Let us suppose that a team scores 750 runs. Of those 750 runs, we are able to say with a fair degree of confidence who created how many; the starting catcher created 56, the starting first baseman created 91, the backup catcher created 22, the third catcher created 8 and the fourth catcher created 1, etc. etc.    We know how to do this; we have known how to do this for thirty years, although we can do it a little better now than we did 30 years ago.

            But let us ask this question instead: How many runs did each fielder save?   I don’t mean how many runs each fielder saved against average; I am asking how many runs he saved in total, as compared to a player making zero defensive contribution.

            I have a theory of how that number can be reached, and I am going to explain that theory in this article.    I will use National League shortstops of the 1980s to illustrate the process; at the end of this process we will have an estimate of the runs saved by every National League shortstop of the 1980s.   But this process is not limited or specific to shortstops, the 1980s, or the National League; it could be used for any fielder.   Some elements outlined today are specific to shortstops, but there are parallel systems for other positions.

            We work toward the answer we need by asking a series of four questions.   Those four questions are:

 

            1) How many runs were saved by the team?

            2) Of those runs that were saved by the team, how many were saved by the fielders and how many by the pitchers?

            3) Of those runs that were saved by the fielders, how many were saved by the shortstops?

            4) Of those runs that were saved by the shortstops on the team, how many were saved by this shortstop as opposed to the team’s other shortstops?

 

            To answer any of those four questions will require us to pose and answer another set of questions.    At points that will require us to do some comically convoluted mathematics which will, at times, disorient us and leave us uncertain as to why exactly we need to know this, but it’s essentially a logical process.

 

 

 

            This actually is easy.   Let us suppose that

 

            a) the team scored 750 runs,

            b) the team allowed 750 runs,

            c) the league run average was 750 runs per team,   

            d) the team played .500 ball, and

            e) the park factor was 1.000 (meaning that the park neither increased nor decreased scoring.)

 

            How many runs did the team "save", against zero?   Obviously, 750.   If this team’s offense are defense are equal (O=D) and the runs scored equal 750 (O=750) then obviously D=750.

            As runs scored rise from zero, runs saved must fall the same distance in order for offense and defense to be equal; therefore, they must fall from twice the league average (2Lg).    Twice the league average, park adjusted, is 2Lgp.

            We can answer this question (How many runs were saved by the team) by asking seven simple questions:

 

            1) What was the league average of runs scored per inning?

            2) How many innings did the team pitch?

            3) How many runs could the team have expected to allow in those innings?

            4) What was the park factor?

            5) Adjusting for the park factor, how many runs could the team have been expected to allow if they were average? (Lgp)

            6) How many runs could the team have been expected to allow at the zero point? (2Lgp)

            7) How many runs fewer than that did they allow?

 

            Let us take the 1988 Los Angeles Dodgers, champions of the World.    The National League in 1988 scored 7,522 runs in 17,481 innings, or .4303 runs per inning.   The Dodgers pitched 1,463 innings.   They could have been expected to allow 630 runs, if they had average pitching and defense and were in an average park.

            Surprisingly, Dodger Stadium in 1988 functioned as a hitter’s park, increasing offense by 8%, an adjusted park factor of 1.042.    Adjusting for the park, the Dodgers could have been expected to allow 656 runs.

            Twice that number (the zero point for runs allowed) would be 1,312 runs.   If the Dodgers had zero pitching and defense, they would have allowed 1,312 runs.

            They actually allowed 544 runs.   Therefore, the team’s pitching and defense saved 768 runs.  

 

            I will post, simultaneous with this article, a spreadsheet named 1980s RS SS 1.wk1 (1980s Runs Saved Shortstops 1), which gives the number of runs saved by every National League team in the 1980s.    These were the top ten run-saving teams of the decade:

 

 

            All ten of these teams played in hitter’s parks.   As a hitter’s park expands the number of runs that are scored, it also expands the number of runs saved. The ten teams that saved the fewest runs in a year, in the 1980s, were all teams from 1981, when a strike wiped out a third of the schedule.    But setting aside 1981, the teams saving the fewest runs were:

 

 

 

            All of these teams except the 1988 Phillies played in pitchers’ parks. 

            Most of these were not very good teams.   A list of teams saving the most runs is generally a list of pretty good teams; a list of teams saving the fewest runs is generally a list of not-very-good teams.  

            The notable exception on this list is the 1988 Mets, a team that won 100 games (100-60) with the formidable starting rotation of Dwight Gooden, Ron Darling, David Cone, Bobby Ojeda and Sid Fernandez.   Surely that collection of pitchers must have saved a large number of runs, no?

            No.   The National League ERA in 1988 was the lowest of the decade, 3.45; thus, the runs scored per inning for the league were very low.   Four of the ten teams on the list above were from 1988. 

            The 1988 Mets scored and allowed 704 runs on the road but only 531 at home, creating an extremely low park factor (raw park factor of .75, park adjustment factor of .877.)   This was the second-lowest park factor for any National League team in the 1980s. 

            The Mets missed a couple of games, so their innings pitched for the season was a little low.   Combining these factors, the Mets faced the potential of allowing only 1,086 runs even if they had zero pitching and defense value—easily the lowest number for any National League team in the 1980s, other than the strike-shortened 1981 season.    They actually allowed only 532 runs—also the fewest of any National League team during the 1980s, other than 1981—but the number saved (554) was still relatively low. 

 

 

 

 

 

            We cannot answer this question with great confidence.   I have a theory, I have a formula; I have a process for answering this question.   You may be able to come up with a better theory, a better formula, a better process.    I hope you can.   Until you do, however, my theory is what we have.

            I operate on the following assumptions:

            1) About two-thirds of the work of run prevention is done by pitchers; about one-third is done by fielders.

            2) If the pitchers’ strikeouts are high, this number is higher, because strikeouts take defensive responsibility away from the fielders and give it to the pitchers. If the pitchers’ strikeouts are low, the defensive responsibility is higher.  

            3) If the pitchers’ walks are high, this number is higher, because there is nothing a fielder can do about walks. If the pitchers’ walks are low, the defensive responsibility is higher.  (The same with hit batsmen, of course.)

            4) If the pitchers’ home runs allowed are high, this number is higher, because, again, there is nothing a fielder can do about home runs allowed.

            5) If the teams’ errors are high, this number is lower, because errors are the responsibility of fielders, rather than pitchers. 

            6) If the teams’ double play total is high, this number is lower, because double plays also are the responsibility of fielders.

            7) If the team has a good Defensive Efficiency Record (DER), this number is lower, because DER is the responsibility of fielders.   DER is an answer to this question: Of all balls put in play against this team, what percentage were turned into outs?

 

            Regarding point 6, double plays are also adjusted for the team’s expected double plays.    Expected double plays are based on the league double play average, adjusted for the ground ball rate of the team, and adjusted for the number of runners on first base against the team.   If a team has a lot of runners on base and their pitchers get ground balls, obviously we expect them to turn more double plays.   The 1985 Atlanta Braves, because they had a ground-ball staff that led the National League in walks, had an expectation of turning 193 double plays. They actually turned 197, so they exceeded expectations, but only by four.   The 1988 Mets, because they had a strikeout staff with relatively few runners on base, had an expectation of turning only 105 double plays.   They actually turned 127, exceeding expectations by 22.   We adjust the defense’s responsibility for runs saved based not only on double plays, but also on double plays versus expectation.   A fuller explanation of how we figure expected double plays will be given in section III of this article (below). 

 

            Based on these six factors, we estimate what percentage of the team’s defensive success—what percentage of their runs saved—should be credited to the team’s fielders.    This is done in the following way.  

 

            Figure 1 (F1) is the batters faced by the team’s pitchers.

            Figure 2 (F2) is figured as follows:

                        Strikeouts,

                        Plus 1.25 * Walks,

                        Plus 1.25 * Hit Batsmen,

                        Plus 6 * Home Runs Allowed

            F2 is a summary of the events for which we hold the pitcher responsible.   We start with the strikeouts, which figure into the end game as a simple percentage of batter’s faced; the higher the percentage of strikeouts by the pitchers, the higher the share of pitcher responsibility.   Walks and Hit Batsmen are multiplied by 1.25 because one walk or hit batsman has more impact on the game than one strikeout.   Home Runs allowed are weighted at 6.00 because these events have an immense impact on the outcomes of games, compared one to one with strikeouts.

 

            Figure 3 (F3) is team’s Defensive Efficiency Record, minus .625, times the number of balls in play against the team.    (As a team’s pitchers get credit for every strikeout, their fielders get credit for every out recorded above a level of zero competence.   A defensive efficiency record of .625 is considered to be a zero-competence level for a team’s fielders.   The team’s fielders get a "point" for every out recorded above that level.)

 

            Figure 4 (F4) is the team’s double plays, times 2, plus 3 times (Double Plays Minus Expected Double Plays), plus two times errors, plus F3.  

 

            Figure 5 (F5) is F1, minus F2, minus F4, times 2/3, plus F2.  

 

            Figure 6 (F6) is F1 minus F5.  

 

            The percentage of the team’s runs saved which are attributed to the team’s fielders, rather than their pitchers, is F6/F1. 

 

            Let’s run through that for the 1988 Dodgers.   Dodger pitchers in 1988 faced 6050 batters; that would be our F1.  

            Of those 6050 batters, Dodger pitchers struck out 1,029, walked 473, and hit 22.   They gave up 84 home runs.   That makes their "F2" score 2152 (1029, + 495*1.25, + 84*6). 

 

            Their fielders had a Defensive Efficiency record of .713 (.71316), which is very good, and there were 4,442 balls in play against the team.   That makes an F3 score of 385, meaning that the Dodger fielders recorded 385 outs above a team of zero-competence fielders.

 

            The Dodgers turned 126 double plays against an expectation of 128.   They committed 142 errors.   That makes an F4 score of 915 (2*126 + (3* (126-128)) + (2 * 142) + 385).  

 

            Dodger pitchers faced 6050 batters, and we have attributed sole responsibility for 2,152 of those to the pitchers, and 915 to the fielders.   That makes 3,067 "attributed" batters, which leaves 2,933 "un-attributed" batters.   Two-thirds of those we now assign to the pitchers, and one-third to the fielders.   That makes 4,141 batters attributed to the pitchers, which leaves 1,909 to be attributed to the fielders.   Thus, 31.6% of the fielding success of the 1988 Dodgers is attributed to their fielders (1909/6050); 68.4% is attributed to their pitchers.  

 

            (At this point I can foresee a long line of misunderstanding and argument which will flow from this, so let me spend a minute to try to stave that off.    People will try to tell me that Vorosian analysis has demonstrated that all a pitcher really does is give up home runs, strike out batters and issue walks; otherwise, one pitcher is the same as another.   Therefore, since one pitcher is the same as another when the ball is in play, the lion’s share of the credit for recording outs on balls in play—if not, indeed, ALL of the credit for recording outs on balls in play—should go to the fielders, not the pitchers. 

            The first problem with that analysis is that it would lead to absurdly low run-prevention values for pitchers.   An attribution system that proceeded on those assumptions would lead to a Cy Young pitcher being credited with preventing an unrealistically low number of runs, and would imply that major league teams were behaving unreasonably in paying pitchers what they pay them and in carrying 12 or 13 pitchers on the roster, since these players would appear to have very little value.

            What that approach essentially fails to recognize is that a pitcher succeeds when he gets a ball in play.   Balls in play generally become outs.   If you visualize sub-major league pitchers on the same scale as major league pitchers, the sub-major league pitchers would issue vast numbers of walks and would give up huge numbers of home runs, leaving very little room for the defense to save the game.   Major league pitchers succeed because they avoid those outcomes, getting balls in play—and Vorosian analysis shows that one ball in play is very much like another one.

            Stated another way, the batter is two-thirds out when he puts the ball in play. Stated in a third way, Vorosian analysis shows that a very large percentage of the composite material of an offense is essentially inert, inactive material.   The fact that a very large percentage of the game is not a variable makes the "Active" or variable component of the equation much more important.  

            Two pitchers each have 900 balls in play, but one of them has 100 strikeouts, 80 walks and 25 homers allowed; the other has 200 strikeouts, 50 walks and 10 home runs allowed.   Stated relative to the batters faced, the differences of 100 strikeouts, 30 walks and 15 home runs are small distinctions—yet because of the interactive nature of offense, which works on long sequences, these are (as we know) huge differences in practice. This is why we attribute the outcomes of balls in play primarily to pitchers, rather than to fielders. )  

           

            Anyway, 31.6% of the run-prevention success of the 1988 Dodgers is attributed to their fielders.    This is a mid-range number, a normal number; the average for all National League teams throughout the 1980s was 31,4%.   The highest figures of the decade, ranging from 36.2% to 34.2%, were by the St. Louis Cardinals of 1981, 1980, 1982, 1986 and 1985, in that order. The lowest figures were 27.2%, by the 1987 Houston Astros and by the 1987 Chicago Cubs, and 28.2%, by the 1986 Chicago Cubs. 

 

            At the time I publish this article I will also post a spreadsheet, 1980s Pitcher v Defense Percentages, which is intended to enable you to follow the math for all 1980s NL teams to whatever extent you might wish to do. 

 

 

 

            Once we have determined how many Runs were Saved by each team and what percentage of those should be attributed to the defense, we can combine those to calculate how many Runs were Saved by each team’s defense.   These numbers are also in the file, 1980s Pitcher v Defense Percentages.  

            These are the ten National League teams of the 1980s which we credit with saving the most runs by defensive play:

 

 

            And these are the ten teams that we credit with Saving the fewest Runs by defense, not counting the strike-blighted 1981 season:

 

 

 

 

 

            We now begin the third stage of our four-stage process, which is dividing those runs saved by the team up among the non-pitching fielding positions.

            Again, we have to make assumptions that we cannot absolutely verify.    Future research may find ways to verify these assumptions or to replace them, but. . .we have to start somewhere.  

            Our system begins with the assumption that 15.4% of the Runs Saved by a team’s fielders are credited to the shortstops, stressing of course that it will not be 15.4% in all cases.    15.4% is a starting point, not an ending point.   The starting percentages we use are:

 

            15.4% for catchers

             9.9% for first basemen

            13.6% for second basemen

            12.4% for third basemen

            15.4% for shortstops

            33.3% for the three outfielders

 

            Prior to 1920 the percentages at second base and third base are reversed (13.6% for third basemen, 12.4% for second basemen) and from 1920-1939 second base and third base are credited with 13% each.   

            We start with 15.4% for shortstops, and we adjust this for:

 

            1) Assists versus expected assists,

            2) Putouts versus expected putouts,

            3) Errors versus expected errors, and

            4) Double Plays versus expected Double Plays.

 

            Assists. To figure expected assists, we take the league percentage of assists that are recorded by shortstops, apply that to the team, and increase that by one assist for every 100 balls put in play by left-handed pitchers, above or below the league average.    Let’s stick with the 1988 Dodgers for illustration.  

            In the National League in 1988 there were 21,246 assists, of which 5,877 were by shortstops (I hope.   These are the numbers I have in my file, and at the moment I am too lazy to double-check them.)   Anyway, that’s 27.66%, so we expect 27.66% of the assists by the Dodgers to be recorded by their shortstops.   

            The 1988 Dodgers had 1,746 assists.   We expect 27.66% of those to be made by their shortstops, so that’s 483 expected assists by Dodger shortstops.

            You will note here that we have adjusted for the Ground Ball tendency of the pitching staff.   The vast majority of ground ball outs result in assists, and the vast majority of assists result from ground balls.    If the team’s pitching staff throws ground balls the team will have a high assists totals, always and absolutely; therefore, we will expect the team’s infielders to have more assists.   Thus we are not misled by the ground ball tendency of the pitching staff.

            However, the 1988 Dodgers had only 875 balls put in play against left-handed pitching, which is a very low number—lowest in the National League.    Balls put in play against left-handed pitching tend disproportionately to go to the left side of the infield (third base and shortstop).    Since the Dodgers had few left-handed pitchers, that reduces somewhat the number of expected assists by their shortstops.

            (You actually can ignore this effect with regard to shortstops, with minimal consequence.   It makes a real difference with regard to third basemen and first basemen, basically a negligible difference with regard to shortstops and second basemen. But since we have to figure it with regard to the corner infielders, we have the data we need and we’ll factor it in with regard to the middle infielders as well.)  

            Anyway, the average National League team in 1988 had 1,526 balls put in play against left-handed pitching.   The Dodgers had only 875.   That’s -651.  For every extra 100 balls put in play against lefties there is an expected increase of one assist by the shortstops, so that’s -6.51 for the Dodgers.   This reduces the expected assists by Dodger shortstops to 476.  

            Dodger shortstopi in 1988 actually had 497 assists.   That’s 21 more than expected.   For every assist above expectations, we will credit them with an additional .13 runs saved.   Put that number aside, and we’ll use it later in summing up.  

 

            Now let’s deal with Putouts.   We begin by figuring the league’s shortstop putouts as a percentage of league putouts, minus strikeouts, minus assists.   Strikeouts are not balls in play, and assisted putouts are ground balls, so we eliminate those as potential shortstop putouts.   The result we can call the League Shortstop Unassisted Putout Percentage.

 

            League SS PO divided by League PO minus Strikeouts minus Assists

           

            We multiply the league shortstop unassisted putout percentage times the team putouts, minus putouts, minus assists.   This is the expected number of putouts by the team’s shortstops. 

            Except that, again, we have to adjust for the left-handed/right-handed bias of the team.   There is an increase of one assist by shortstops for every one hundred balls in play against left-handed pitchers; there is a decrease of one putout by shortstops for every 110 balls in play.   That’s why you can kind of ignore the left-handed/right-handed bias for shortstops; it pretty much evens out.  

            Anyway, let’s do the 1988 Dodgers for illustration.   In the National League in 1988 there were 52,442 putouts (I hope.   I’m not double-checking this data as I work.)   Of those, 11,032 were strikeouts (that leaves 41,410), and 21,246 were assisted. That leaves 20,164 un-assisted putouts for the league, a high percentage of which are balls caught in the air.   Of those 20,164 un-assisted putouts, 3112 were by shortstops.    That’s 15.4%--coincidentally the same percentage of the run prevention value that we are attributing to shortstops.  

            Anyway, the 1988 Dodgers had 4,390 putouts, of which 1,029 were strikeouts (leaving 3,361) and 1,746 were assisted (leaving 1,615).    We expect Dodger shortstops to record 15.4% of those 1,615 putouts.   That’s 249.   We expect Dodger shortstops to have 249 putouts.  

            Except that batters tend to pop out the ball to the opposite field, so this figure should be higher for the Dodgers, because they have little left-handed pitching (which means that they have lots of right-handed pitching, which means that they faced lots of opposition left-handed batters, who tend to pop out to shortstop and third base.)   The Dodgers, as we established earlier, had 651 fewer balls in play against left-handed pitchers than average, and there will be an increase of shortstop putouts of one for every 110 of those.   That’s an increase of.. .well, let’s call it six. So we expect Dodger shortstops (1988) to have 255 putouts, rather than 249.  

            Dodger shortstops actually had 277 putouts, 22 more than expected.    For each one putout over expectation, we credit the shortstop with .04 runs saved. Again, we will put this figure aside, and come back to it when we are summing up.

 

            Errors.   The error percentage if the complement of the fielding percentage.    If the league fielding percentage at a position is .900, the error percentage is .100; if the fielding percentage is .950, the error percentage is .050. 

            We figure the number of expected errors for the team at the position, based on the league error percentage at the position.    The fielding percentage of National League shortstops in 1988 was .967; therefore, the error percentage was .033 (.0326).   

            Dodger shortstopi in 1988 had 794 total chances. We expect them, then, to have 26 errors.   They actually had only 20 errors.  

            For each 4 errors less than the league norm, we credit the shortstops with one extra run saved.   Again, set this number aside, and we will come back to it in summing up. 

 

            Double Plays.   We have to start by estimating the number of runners on first base against each team.    We have to start there because, to interpret the double play data, we have to calculate expected double plays, and, to estimate expected double plays, we have to consider how many runners are on first base against each team. 

            The formula for estimated runners on first base (ERO1B) is Hits minus Home Runs, times .781, plus walks, plus hit batsmen, minus wild pitches, minus balks, minus passed balls, minus stolen bases allowed, minus runners caught stealing.  

           

ERO1B = (H-HR)*.781 + BB + HBP - WP - BK - PB - SB - CS

 

I would explain how we derived that formula, but you’d never get that hour of your life back.    We figure the number of estimated runners on first base against the team, and against the league.    Find the percentage, team divided by league.   Multiply the league double plays by that percentage.    That’s ExpDP1, expected Double Plays, stage 1.  

            This we have to modify by the team’s number of assists per inning pitched.   Figure the team’s assists per inning pitched, and divide by the league norm.   Multiply ExpDP1 by that figure, and the result is expected Double Plays.

            Subtract expected from actual Double Plays for the team.   For each 10 double plays above or below expectation, credit the shortstop with one run saved.

            One Run Saved for each ten Double Plays (I can hear you asking).   Why so few?

            For shortstops and second basemen, we don’t look at the individual double play total; we look at the team number.    It just works better; the individual double play totals are subject to a variety of biases, and they’re difficult to work with.   Unlike almost every other offensive and defensive stat, they don’t even add up to the team total. It’s much cleaner to ask the question, did the team turn more double plays than we would expect them to turn?   If the team turned more double plays than expected, we can assume that that reflects well on the second basemen and shortstops for the team.  

            But on the individual level, there are a number of issues.   First, when shortstops and second basemen participate in a double play, they are credited with putouts and assists.   We have already given them credit for those putouts and assists.   We are now double-counting the credits. 

            Second, we are evaluating team double plays here. Some of the double plays that we are crediting here go 5-4-3, 1-4-3, or. ..well, 3 un-assisted, or 4 un-assisted.   Some of them didn’t have anything to do with the shortstop. We are not crediting specific double plays; we are crediting the shortstop for his presumed contribution to the double play excellence of the team, which sometimes involves plays that he didn’t have anything to do with.  

            What happens if the team’s second baseman is superb at turning the double play, but their shortstop is lousy?   What happens is, you’re going to have one hell of a time sorting that one out, no matter how you approach it.   My approach is to credit the team with the team’s ability to turn double plays, and then to presume that the shortstop is a contributor to that.   I doubt that you can do much better, but feel free to try. 

            Anyway, that’s why the ratio of runs saved to double plays is so low; there are issues of attribution.   

            Let’s do the 1988 Dodgers.   In the National League in 1988 there were 14,293 estimated runners on first base, of which 1,158 were against the Dodgers.   That’s 8.1%.  

            There were 1,609 double plays in the league.   8.1% of that would be 130.   We expect the Dodgers to turn 130 double plays, but now let’s look at the ground ball rate.  

            In the National League in 1988 there were 21,246 assists (ground balls) in 17,480.2 innings, or 1.215 assists per inning.   For the Dodgers, there were 1,746 assists in 1463.1 innings, or 1.193 assists per inning.   The Dodgers’ ground ball rate was 1.8% below the league norm.   We thus have to reduce their expected double plays by 1.8%. 

            OK, that cuts the Dodgers’ expected double plays from 130 to 128.   The Dodgers in 1988 actually turned 126 double plays, two less than expected.   Put this number aside, and we’ll pull it into the overall estimate of the team’s defensive performance at the position, which begins now. 

 

            OK, the Runs Saved by Dodger Shortstops in 1988 are:

 

            37 as a base number (242 * .154),

            plus 3 because the team exceeded its expected shortstop assists,

            plus 1 because the team exceeded its expected shortstop putouts,

            plus 1 because the team had fewer shortstop errors than expected,

            minus zero (minus 2/10) because the team turned two fewer double plays than expected.

 

            Altogether that makes 42 Runs Saved by Dodger shortstops in 1988—the highest total in the National League in 1988.  

            I have posted the file 1980s RS SS 2, which contains all of the information necessary to figure these estimates for every National League team in the 1980s.  

 

            Since we have come this far, we might now observe the year-by-year team leaders:

 

 

 

            Finally, we have to move the credit for preventing runs from the position to the individual shortstop. 

            This is work, but it’s conceptually simple.   I can explain it in one paragraph, two sentences.   We take the defensive statistics of the team at the position, and pro-rate those to the innings played by each shortstop, thus creating an "expected putouts", "expected assists", "expected errors" and "expected double plays" by each individual shortstop.   We credit the shortstop with his share of the Runs Saved by the team at the position, based on innings, but modified by the same rates used on the team level--.04 for each putout, .13 for each assist, .25 for each error, and .10 for each double play.  

            These are the defensive statistics for the Los Angeles Dodger shortstops in 1988, aggregate:

 

 

            DI is "defensive innings"; DI3 is "thirds of a defensive inning", also known as "Outs".   Of the 4,390 DI3, Alfredo Griffin was in the field for 2,378, and Dave Anderson for 1,947:

 

            Based on the defensive innings, then, we could expect Alfredo Griffin to have recorded 150 putouts and 269 assists, Dave Anderson 123 putouts and 220 assists, Mike Sharperson 4 and 6, and Jeff Hamilton one of each:

 

 

            In fact, though, Griffin recorded only 145 putouts, and only 264 assists. These are the actual defensive statistics of the four Dodger shortstops:

 

            On a per-inning basis, Anderson did better than Griffin in all four categories—more putouts, more assists, fewer errors and more double plays.   This chart compares the actual to the expected data:

 

            The Dodger shortstops in 1988 were credited with saving 42.13 runs.   When we apportion those based on innings in the field, we get 22.82 Runs Saved for Griffin, 18.68 for Anderson, and 0.54 for Mike Sharperson:

 

 

            However, when we subtract .2 runs from Griffin for Putouts (-5 * .04), .65 runs for Assists (-5 * .13), 1 for Errors (4 * .25) and .7 for Double Plays (-7 * .10), Griffin drops to 20 Runs Saved, and Anderson goes up to 21:

 

 

            Noting for the record that Griffin does not have bad defensive stats in 1988; he merely has bad defensive stats compared to Anderson.   The Dodgers, after all, have the best defensive stats in the league at the position.  

 

Make That

 

 

            By the process outlined here, the top three Run-Saving shortstops for each year in the 1980s were as follows:

 

 

            Apparently Ozzie Smith was pretty good; I’ll put out a news release.   There are no actual ties in this data, of course; the appearance of ties is due to rounding off to the nearest run.  

            Simultaneous with the publication of this, I will publish the spreadsheet 1980s RS SS 3,

which will have full data for every National League shortstop of the 1980s.  

 

            This is the career data for those players who had 900 or more innings at shortstop during the decade, plus Luis Gomez, who had 898:

 

 

            On a per-inning basis, we estimate that Ozzie saved 30 runs per 1,000 innings. These are the shortstops, rated on a per-inning basis:

 

 

 

            Tomorrow, I’ll debate myself about some of the choices I have made here, and talk a little bit about how else this might have been done.