 the average has been +10.0 runs. That difference has to do with the greater number of stolen base opportunities that then generate high EqSBR values when accompanied by high success rates, as in the case of Raines. So how much was Raines worth on the bases?

In a post on my blog, I total it up for his career (minus 1999) and come up with a total of 102.5 career EqBRR for Raines. That actually ranks him third behind Willie Wilson at 109.6 (in the blog post I had Willie at 108.7 but was missing the data for 1977, when he contributed just under another run) and Rickey Henderson at 107.1. Of the three, Raines had by far the most value tied up in EqSBR (65 percent, with a value of +66.5 runs due to his 84.7 percent stolen base percentage, which, somewhat paradoxically, probably indicates that perhaps he didn't run enough) while Henderson was more well-rounded and did better on advancing on hits (+31.2 in EqHAR) and other advancement (+14.6 in EqOAR). Wilson was somewhere in the middle, and did well both in EqSBR at +56.9 and EqHAR at +26.5. As we'll see shortly, those three remain head and shoulders above the rest of the pack, with the next highest totals below 80 runs.

Raines received just 24.3 percent of the vote, a total the writers should feel embarrassed about, especially when you consider that Jim Rice received 72.2 percent on his way to an all but certain election next year. But despite the disappointment, the queries from Rosenheck prompted me to do something I had put on the back burner for many months: running the baserunning framework using all of the Retrosheet data available going back to 1956. Today, we'll examine those results, and in the future, yes, plans are in the works to publish these metrics on the site in the stats section in the future.

Crowning a Royal

Let's start where we left off above: the career leaders in total runs contributed on the bases. The following table shows the top 25 runners from 1956 through 2007 in terms of EqBRR:


Name          Years Opps EqGAR  Opps EqSBR  Opps EqAAR  Opps EqHAR  Opps EqOAR EqBRR  550
Willie Wilson 76-94  526   6.4   822  56.6   674  14.0   580  26.5  4681  6.0  109.6  8.3
R. Henderson  79-03  930  11.7  1773  42.9  1052   6.7  1005  31.2  7260 14.6  107.1  4.9
Tim Raines    79-02  658   7.6   969  66.5   802   7.7   733  16.8  6121  3.8  102.5  6.1
Davey Lopes   72-87  489   6.4   710  38.4   543   1.8   543  23.4  3929  6.2   76.1  6.7
Paul Molitor  78-98  745  12.0   641  32.0   978   8.0  1019  24.9  7051 -1.1   75.8  4.0
Vince Coleman 85-97  456   7.7  1011  39.1   409   4.4   415  10.7  3303  8.1   70.0  6.9
Luis Aparicio 56-73  759  11.3   693  13.0   693   5.2   794  22.1  6095 12.1   63.8  3.9
Willie Davis  60-79  438   6.4   556   7.1   566  11.3   609  32.7  4545  4.6   62.0  5.1
Ozzie Smith   78-96  724   8.9   757  19.7   704   6.0   830  19.4  6031  5.8   59.9  3.6
Barry Larkin  86-04  427   0.6   422  17.1   525   7.0   594  23.0  4690  8.7   56.5  4.7
Kenny Lofton  91-07  603  12.1   782  11.5   678  -0.8   755  28.6  4930  3.5   54.9  3.9
Mookie Wilson 80-91  372   6.4   449  10.7   359   8.7   376  21.5  2853  7.2   54.4  6.8
Robin Yount   74-93  618   5.3   380  -6.8   862  16.7   921  39.4  6527 -0.5   54.1  3.2
Joe Morgan    63-84  629   1.5   903  34.2   817   1.0   868  -0.6  6375 16.5   52.6  3.0
Johnny Damon  95-07  477   1.9   391  15.1   532   5.8   610  22.6  4316  7.0   52.3  4.5
Lenny Dykstra 85-96  424   6.8   374  19.7   412   5.9   443   9.4  3283  4.9   46.6  5.2
Ron LeFlore   74-82  414  10.2   627  18.5   370   5.2   348  11.8  2793  0.1   45.7  5.5
Otis Nixon    83-98  390   3.9   795  12.6   431   5.7   505  18.4  3555  4.7   45.3  4.4
M. Grissom    89-05  404   2.6   538  16.0   450   8.7   509  13.4  3896  2.8   43.5  4.1
Eric Davis    84-01  227  -1.3   415  24.5   326   2.2   348  11.6  2618  6.2   43.3  6.0
Juan Pierre   00-07  383   9.8   552  -1.0   339   6.0   461  21.4  3203  6.5   42.8  4.8
Craig Biggio  88-07  774   6.3   517   9.0   823   8.6   963   7.3  6822  9.1   40.2  2.2
Willie Mays   56-73  398   2.9   398   2.0   561   8.5   648  19.4  4865  7.0   39.9  3.2
Cesar Cedeno  70-86  367   5.5   759   9.5   454   2.0   499  10.9  3946 10.8   38.8  3.5
Gary Redus    82-94  279   3.1   425  16.3   278   6.1   244   9.8  2120  3.1   38.4  6.3

Davey Lopes (+76.1) and Paul Molitor (+75.8) fall well behind the ruling triumvirate, and are joined by Vince Coleman (+70.0) as the only other three players to reach 70 or more runs. As you look at those players--and the rest of the top 25--you'll notice that there are a variety of routes these players took to crack this threshold. Like Raines, Lopes was a terrific percentage basestealer, but didn't fare as well on advancing on groundouts or fly balls. Robin Yount reached 13th (+54.1) on the strength of EqAAR (+16.7) and EqHAR (+39.4), and actually amassed negative values in EqSBR and EqOAR, where pure speed plays a larger role. Joe Morgan excelled in EqSBR and EqOAR but was decidedly average in the other three categories, while Ron LeFlore seemed to be very well-rounded. You'll also notice that three active players--Kenny Lofton, Johnny Damon, and Juan Pierre--make the list, but almost half the leaders consist of players whose peak seasons occurred in the 1980s.

To the right of the EqBRR column you'll notice a column titled 550, which is a prorated total per 550 opportunities. This is used as a quick and dirty method to find out who took the most advantage of their opportunities; we'll take a more sophisticated route below. Willie Wilson (+8.3) comes out well above the rest, with Vince Coleman (+6.9) coming in second, surprisingly followed by--surprising to me anyway--Mookie Wilson (+6.8), Davey Lopes (+6.7), and Gary Redus (+6.3). Players not shown in the table above who did well in the rate statistic and who played 10 or more seasons include Tom Goodwin (+5.6) and Gary Pettis (+5.5). So does this mean that Willie Wilson was the best on the bases in the past 50 years? No metrics are perfect, but it at least provides very strong support for those who think so.

Some may be wondering where this puts Lou Brock, since he did not crack the top 25. Let's take a look at his seasonal totals:


Year Opps EqGAR  Opps EqSBR  Opps EqAAR  Opps EqHAR  Opps EqOAR  Opps EqBRR
1961    0   0.0     0   0.0     0   0.0     0   0.0     7   0.1     7   0.1
1962   40   1.4    25  -0.4    27   0.1    24   2.7   226   0.1   342   4.0
1963   42  -0.9    40  -1.3    28  -0.1    43  -0.2   299  -0.2   452  -2.8
1964   43  -0.3    64   0.1    29   0.0    53   0.7   309  -0.5   498  -0.1
1965   55   2.7    99  -2.8    34   0.7    35  -0.9   304  -1.5   527  -1.8
1966   39   0.4    96   4.2    47   1.0    46   2.5   325  -0.4   553   7.7
1967   47  -0.3    78  -0.7    32   0.0    63   0.3   371   1.5   591   0.7
1968   62  -0.3    76   4.3    36  -0.3    58  -1.4   420  -0.3   652   1.9
1969   66   1.0    69   3.8    38   0.3    50  -0.1   395  -1.5   618   3.6
1970   51   0.5    66   1.2    42   0.8    64   3.5   399   0.3   622   6.3
1971   66  -0.4    84   3.0    67  -2.2    80  -0.5   504   0.3   801   0.3
1972   52  -0.5    88   1.6    51   0.9    51  -0.8   383   0.2   625   1.4
1973   62   2.5    98   1.9    45   1.3    40   2.1   413   1.7   658   9.5
1974   54   0.6   153   5.4    56  -4.1    61  -0.3   438   0.6   762   2.2
1975   47   0.7    75   2.5    48  -0.3    40   0.4   327  -0.1   537   3.3
1976   28  -0.2    78  -1.1    24  -0.4    43  -0.5   276  -0.2   449  -2.4
1977   30  -0.9    59  -3.4    26   0.4    51   1.2   245   0.0   411  -2.6
1978   25   0.4    23   0.9    22   0.2    22   1.0   175   0.1   267   2.6
1979   21  -0.5    35  -1.8    31   0.0    41   0.7   246   0.1   374  -1.5
      830   5.8  1306  17.4   683  -1.5   865  10.3  6062   0.4  9746  32.4

His career total of +32.4 runs puts him just outside of the top 25, sandwiching him between Lonnie Smith (+33.0) and Delino DeShields (+32.2) in 37th place. He's hurt by three of his four final seasons and some very average to below-average running from 1963 through 1965. Despite leading the league in 1966 and 1973, he would periodically rate very poorly in EqAAR or EqHAR, thereby holding his totals down. His runs per 550 opportunities sits at +1.8 ranking him 94th, just ahead of Hank Aaron (+1.8 and +25.2 EqBRR).

On the flip side of the coin, the following table shows the 25 runners who find themselves on the bottom of pile:


Name         Years  Opps EqGAR  Opps EqSBR  Opps EqAAR  Opps EqHAR   Opps EqOAR EqBRR   550
Frank Thomas 90-07   355  -8.2    50  -6.1   631  -0.4   722 -18.0   4956  -4.6  -37.1 -3.0
Jorge Posada 96-07   243  -4.5    37  -9.2   327  -3.3   371 -16.6   2661  -3.6  -37.1 -5.6
Gary Carter  74-92   379  -7.0    90 -16.8   510  -4.8   535  -7.6   4095  -1.0  -37.4 -3.7
Dave Parker  73-91   380   3.5   277 -30.6   606  -6.8   671  -8.1   4709   4.4  -37.6 -3.1
Jim Thome    91-07   319  -5.7    39  -7.9   474  -8.8   639 -16.9   4057   1.7  -37.6 -3.7
Tim Wallach  80-96   428  -0.1   122 -29.5   500   1.5   569  -8.5   4138  -1.4  -38.1 -3.6
C. Delgado   93-07   281  -3.0    20  -6.2   453  -5.8   519 -24.0   3693   0.2  -38.7 -4.3
Boog Powell  61-77   319  -4.8    44 -10.0   462   3.0   517 -22.7   3718  -5.4  -39.9 -4.3
Fred McGriff 86-04   383  -6.7   104  -9.7   555  -1.2   623 -19.1   4368  -3.1  -39.9 -3.6
Alvin Davis  84-92   208  -2.7    24  -8.4   355  -3.2   354 -21.2   2620  -4.8  -40.3 -6.2
H.Baines     80-01   361  -4.7    68 -12.2   673  -7.3   694 -12.8   5023  -3.8  -40.9 -3.3
Rusty Staub  63-85   519  -5.9    92  -8.3   686  -3.4   773 -26.1   5668   2.7  -41.1 -2.9
Rick Cerone  75-92   245  -2.5    33 -11.7   258  -2.7   336 -21.6   2123  -3.0  -41.4 -7.6
G. Luzinski  70-84   277  -4.0    69  -8.9   461  -4.9   533 -26.2   3537   1.5  -42.5 -4.8
W. McCovey   59-80   358  -8.8    59  -7.7   506  -0.6   633 -25.6   4365  -0.1  -42.8 -4.0
Bob Boone    72-90   429   0.3   109 -25.0   406   3.2   486 -18.1   3620  -3.8  -43.4 -4.7
Eddie Murray 77-97   539  -8.5   171 -10.7   845  -8.1   821 -19.4   6245   2.8  -43.9 -2.8
Tony Pena    80-97   374   0.8   150 -20.0   419  -3.6   455 -17.9   3415  -3.2  -43.9 -5.0
E. Martinez  87-04   394  -7.3    71  -9.5   553  -1.0   634 -23.7   4488  -2.6  -44.0 -3.9
Ln. Parrish  77-95   311  -5.0    69 -15.2   453  -9.8   471 -10.2   3333  -4.8  -44.9 -5.3
Mike Piazza  92-07   224  -4.3    31  -8.4   444  -6.8   476 -26.3   3394  -1.6  -47.4 -5.7
H. Killebrew 56-75   345  -9.1    42  -7.6   534  -0.3   612 -24.7   4291  -5.8  -47.6 -4.5
Wade Boggs   82-98   708  -7.7    65 -17.6   901  -2.2  1057 -12.2   7027  -8.5  -48.1 -2.7
Todd Zeile   89-04   331  -6.2   111 -20.7   478  -2.4   596 -18.6   3712  -0.4  -48.4 -5.1
Ted Simmons  68-88   449  -8.0    62 -18.0   603  -1.6   677 -25.1   4757   2.0  -50.6 -4.3

In an earlier blog post, I had noted that Todd Zeile (-48.4) and Wade Boggs (-48.1) were at the bottom; in calculating the additional Retrosheet years, Ted Simmons just barely gets under them at -50.6 runs. It should probably come as no surprise that nine of the twenty-five were primarily catchers, with the rest first basemen, corner outfielders, and a few third basemen and DHs. It's also apparent that none of them--save perhaps Dave Parker--was ever considered above average in terms of running speed.

Parker's case is interesting because he did finish his career above average in EqGAR and EqOAR, yet was almost 40 runs below average overall. His seasonal totals reveal that his poor stolen bases percentages dragged him down, -30.6 over the course of his career (154 stolen bases and 113 caught stealing); a representative season might be his 17-for-36 performance in 1977. On those very rare occasions (exactly twice in his career) when he took more caution--such as 1979, when he was 20 of 24 and contributed +1.1 runs in EqSBR--he ended up at +7.5 overall. Looking at Parker's career:


Year  Opps EqGAR  Opps EqSBR  Opps EqAAR  Opps EqHAR  Opps EqOAR  Opps EqBRR
1973     9   0.0     2   0.0    10  -0.7     8   0.6    68  -0.2    97  -0.2
1974    14  -0.1     6  -1.4    12   0.3    17   0.6   115   1.2   164   0.6
1975    35   1.3    14  -2.1    42  -2.9    45  -0.8   307  -0.4   443  -4.9
1976    22  -0.2    28  -0.9    39   1.4    39   2.0   260  -1.3   388   1.0
1977    32  -0.4    37  -6.4    44  -0.9    58   0.7   360  -0.8   531  -7.8
1978    15   0.1    28  -0.8    45  -1.6    40   0.4   335   1.5   463  -0.4
1979    30   2.2    24   1.1    46   1.4    46   1.7   416   1.2   562   7.5
1980    22   0.0    17  -1.4    33  -1.9    39   0.6   253   0.1   364  -2.6
1981    12   0.3     8   0.2    12   0.1    15   1.8    97   0.6   144   3.0
1982     9  -0.9    12  -1.2    21   0.6    24  -0.6   130   0.3   196  -1.8
1983    25   0.9    23  -2.9    31   0.3    39  -0.7   256  -0.6   374  -3.0
1984    15   0.5    21  -2.6    37   0.2    41  -1.5   291   0.8   405  -2.5
1985    24   0.3    17  -4.1    44  -1.0    46  -1.3   296  -0.9   427  -7.0
1986    23   0.3     8  -2.9    27  -0.6    38  -1.4   295   1.1   391  -3.6
1987    24   0.3    11  -0.9    39  -0.2    37  -4.1   265  -0.1   376  -5.0
1988    14  -0.6     1  -0.6    23  -0.8    26  -0.9   189   0.5   253  -2.4
1989    18  -0.5     0   0.0    32   0.2    30  -2.0   252   0.6   332  -1.8
1990    24   0.6    13  -2.9    42   0.1    46  -2.4   302   0.0   427  -4.6
1991    13  -0.4     7  -0.9    27  -0.6    37  -0.9   222   0.7   306  -2.1
       380   3.5   277 -30.6   606  -6.8   671  -8.1  4709   4.4  6643 -37.6

Parker's extremes, however, are not the largest historically. There were twelve other players with larger differences in separate seasons, including Kenny Lofton's +13.3 in 1993 coupled with a -8.5 in 1997, and Bobby Bonds' -7.2 in 1979 and a +13.6 in 1972. But the largest difference in two seasons belongs to Maury Wills, who scored an amazing +20.6 in his record-breaking 1962 thanks to a +13.8 in EqSBR, and a -7.5 in 1966 when he was caught stealing 24 times in 62 attempts. Both totals were the extremes in the league, and Wills' 1962 performance was the top single-season value of all time.

From a rate perspective, you probably won't be surprised to learn that pitchers dominate the bottom of the list. John Smiley (-17.4) and Jose DeLeon (-17.2) take the bottom two spots; further, fully 65 of the bottom 100 rates for players playing 10 or more seasons belong to pitchers. We already knew pitchers don't contribute much on the bases, so I've filtered them out of the following table that shows the bottom ten runners ordered by rate:


Name          Years  Opps EqGAR  Opps EqSBR  Opps EqAAR  Opps EqHAR  Opps EqOAR EqBRR   550
John Bateman  63-72   152  -2.0    19  -4.6   140  -3.1   163 -13.1  1299  -0.7 -23.5  -7.3
Pat Borders   88-05   165  -0.2    29  -7.4   187  -7.1   199 -10.1  1486  -2.6 -27.4  -7.3
Rick Cerone   75-92   245  -2.5    33 -11.7   258  -2.7   336 -21.6  2123  -3.0 -41.4  -7.6
Ron Hodges    73-84   100  -0.8    26  -6.2   117  -1.1   103  -7.0   826  -1.3 -16.5  -7.7
Todd Greene   96-06    52   0.6     4  -0.7    52  -3.5    59  -4.5   455  -0.8  -8.8  -7.8
Buck Martinez 69-86   123  -2.9    19  -6.1   142  -0.5   180 -13.3  1218  -1.3 -24.1  -7.9
M.LaValliere  84-95   188  -1.4    23  -6.5   140  -3.3   170 -15.2  1437  -2.4 -28.8  -8.1
Jamie Quirk   75-92   115  -1.4    22  -8.5   116  -1.8   133  -7.3   994  -1.3 -20.4  -8.1
Randy Knorr   91-01    28  -0.3     1  -0.7    37  -1.1    44  -4.5   277  -0.3  -6.9  -9.9
Eddie Perez   95-05    68  -1.5     4  -1.7    50  -0.5    77  -8.8   536  -0.8 -13.4 -10.0

Here we see illustrated in stark relief the idea behind the old saying "runs well for a catcher," as all ten of the worst baserunners measured by the rate stat wore the tools of ignorance. The first non-catcher on the list was reserve outfielder and pinch-hitter Jerry Lynch at 17th (-6.7), who played for the Reds and Pirates in the fifties and sixties and who played a critical role in the 1961 NL pennant race.

Before moving on to some analysis, let's take a look at one more set of leader boards by showing the career leaders and trailers in each of the five metrics:


Advancing on Ground Outs           Stolen Bases and Pickoffs
Name                 Yrs  EqGAR    Name               Yrs EqSBR
Brett Butler          17   13.7    Tim Raines Sr       22  66.5
Steve Sax             14   12.9    Willie Wilson       19  56.6
Kenny Lofton          16   12.1    Rickey Henderson    24  42.9
Paul Molitor          21   12.0    Vince Coleman       13  39.1
Rickey Henderson      24   11.7    Davey Lopes         16  38.4
-------------------------------    ----------------------------
Carl Yastrzemski      23   -8.6    Bob Bailey          17 -31.2
Willie McCovey        22   -8.8    Brett Butler        17 -33.0
Pete Rose             24   -9.0    Pete Rose           24 -33.3
Harmon Killebrew      20   -9.1    Buddy Bell          18 -34.0
Joe Torre             17  -12.5    Alfredo Griffin     18 -34.4

Advancing on Air Outs              Advancing on Hits
Name                 Yrs  EqAAR    Name               Yrs EqHAR
Robin Yount           20   16.7    Robin Yount         20  39.4
Willie Wilson         19   14.0    Willie Davis        18  32.7
Pete Rose             24   11.9    Rickey Henderson    24  31.2
George Brett          21   11.3    Glenn Beckert       11  29.4
Willie Davis          18   11.3    Kenny Lofton        16  28.6
-------------------------------    ----------------------------
Dave Kingman          16   -8.5    Ted Simmons         21 -25.1
Glenn Hubbard         12   -8.6    Willie McCovey      22 -25.6
Jim Thome             16   -8.8    Rusty Staub         23 -26.1
Lance Parrish         19   -9.8    Greg Luzinski       15 -26.2
Tony Perez            23  -15.2    Mike Piazza         15 -26.3

Advancing on Balks, PB, and WP
Name                 Yrs  EqOAR
Joe Morgan            22   16.5
Rickey Henderson      24   14.6
Luis Aparicio         18   12.1
Cesar Cedeno          17   10.8
Bert Campaneris       19   10.8
-------------------------------
Clete Boyer           15   -5.8
Harmon Killebrew      20   -5.8
Chris Chambliss       16   -6.3
Sammy Sosa            17   -6.6
Wade Boggs            17   -8.5

Tony Perez far outdistances the competition in giving up runs on fly outs at -15.2, but when we look closer we find that while he did record negative values in 15 of his 23 seasons, it was 1980 that really did him in, when he was thrown out at the plate five times in 33 opportunities (costing him -5.5 runs). Mercifully, the 1981 season was shortened, as Perez was on a pace to match 1980 by being nailed three times in 21 chances. We also see that Big Red Machine teammate Pete Rose did very well in advancing on fly outs, while seemingly unable to do so on ground outs, and being simply awful in attempting to steal bases. Also, as noted before, we see here why Robin Yount did so well in the career rankings, as he took the top spot in both EqAAR and EqHAR.

Two surprising players are Glenn Beckert (with his excellent showing in EqHAR) and George Brett (with his ability to advance on fly outs). Beckert managed to record positive values on advancing on hits in ten of his eleven seasons, and +3.5 runs or more five times, recording the second highest single season total at +5.7 in 1970. Not only was he able to take the extra base, he enhanced his numbers by not getting thrown out: he was caught trying to advance just five times in 491 career chances. Brett's case was much the same: he was thrown out advancing on fly balls just eight times in 807 career chances (and not at all from 1981-1987, but three times in 1989) while advancing 216 times.

Pure Baserunning

Thus far we've looked at career totals in the various metrics and created a simple rate statistic that takes all five metrics into account, scaled to roughly approximate the number of opportunities a runner would get in a single season. But we can do better. The "per 550" rate statistic has two major weaknesses: it treats all opportunities equally, and it's not really a measure of "pure" baserunning since it includes EqSBR, which is almost entirely discretionary.

The first of these weaknesses can be thought of as two distinct issues. First, the simple rate statistic makes the assumption that an opportunity to advance in one metric is the same as that in another. We know, however, that that isn't the case. In the extreme example an opportunity--as counted by EqOAR--has much less value than one credited for EqHAR, as evidenced both by the far greater number of opportunities counted for EqOAR and the much smaller range in terms of runs it represents. As a result, it's not really fair to weight them equally when players accumulate disproportionate numbers of opportunities in one or more metrics. Second, Per 550 assumes that all opportunities within a metric are created equal. Those who have read my previous columns on this topic will know that context plays a large role in assigning expected and actual run values to the underlying events in the various metrics, so in a sense the framework is built around the idea that opportunities vary widely in their quality. For example, a runner who finds himself on second base with one out disproportionately will have his ability to rack up large EqGAR numbers reduced, since taking third in that situation nets his team relatively fewer runs than advancing with nobody out. While runners are credited fairly within the metric itself, since each opportunity is judged in context, taking a simple total divided by opportunities approach won't always be fair.

As far as the second weakness goes, it turns out that when many folks talk about baserunning, they're not really thinking about discretionary stolen base attempts, but instead that combination of speed, risk taking, and judgment that goes into evaluating situations, and that when aggregated leads us to assert that a particular player is a good baserunner. Since EqSBR is primarily comprised of stolen base attempts (with a few pickoffs thrown in) our new rate statistic, which we'll christen Equivalent Baserunning Rate (EqBRRate), will omit this aspect.

So to eliminate both of these weaknesses, we'll define EqBRRate as the ratio of actual or total runs to expected runs contributed across the four remaining metrics. Since both values for individual opportunities consider the context and are weighted appropriately (an EqOAR opportunity has both a lower expected and usually actual run value associated with it than an opportunity of EqHAR) and since we're eliminating EqSBR, both weaknesses discussed above addressed. To illustrate how this works, let's consider Chone Figgins' 2007 season:


Metric    Opps  TotRuns ExpRuns
EqOAR      314      0.1     1.2
EqGAR       31      3.2     2.6
EqAAR       44      5.7     4.7
EqHAR       53     10.1     5.6
           442     19.0    14.2

Taking the context of the opportunities into account, we would have expected Figgins to net +14.2 runs across the four metrics, but he actually contributed +19.0 runs. When we divide the total by the expected we get a ratio of 1.34, indicating that he contributed, or manufactured if you will, 34 percent more runs than expected.

Of course, when creating a rate statistic, one needs to form a cutoff, since otherwise players with small samples will dominate the leaders and trailers. Because the magnitude of the opportunities for EqOAR is much greater than the other metrics, I've divided EqOAR opportunities by ten and then summed all the opportunities to create a Scaled Opportunities value that can be used in single-season and career comparisons. So for Figgins, we calculate this value to be 159. For the career leaders we'll use a fairly arbitrary cutoff of 550 opportunities, and for single-season leaders we'll use 75.

Armed with this metric, we can now reveal the career leaders and trailers in EqBRRate, our measure of pure baserunning ability stretching from 1956 through 2007:


Name               Years     Span    EqBRR  ScaledOpps  EqBRRate
Chone Figgins          6  2002-2007   31.0        756     1.35
Tom Goodwin           12  1991-2004   34.1       1017     1.33
Juan Pierre            8  2000-2007   42.8       1499     1.31
Grady Sizemore         4  2004-2007   18.4        633     1.30
Cristian Guzman        7  2000-2007   11.8        876     1.29
Mookie Wilson         12  1980-1991   54.4       1386     1.28
Willie Davis          18  1960-1979   62.0       2058     1.27
Ray Durham            12  1995-2007   35.6       1819     1.26
Tony Scott            11  1973-1984    6.9        758     1.26
Jose Reyes             5  2003-2007   25.6        685     1.26
Ken Landreaux         11  1977-1987   18.7        977     1.25
Gerald Young           8  1987-1994   11.9        559     1.24
Glenn Beckert         11  1965-1975   26.4       1517     1.24
Lonnie Smith          17  1978-1994   33.0       1586     1.23
Dave Hollins          11  1990-2002   12.3        737     1.23
Scott Podsednik        7  2001-2007   21.3        684     1.23
Oddibe McDowell        7  1985-1994   23.2        773     1.23
David DeJesus          5  2003-2007    3.4        648     1.22
Tony Graffanino       11  1996-2007   10.4        739     1.22
Gary Pettis           11  1982-1992   38.2       1140     1.22
----------------------------------------------------------------
Clay Dalrymple        12  1960-1971  -26.7        654     0.71
Javier Lopez          14  1992-2006  -36.1       1127     0.71
Pat Borders           16  1988-2005  -27.4        687     0.71
Alvin Davis            9  1984-1992  -40.3       1176     0.69
Dave Valle            13  1984-1996  -20.5        681     0.69
Steve Balboni         11  1981-1993  -16.1        587     0.68
Ed Bailey             10  1956-1965  -32.9        834     0.67
Mike Piazza           15  1992-2007  -47.4       1471     0.67
Buck Martinez         17  1969-1986  -24.1        560     0.67
Jody Davis            10  1981-1990  -26.9        705     0.66
Cecil Fielder         13  1985-1998  -34.1       1010     0.66
Rich Gedman           13  1980-1992  -25.2        702     0.65
Fred Kendall          12  1969-1980  -20.6        572     0.65
John Bateman          10  1963-1972  -23.5        580     0.65
Darrin Fletcher       13  1989-2002  -24.4        722     0.65
Smoky Burgess         11  1956-1966  -22.9        565     0.59
Gus Triandos          10  1956-1965  -22.6        662     0.58
Willie Aikens          8  1977-1985  -26.1        584     0.58
Mike LaValliere       12  1984-1995  -28.8        634     0.57
Bengie Molina          8  2000-2007  -26.6        678     0.57

Chone Figgins takes the title of the best pure baserunner of the last 50 years, while Bengie Molina... well, let's just say that coaches don't have to concern themselves with waving him around very often.

What's interesting about the top part of this table is that it doesn't contain the career leaders in stolen bases--or for that matter EqBRR--but instead is populated by primarily fast runners with presumably good judgment. I've included the EqBRR career totals as well, which make it obvious that Tony Scott and David DeJesus aren't much for stealing bases, but certainly could or can run the bases. This table also reveals that elite runners like Figgins are worth approximately 25-30 percent more runs than an average runner, while plodders might cost their team 30-40 percent. You'll also notice that nine of the top twenty runners were active in 2007. While this may simply be random, it just may reflect a widening of the gap between the best and worst runners of recent years that creates more space for better runners to excel. It should also be noted that the bottom of the list doesn't consist exclusively of catchers this time and instead throws in a few players like Willie "Nothing like Mays" Aikens, Cecil Fielder, Steve Balboni, and Alvin Davis.

To finish up today we'll explore two questions that come up frequently in email from readers: aging and correlation. Once we have a rate statistic we can easily analyze how that rate varies with age. To do this we can simply weight EqBRRate by Scaled Opportunities for all seasons by age (leaving out pitchers) to come up with the following graph:

The graph shows that starting at an above average rate, players improve in their running from age 20, and peak at 23. We can speculate that this increase in performance in the first three seasons--despite already likely having achieved maximum running speed--could be the result of a learning curve that players undergo as they adjust to the league. After declining fairly slowly through age 27, the descent picks up speed through the late 20s and through their mid 30s before slowing around age 34, no doubt due to the selection bias inherent in a graph like this, as players are selected out of the league for many reasons, perhaps including their baserunning.

We can also break the curves down by position with results that shouldn't be too shocking:

Center fielders (using data from 1996-2006) are clearly the best baserunners overall (as evidenced by our top 20, more than half of whom played center), remaining 10-20 percent above average from ages 22 through 35. Second baseman and shortstops also remain above average throughout, as do all outfielders from 1956 through 1995. Next, we find left fielders (again, since 1996) just slightly ahead of right fielders for most of the span, with third basemen trailing somewhat. First basemen and designated hitters, often interchangeable, track fairly well with each other. And, of course, on the bottom of the list we find our catchers, who start out at about 90 percent of average, and descend from there.

On the question of correlation, what readers generally want to know is how persistent baserunning is as a skill from year-to-year. In order to measure this, we can split the careers of non-pitchers into even and odd seasons, and using our 75 Scaled Opportunities threshold we can pair those career halves for players with at least three seasons in each half. This resulted in data for 696 players. Performing a correlation on those pairs results in the plot with the linear regression line we see below.

The correlation coefficient here is a fairly healthy 0.64, resulting in an R-square (coefficient of determination) of 0.42. This suggests that 42 percent of a player's EqBRRate can be attributed to skill and 58 percent to other factors, including causes such as luck and coaching. I did check whether aging--for example, that fact that when splitting a career consisting of consecutive seasons into even and odd halves, one of the halves will necessarily include, on average, seasons when the player was younger--would have relevance here by first normalizing the EqBRRate using the aging curve above; overall, it had no effect on the strength of the correlation.

To put this result in perspective, we can note that for the same time period the career half correlation of determination for batting average was 0.56 (using a 200 AB seasonal cutoff), indicating that the skill component involved in baserunning (using these metrics anyway) is somewhat smaller than that contained in batting average.

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