MEASURING RUNS CREATED: THE VALUE ADDED APPROACH 


The following appeared in The 1987 Bill James Baseball Abstract.
— Gary R. Skoog
One of the major interests of baseball research has long been the attempt to measure how many of a team's runs are created by each player. This article discusses how runs created can be measured from event data (that is, looking at each event in the context of play) rather than from cumulative data, as has been necessary in the past when only category totals were available. For all regulars from the 1986 season, we compute both proposed and older measures of runs created. This paper expands on results reported by the author at the 1986 SABR convention and presented to an American Statistical Association meeting.
With only a season's totals available for each player ("aggregate data") the subject of the proper attribution of runs created continues to receive refinement and controversy. Two methods, Bill James's runs created and Pete Palmer's linear weights, have defined the present state of the art. Both methods attempt to construct an index that measures runs created by each player using aggregate data. Both men have attempted to design runs created methods that are not situation dependent, as are runs scored and RBI counts, but the act of scoring runs itself is situation dependent, and so its removal per force creates a measure that varies from the ideal: We want a statistic that doesn't penalize a player for batting in fewer run producing situations than another, but at the same time rewards players who perform well in those situations. Our methodology cuts this Gordian knot by directly measuring the object of interest, the improvement or deterioration in the run expectation of the player's team at the moment of his contribution.
Given the precise event data, our first statistic, RC1 (read, runs created, version 1; marginal runs created) is appropriate for many comparative purposes in the same way that marginal cost is the appropriate cost measure in economics. Like Pete Palmer's linear weights, it is essentially meancorrected, so that zero denotes average performance, and players are measured relative to the average. A second variant, RC2 (read, runs created, version 2) is presented, which is more descriptive in that it is generally nonnegative and adds to the team's actual runs scored when aggregated over a season. As such, it is comparable to the James runs created, which will be referred to below as RCJ. Indeed, 94% of the variation in RC2 is explained by RCJ in the American League 1986 data, and 91% in the National League.
Although we don't emphasize it here, our approach unifies the sabermetric study at the micro, or event, level. It opens up a potentially more powerful and precise approach to the assessment of runs allowed by pitchers, runs created or lost on the bases, runs cost by errors in the field. Or even runs lost by bad coaching decisions or umpires mistakes. Of course, for starting pitchers ERA does approximately the same thing, but the biases of this statistic for relief pitchers are purged with the value added approach.
When a batter steps up to the plate, there may be 0, 1, or 2 outs, and any one of 8 runner on base situations. Thus there are 24 initial game states, abstracting from other characteristics such as the score, which teams are playing, who the players on base are, etc. When he finishes his turn at bat, he will have put his team in any one of 25 possible states (the extra state is "3 outs" and for our purposes here, no loss of generality is incurred in ignoring the configuration of the men left on base at the end of an inning). Let us denote the beginning and ending states by "s" and "t," respectively. For each state, from his team's and the league's data, we may accurately measure the distribution of runs scored in an inning, conditional on a team being in that state. Denote the means of these random variables (technically, stopping times on a specially constructed sigma algebra) by E(s) and E(t) and let R denote the runs scored during this transition Then this at bat produced R + E(t)  E(s)=actual runs scored on at bat plus expected team's runs in inning after player bats minus expected total team's runs in inning before player batted. There are refinements, some of which will be discussed below, but this is the basic idea.
In words, the RC1 in a plate appearance is positive to the extent that the batter advanced his team's cause more than an average amount, and similarly for negative contributions. It is measured in units of runs. For the general manager confronted with a  30 run player, this statistic tells him how many runs his team would improve if he could bring this position up to the league average. The extra runs then could be converted into extra wins by Pythagorean theory.
The transitions as a team bats through an inning must, as is shown below, sum to the actual number of runs scored, minus the expectation of the state which leads off each inning of .454 (see Table 1). This is due to the telescoping nature of the sum, and the fact that there is an absorbing state, "3 outs," to which almost all innings converge An example below will make this clear. The exceptions are games won in the bottom of the last inning, and games suspended in the middle of an inning and not resumed.
Since, if a hitter does not increase the out count, his contribution must be positive (we haven't yet discussed errors) there can be at most 3 negative contributions in an inning.
We might prefer that the decrements of .454 be redistributed among the batters in the inning, so that the runs created becomes a total measure, calibrated so as to give the actual number of runs scored. We call this kind of total measure RC2, and briefly consider ways of doing this.
To fix ideas, consider an inning in which the leadoff hitter homers, and the next 3 batters make outs. Using Table 1, RC1 gives the measures l 000, .205, .154, and .095, summing to 1 .454=.546. Suggestions to redistribute the .454 and get exactly one run produced include 3 philosophies:
An advantage of l and 3 is that they yield the same differential contributions as RC1. The leadoff home run in the example above left the team on average 1.205 ahead of where they would have been with an out, which uses up .205 run when it is the first out. This argument has much appeal. A drawback is that it gives the leadoff man more than one run created for his home run, which after all does return the team to the beginning state but with an extra runall of which should yield precisely one run created. Another advantage is that runs created equals runs scored in every (half) inning, so a fortiori for every game for every teamseason, and for the leaguethe various levels of aggregation. Note that the entries of Table 1 are estimated from an entire season, and so are average in this sense. (We have not preserved the distinction between population averages, the E(s), and their sampled counterpartsa reader sophisticated enough to look for the difference will not be confused.)
The drawback above suggests 2, which redistributes the decrements among those players most likely to have negative runs created. It maintains one run for the solo home run, and implicitly suggests a nonnegativity of runs created per plate appearance desideratum: Since runs are negative, why not extend this same property to runs created? This method does more to move the negatives toward zero than 1, although it can't totally succeed, without causing further difficulties. To see this, note that to bring all batters to nonnegative numbers, we'd have to overcompensate by adding .205 times 3=.615, and we'd have to take .615  .454=.161 off the home runand this for a scheme which awarded .205.095=.110 of a run for making the final out! Another objection is that outs are already taken into consideration by RC1, so an adjustment based on them would result in "double count
ing." This method shares the advantage of having the runs balance out over every halfinning.
Both submethods 1 and 2 divide .454 explicitly; instead, we could use 3 above and take the total plate appearances divided into the total runs for a league season and add this to each at bat; this would give correct runs created on average, although inning totals wouldn't necessarily be correct. The argument is, there is unnecessary noise introduced by requiring them to add, along with a mixing of the level of aggregation. This is the method used below in the RC2 calculation. The author is not adamant in its use, however, and encourages discussion on this point in the sabermetric community before the next edition of this book.
From Palmer's simulations reported in The Hidden Game, we report his table giving the E(s) entries for the 24 states:
Table 1
Expected Future Runs In An Inning,
Conditional On The State
Outs 

Runners 
0 
1 
2 

None 
A 
.454 
B 
.249 
C 
.095 
1st 
D 
.783 
E 
.478 
F 
.209 
2nd 
G 
1.068 
H 
.699 
I 
.348 
3rd 
J 
1.277 
K 
.897 
L 
.382 
1st,2nd 
M 
1.380 
N 
.888 
O 
.457 
1st, 3rd 
P 
1.639 
Q 
1.088 
R 
.494 
2nd, 3rd 
S 
1.946 
T 
1.371 
U 
.661 
1st, 2nd, 3rd 
V 
2.254 
W 
1.546 
X 
.798 
We have added the Project Scoresheet notation for the states. The idea of using these states, incidentally, goes back at least to the fundamental 1963 paper in Operations Research, "An Investigation of Strategies in Baseball," by George Lindsey, and is implicit in the work of anyone having done serious study in any branch of science. The RC measures proposed here are similar in spirit to the Mills's "player win average," although the measures address quite different questions.
Rather than simulate, we will in the future estimate these expectations from the 2106 x 80  168,480 or so such situations which arise over a major league season. There will be some statistical subtley here, for we are doing inference on realizations of a Markov chain with no ergodic events and with obvious statistical dependences. Variances, rather than our estimates themselves meanswill be affected by the fact that the same inning, say, with a leadoff home run, will have the 0000 or "a" state occurring at least twice, followed by the same events for the rest of the inning entering into the sample. In theory, one could estimate a Markov half inning transition matrix and derive estimates for the entries in Table 1. This method has two drawbacks. First, the standard errors are very complicated functionals of the model parameters. Worse, model specification error would enter, and would be avoidable with the direct, nonparametric approach suggested above. The parameters of the transition matrix nevertheless are of independent interest, however, and will be estimated for various subsets of the data.
The measures of runs created reported below use Table 1. We will sometimes refer to a state not by its letter but by four numbers, as the 0000 above. The first is O. 1, or 2 and gives the outs; the next 3 are 0 or 1, depending on whether the base is unoccupied or not.
We do expect to see league differences in our estimated versions of Table 1, since pitchers bat in the National League. Consequently the relevant sample size will be smaller by roughly half. In fact, RCI for National League pitchers have been computed (but not reported below) and are uniformly negative, as expected.
A runner is on first, nobody out. The batter singles, the runner on first stopping at second. The third batter follows with an RBI single, leaving runners at first and second. The next batter grounds into a 643 double play, the runner advancing to third. A strikeout ends the inning.
The official statistics give the second batter a hit only. He didn't score the run or bat it in, yet he was as instrumental in manufacturing the run as the players who received the RBI or run scored. The value added approach (refer to Table 1 above) gives him 1.380  .783=.597 runs. The leadoff leadoff hitter gets .783  .454  .329 and the third hitter gets 1 run, since the runners ended up at first and second, the same state he found them in. The double play gave the fourth batsman 382  1.380= 998, and the strikeout stranding the runner on third was  .382 The team earned 1.926 runs and lost 1.380 runs, giving a total of .546 above the initial state or league average of .454.
If the total decrements of .454 are added by redistributing them among the batters in the inning, we get an RC2 measure of exactly 1.
For each transition, we know whether the batter's turn at bat terminated or not. In Project Scoresheet these are referred to as batting events and nonbatting events, respectively. If the leadoff batter walks and steals second, (the latter is a nonbatting event), then the second batter's initial states is 0010  0 outs, man on second, not the 0100  0 outs, man on firstthat prevailed when he came to the plate. The man who stole second earned 1.285  .783=.402 of a run (RC1) for his stolen base, and baserunning runs created may be kept as a separate category in this way. Similarly, errors create runs for the opposition, and may be accounted for by introducing a fictitious state of errorless play between the events involving the error. Another example will make this clear.
Say the leadoff man reaches on an error. Just as in batting average calculation, we may act from the batter's perspective as though he had been put out. The fictitious state here is 1000  I out no one on. Now the transition 0000 to 1000, worth .249  .454=.205 is awarded the batter, and the transition 1000 to 0100 worth .783  249=.534 gives the runs created by the error. If the next 3 batters strike out, the team run potential is again reduced to 0, and their RC1 decrement is .783. Thus, the team has an RC1 total of .205 + .783=.988; they were given .534 of a run by the opposition, bringing us back to the familiar .454. Since they scored no runs, to get an RC2 to equal zero, there were in effect 4 "outs" inflicting negative runs created, and the "gift" of the error might be redistributed along with the .454. Errors are not so treated in the results given below, although further refinements may incorporate them.
Observe that the 1000 to 0100 transition causes outs to decrease, and so is impossible according to baseball rules. Nevertheless, there is nothing stopping our evaluating this contrafactual state transition, and indeed there is a necessity to do this to properly evaluate the error.
Present Project Scoresheet data structures, and doubtless others as well, will make this decomposition difficult for some errors, notably errors allowing runners to advance on a play. Errors allowing the batter to reach are more adequately represented. Unfortunately, we need in both cases a set of heuristics to guess the result of errorless play. Here as in many areas, theory runs ahead of practice.
Besides measuring precisely and directly our objective, the value added approach has a reasonable chance at correcting for "situation dependence.'' Several factors point to this conclusion, although ultimately a minor refinement may still be in order.
A player who bats with many men on base will have high E(s) values for leaving lots of men on base to subtract from the high R and E(t) values he earns. In the example. the three singles were worth .329, .597, and 1 run and not equal amounts, reflecting the obvious fact that run production is situation dependent. The batter who hit with 2 men on base also had most to lose by not producing, as the next paragraph shows.
To see the way the value added approach corrects for situation dependence while properly acknowledging it. consider a player batting with the bases loaded and 2 out. A walk credits him with an entire run, whereas a leadoff walk in an inning is only worth .299. But had he struck out with the bases loaded and 2 out, he would have cost his team .798  0 (expected runs after 3 outs!)=.798 of a run, whereas a leadoff strikeout costs .454propitious situations will amass high totals of the traditional count data (runs and RBI) but these should have subtracted from them many runs destroyed from his failures.
At a higher level of sophistication, consider a hitter, say Wade Boggs (our 1986 AL RC leader), batting in the highest E(s) state, 0111, from which 2.254 runs are expected, and the lowest state, 2000, from which .095 runs are expected. We can take Boggs' season totals and make educated guesses as to the transition probabilities from these states to any other states. This would let us compute conditional runs created from each state, for both an individual player and the league average. Then, for there to be bias for Boggs, two things must be present. First, there must be variation in the conditional runs created across the states, which the paragraph above argues (but does not prove) will be minimal. Second, Boggs must find himself with a distribution of at bats among the 24 states that is significantly different from the league averages. This may happen for pinch hitters, and to a lesser extent for leadoff hitters, who start off the game in the same state. It is an empirical question how large these discrepancies are, if any. If found significant, a further correction to RC2 is in order.
The Tables below give (mean corrected) RC1, (total, positive) RC2 and the technical version of Bill James's runs created, listed under RCJ.
While we leave extensive comparison to another time, a few points may be made. First, our measure does not give "runs created or destroyed attempting to steal," which Bill's runs created method does allow for. A further refinement of RC1 and RC2 on this issue is obviously appropriate. This explains our understatements for Coleman. Henderson and Wilson. Second, the high percentage of explained variations of RC2 by RCJ94% in the American League, 91% in the National Leaguehave been noted. Third, the names of Boggs and Mattingly atop the AL and Schmidt and Raines atop the NL according to both methods is expected and reassuring. Finally, the diminution of agreement as one progresses toward lower RC2 and RCJ totals reminds us that RCJ was constructed on the basis of team aggregate data. Forcing it to apply to regular player totalsa sample of 600 or 700 plate appearances is one thing; applying it to smaller totals requires its extrapolation outside the region in which it was fit. Statistical models always show such "out of sample" deterioration.*
*Editor's note: The runs created formulatechnical version works with very small data samples, as is shown by the fact that it works well with games, and with very large ones such as leagues. I strongly suspect that the failure of agreement at low levels of plate appearances occurs because the failures of both methods are most apparent in small data sets where longterm randomizing factors have not acted to disguise them.
Name, Tm  RC1  RC2  RCJ  Name, Tm  RC1  RC2  RCJ  Name, Tm  RC1  RC2  RCJ  
Allanson, Cle    12  27  22  Gedman, Bos  +  2  63  59  Paciorek, Tex  +  2  28  22  
Armas, Bos  +  14  68  49  K. Gibson, Det  +  26  88  88  Pagliarulo, NY  +  7  75  74  
Baines, Chi  +  29  103  87  Grich, Cal    2  42  46  Parrish, Det  +  16  61  57  
Baker, Oak    3  29  24  Griffey, NY    1  25  31  Parrish, Tex  +  28  91  80  
Balboni, KC  +  6  73  67  Griffin, Oak    8  70  71  Pasqua, NY  +  22  62  62  
Bando, Cle    2  32  27  Grubb, Det  +  33  62  54  Petralli, Tex  +  1  18  14  
Bartiold, Tor  +  44  125  122  Gruber, Tor  +  9  28  8  Penis, Cal  +  1  76  71  
Barrett, Bos  +  16  102  87  Gulilen, Chi    23  46  43  Phelps, Sea  +  33  86  81  
Bathe, Oak    8  6  7  Gutierrez, Bal    14  4  6  Phillips, Oak  +  11  75  63  
Baylor, Bos  +  9  92  91  Hairston, Chi  +  2  32  31  Porter, Tex  +  11  32  30  
Beane, Minn    13  10  12  M. Hall, Cle  +  24  82  75  Presley, Sea  +  11  91  80  
G. Bell, Tor  +  30  113  113  Harrah, Tex  +  1  42  35  Pryor, KC    11  3  3  
Beniquez, Bal  +  7  54  51  Hatcher, Minn  +  2  43  36  Puckett, Minn  +  37  124  127  
Bergman, Det    5  14  15  Heath, Det    2  10  12  Quirk, KC    8  21  22  
Bernazard, Cle  +  15  92  96  R. Henderson, NY    4  89  112  Randolph, NY  +  10  83  77  
Berra, NY  +  3  17  12  Hendrick,Cal  +  9  47  42  Rayford, Bal    16  11  14  
Biancalana, KC    3  22  20  Herndon, Det    3  35  36  Reed, Minn    8  14  17  
Bochte, Oak  +  14  71  52  D. Hill, Oak    9  35  41  Reynolds, Sea    36  22  37  
Boggs, Bos  +  58  142  133  Howell, Cal  +  10  31  27  Rice, Bos  +  28  112  115  
B. Bonilla, Chi  0  32  32  Hrbek,Minn  +  36  112  93  Riles, Mil    11  60  59  
J. Bonilla, Bal    10  28  25  Hulett, Chi    30  36  49  Ripken, Bal  +  25  110  102  
Boone, Cal    20  41  39  Incavigila, Tex  +  8  81  82  Robidoux, Mil    5  21  19  
Boston, Chi    3  24  28  G. Iorg, Tex  +  3  45  35  Roenicke, NY  +  4  24  22  
P. Bradley, Sea  +  26  100  99  Re. Jackson, Cal  +  13  75  68  Romero, Bos    1  31  19  
Braggs, Mil    9  19  20  Jacoby,Cle  +  26  102  88  Salas, Minn    9  25  27  
Brantley, Sea    7  6  9  Javier, Oak  +  8  23  11  Salazar, KC    3  35  26  
Brett, KC  +  29  92  89  C. Johnson, Tor  +  19  66  52  Schofield, Cal  +  4  67  63  
Brookens, Det    2  36  32  R. Jones, Cal  +  9  65  60  Schroeder, Mil    7  22  22  
Brunansky, Minn    5  74  78  Joyner,Cal  +  26  107  96  Sheets, Bal  +  21  65  47  
Buckner, Bos  +  4  86  76  Kearney, Sea    3  24  20  Shelby, Bal    3  49  39  
Buschele, Tex    7  55  54  Kingery, KC    6  21  23  Sheridan, Det  +  3  34  27  
Burleson, Cal  +  9  46  40  Kingman, 0ak    11  62  57  Sierra, Tex    10  40  51  
Bush, Minn  +  12  61  53  Kittle, NY    3  37  34  Slaught, Tex  +  5  46  42  
Butler, Cle  0  82  84  Lacy, Bal    3  62  62  Smalley, Minn  +  11  74  70  
Calderon, Chi    8  9  11  Lansford, Oak    1  76  80  Lo. Smith, KC  +  2  70  77  
Cangelosi, Chl    7  56  55  Laudner, Minn  0  27  30  Snyder, Cle  +  10  62  58  
Canseco, Oak  +  23  106  89  R. Law, KC  +  7  48  40  Stefero, Bal  +  1  18  12  
Carter, Cle  +  36  122  116  R. Leach,Tor  +  3  35  35  Sullivan, Bos    6  10  9  
Castillo, Cle  +  7  33  25  Lemon, Det    4  51  52  Sundberg, KC    7  52  44  
Cerone, Mil    7  22  25  Lombardozzi, Minn    15  47  50  Sveum, Mil    5  38  37  
Coles, Det  +  7  78  81  Lowry, Det  +  4  25  24  Tabler, Cle  +  14  75  74  
Collins, Det    22  36  49  Lynn, Bal  +  28  83  69  Tartabull, Sea  +  29  99  85  
Cooper, Mil  +  10  80  60  Lyons, Chi    3  14  13  Tettleton, Oak  +  2  33  31  
J. Cruz, Chl    7  23  20  Manning, Mil  +  15  42  27  Thornton, Cle  +  12  70  55  
A. Davis, Sea  +  20  88  78  Martinez, Tor    6  16  12  Tolleson, NY    5  32  33  
M. Davis, Oak  0  64  72  Mattingly, NY  +  48  137  150  Traber, Bal  +  13  42  32  
DeCinces, Cal  +  13  82  72  McDowell, Tex    13  64  83  Trammell, Det  +  17  96  95  
Deer, Mil  +  18  84  82  McRae, KC    2  34  29  Upshaw, Tor  +  4  83  80  
Dempsey, Bal    19  27  41  Meacham, NY    13  10  13  Walker, Chi  +  24  62  48  
Downing, Cal  +  37  113  96  Mercado, Tex    11  3  7  Ward, Tex  +  7  57  56  
Dwyer, Bal  +  1  24  27  Molitor, Mil  +  13  71  65  Washington, NY    4  13  16  
Easler, NY  +  14  79  76  Moore, Mil  +  1  32  27  Whitaker, Det  +  4  82  82  
Da. Evans, Det  +  12  84  85  Morman, Chi    2  20  19  F. White, KC  +  13  88  84  
Dw. Evans. Bos  +  34  111  100  Moseby, Tor  +  9  89  86  Whitt, Tor    2  50  56  
Felder, Mil    8  13  17  Moses, Sea    16  37  40  Wiggins, Bal    9  23  24  
Fernandez, Tor  +  7  95  99  Motley, KC    14  14  16  Wllfong, Cal    11  28  23  
Fischlin, NY    5  9  6  Mulilniks, Tor  +  16  63  48  Wilkerson, Tex    5  25  19  
Fisk, Chi    10  49  39  Dw. Murphy, Oak  +  4  52  51  Willard, Oak  +  6  29  23  
Fletcher, Tex  +  7  79  76  E. Murray, Bal  +  32  101  92  W. Wilson, KC    36  46  76  
Foster, Chl    3  3  4  Nichols, Chl  +  2  20  12  Winfield, NY  +  25  104  89  
Franco, Cle  +  4  81  76  O'Brien,Tex  +  42  119  98  G. Wright, Tex    7  6  7  
Gaetti Minn  +  21  100  99  O'Malley, Bal  +  2  26  18  Wynegar, NY    1  26  20  
Gagne, Minn  +  1  64  57  Oglivie, Mil  +  6  52  45  Yeager, Sea    4  13  9  
Gantner, Mil    22  43  56  Orta, KC  +  2  45  42  M. Young, Bal  0  51  47  
D. Garcia, Tor    5  49  44  S. Owen, Bos    18  36  40  Yount, Mil  +  26  98  94 
Name, Tm  RC1  RC2  RCJ  Name, Tm  RC1  RC2  RCJ  Name, Tm  RC1  RC2  RCJ  
Aguayo, Phi    3  13  13  Gwynn, SD  +  20  97  113  Pendleton, SlL    32  37  50  
Aldrete, SF  +  2  30  31  J. Hamilton, LA  +  6  23  12  Perez, Cin  +  6  31  24  
Almon, Pln  +  14  39  25  T. Harper, Atl    5  27  30  Puhl, Hou    11  11  18  
Anderson, LA    3  23  20  B. Hatcher, Hou    6  43  47  Quinones, SF  0  13  6  
Ashby, Hou    6  33  40  Hayes, Phi  +  36  112  111  Raines, Mon  +  24  96  130  
Backman, NY    5  43  59  Hearn, NY    5  11  16  Ramierez, Atl    40  18  42  
Bailey, Hou    5  15  13  Heath, StL    7  17  17  Ray, Pitt  +  16  87  79  
Bass, Hou  +  13  83  97  Heep, NY  +  12  37  21  Redus, Phi  +  3  46  55  
Bell, Cln  +  16  88  91  K. Hernandez, NY  +  39  111  106  C. Reynolds, Hou    5  31  28  
Belliard, Pitt    14  25  26  Herr, StL    16  56  69  R.J. Reynolds, Pit  0  50  55  
Benedlct, Atl    4  16  13  Horner, Atl  +  22  85  79  Rn. Reynolds, Phi    9  5  9  
Bilardello, Mon    12  11  13  Hubbard, Atl    5  48  47  L. Rivera, Mon    5  15  15  
Bochy, SD  +  2  18  21  Hurdle, StL    4  16  16  Roberts, SD  +  1  29  20  
Bonds, Pitt  +  5  58  64  D. Iorg, SD    5  7  8  R. Roenicke, Phi  +  9  47  42  
Bonilla, Pin    10  15  21  Jeltz, Phi    13  43  40  Rose, Cln  +  3  33  23  
Bosley, Chl    2  13  17  H. Johnson, NY  +  12  40  36  Royster, SD    4  29  31  
Bream, Pm  +  11  75  79  W. Johnson, Mon    1  13  14  Russell, LA    4  23  21  
Brenly, SF  +  3  64  71  Kennedy, SD  +  2  54  54  Russell, Phi  +  7  45  42  
Brock, LA  +  5  45  42  Khalifa, Pitt    19  0  9  Sample, Atl  +  1  25  31  
Brooks, Mon  +  18  55  65  Knight, NY  +  18  77  70  Samuel, Phi  +  3  72  80  
Brown, SF  +  18  69  65  Krenchicki, Mon    8  19  22  Sandberg, Chi  +  2  77  86  
M. Brown, Pltt    10  20  20  Kruk, SD  +  16  52  47  Santana, NY    19  28  27  
Butera, Cin  +  3  18  15  Kutcher, SF    10  12  20  Sax,LA  +  11  88  110  
Cabell, LA    5  27  26  Landreaux, LA    2  32  32  Schmidt, Phi  +  47  119  122  
Candaele, Mon    8  4  6  Landrum, StL    8  17  17  Schu, Phi    1  25  32  
G. Carter, NY  +  15  78  72  Larkin, Cin  +  4  22  22  Scioscla, LA    10  39  49  
Cey, Chl  +  13  46  53  Lavalilere, StL    7  31  31  Simmons, Atl  +  5  21  16  
Chambliss, Atl  +  10  25  20  V. Law, Mon    4  40  34  O. Smith, StL  +  10  77  73  
J. Clark, StL  +  2  33  38  Leonard, SF    2  39  44  Speier, Chi  +  16  35  24  
W. Clark,SF  +  1  51  62  Lopes, Hou  +  12  33  34  Stillwell, Cin    9  25  24  
Coleman, StL    42  32  67  Madlock, LA  +  10  56  52  J. Stone, Phi    6  24  36  
Concepcion, Cln    7  31  33  Maldonado SF  +  10  58  51  Strawberry, NY  +  19  80  92  
J. Cruz, Hou  +  26  84  68  Marshall, LA  +  9  49  42  Stubbs, LA    3  48  51  
Daniels, Cin  +  17  39  40  C. Martinez, SD    6  25  31  Templeton, SD    26  34  44  
Daulton, Phl  +  7  27  26  D. Martinez, Chi    1  11  4  Teufel, NY    1  34  34  
C. Davis, SF  +  10  78  83  Matthews, Chi  +  4  51  63  A. Thomas, Atl    13  24  26  
E. Davis, Cln  +  31  84  95  Matuszek, LA  +  5  30  29  M. Thompson, Phi    8  28  34  
G. Davis, Hou  +  21  93  100  Mazzilli, NY  +  4  17  13  R. Thompson, SF    18  49  64  
J. Davis, Chi    3  61  66  McGee, StL    18  41  53  Thon, Hou    9  25  28  
Dawson, Mon    2  58  75  McReynolds,SD  +  24  94  103  Trevino, LA  +  1  27  28  
Dernier, Chi    10  29  30  Melvin, SF    14  17  23  Trillo, Chi  +  12  31  21  
B. Diaz,Cln    3  54  59  Milner, Cin  +  5  55  59  Uribe, SF    17  40  43  
M. Diaz, Pltt  +  3  28  33  K. Mitchell, NY    6  34  52  Van Slyke, StL  +  16  67  68  
Doran, Hou    10  60  81  Moreland, Chi    12  60  72  Venable, Cin    2  16  15  
Duncan, LA    34  15  38  Moreno, Atl    16  26  32  Virgil, Atl  +  1  48  49  
Dunston, Chl    16  51  64  Morris, StL    3  9  8  C. Walker, Chl    8  4  14  
Durham, Chi  +  12  73  78  Motley, Atl  +  1  2  1  Wallach, Mon    5  54  57  
Dykstra, NY  +  15  69  80  Mumphrey, Chi    2  35  45  Walling, Hou  +  19  65  67  
Esasky, Cin    4  38  44  D. Murphy, Atl  +  28  104  102  Washington, Atl    6  10  18  
Fitzgerald, Mon  +  4  31  34  Nettles, SD  +  4  48  41  U. Washington, Pitt  0  17  12  
Flannery, SD    1  46  50  Newman, Mon  0  23  23  Webster, Mon    5  66  90  
Ford, StL  0  26  27  Oberkfell, Atl  +  1  66  72  Williams, LA  +  8  45  37  
Foster, NY    2  26  28  Oester, Cin    8  56  59  G. Wilson, Pitt  +  16  86  76  
Francona, Chi  +  1  16  11  Oquendo, StL  +  4  21  17  M. Wilson, NY  +  4  50  58  
Galarraga, Mon  +  1  40  43  Ortiz, Pitt  +  5  18  16  Winningham, Mon    9  13  17  
Garner, Hou    1  37  39  Pankovitz, Hou    4  10  14  G. Wright, Mon    11  4  8  
Garvey, SD    7  57  59  Parker, Cin  +  36  113  94  Wynne, SD  +  7  41  32  
Gladden, SF  +  8  52  49  Pena, Pitt    9  52  68  Youngblood, SF  +  7  30  25 
It is not surprising that a different sabermetric approach to runs created emerges when methodologies from statistics (regression, expectation, state space Markov chain framework) and economics (valueadded, marginal and average) are combined with a vastly superior database, as has been made available by Project Scoresheet. As is always true in science, the new builds on the old, and will in turn be refined. It is hoped that the new methodology introduced here will be developed and incorporated into mainstream sabermetric analysis.
Excerpted from 1987 Bill James Baseball Abstract. Ballantine Books. 1987. James, Bill. "Measuring Runs Created: The Value Added Approach".
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