Designated HitterMarch 14, 2007
Quantifying Coachers, Part I
By Dan Fox and Neal Williams

"The employment of one of the side who are in to watch the movements of the field and advice the runner accordingly is a quaint device of American acuteness." - quote from an English newspaper during an 1874 tour by American ballplayers as recorded in Sporting News, February 25, 1909

As that quote attests, the idea of on-field coaches has a long history in baseball. Peter Morris, in his excellent book A Game of Inches: The Stories Behind the Innovations that Shaped Baseball Volume I, The Game on the Field, informs us that base coaches (or "coachers" as they called the name deriving from the likeness to a stagecoach driver) were apparently common since rules were in place by 1872 which specified that a baserunner's teammates had to keep a distance of at least 15 feet.

Unlike today, however, it seems the primary job of the coaches was to "disconcert the opposing players - generally the pitcher - not to 'coach' or assist the base-runner" as Sporting News put it in 1893. As a result, the primary qualifications for a coach of that time was a megaphone like voice (yes megaphones were tried in college games in the early 1900s but fortunately never found a foothold in professional baseball) and a cruel disposition. In fact, it was the abusiveness of coachers like Charles Comiskey and Bill Gleason, who would stand on either side of the catcher commenting on everything from his skill as a catcher to his breeding and personal habits, which precipitated a move to first ban coaching altogether but then to restrict coaches to boxes down the line beginning in 1886. In addition to their primary job as unsettlers of the opposition, third base coaches would also attempt to get opposing fielders to mistake them for a runners, a ploy was which was severely hampered following the 1886 rule change.

Be that as it may coaching did eventually come to be taken more seriously with Arlie Latham the first full time coach hired by the Cincinnati Reds in 1900. And Latham was apparently performing the modern function since in July of that season Sporting Life reported that "Manager [Bob] Allen says he is delighted with the coaching of Latham. He says the baserunning of the team has improved 100% after the veteran got on the lines". As is true for advances in other fields Cincinnati's experiment proved to be an early, if successful, trial balloon and it would another decade before the idea took hold. In between there were still calls to ban coaching leading non other than Henry Chadwick in 1904 to denounce coaching as it had "degenerated into a dirty-ball method of annoying the pitcher". Other innovations in the game including increased managerial strategy and signaling finally drove the need to move beyond the "old school of clowns" as Christy Matthewson famously said of this earlier period in Pitching in a Pinch. Not surprisingly it was John McGraw who hired Latham and Duke Farrell as full-time coaches in 1909. By 1912 Sporting Life noted that Latham "does get a percentage of runs across - runs that might not otherwise be made". From there it was generally recognized that coaches paid dividends and although for some time there was apparently a subset of coaches who seemed more preoccupied with rattling the opposition, coaching as a profession gained strength and was here to stay by the early 1920s. Their duties have expanded over time as well. As just one example the first base coach now routinely times the pitcher's delivery to the plate relaying that information to the runner.

Figure 1: Rangers first base coach Gary Pettis (with a stop watch in his right hand that you can't see but trust me), himself an excellent baserunner, times the pitcher's delivery to the plate with Michael Young on first base in a spring 2007 exhibition game.

It's now been almost 100 years since full time coaches were employed and their performance is routinely scrutinized although not very often quantified. The question then (first suggested to Dan by Rich Lederer of all people) from an analyst's viewpoint is two-fold. First, is the job of coaching quantifiable? In other words, can we create a metric or metrics that measure the success and failure of this component in a reasonable way? And second, if it is measurable, can some coaches be said to be more skilled at this half of their job than their peers? In this article and the one to follow we'll take a crack at answering both questions for third base coaches related to their secondary job (relaying signs being the primary) of directing traffic on the bases.

Quantifying the Wave

In the summer of 2006 in a series of six articles published on the Baseball Prospectus web site one of us (Dan) endeavored to more formally quantify baserunning by developing a series of metrics measured in terms of runs. Those metrics are:

  • Equivalent Ground Advancement Runs (EqGAR). Measures the contribution of baserunners above and beyond what would be expected in opportunities they have for advancing on outs made on the ground. For example, advancing from second to third on a ground out to shortstop or getting gunned down at home on a grounder to second.
  • Equivalent Air Advancement Runs (EqAAR). Measures the contribution of baserunners above and beyond what would be expected in opportunities they have for advancing on fly ball and line drive outs. For example, scoring on sacrifice flies or advancing from first to second on a fly ball to left field. This metric is park adjusted.
  • Equivalent Stolen Base Runs (EqSBR). Measure the contribution of baserunners in their stolen base attempts and pick offs.
  • Equivalent Hit Advancement Runs (EqHAR). Measures the contribution of baserunners above and beyond what would be expected in opportunities they have for advancing on singles and doubles. For example, moving from first to third on a single to left field or scoring from first on a double. This metric is park adjusted.
  • When totaled, these give us a fairly complete picture of the contribution made by a player on the bases beyond what would have been expected given their opportunities. And therein lies the rub. The methodology that underlies these metrics isn't a simple totaling of the number of bases gained in these situations but rather an application of changes in the expected number of runs across several dimensions including the base/out situation (the Run Expectancy matrix), handedness of the batter, and the position of the fielder who fielded the ball.

    By calculating how often runners typically advance in a whole host of scenarios (for example with a runner on second and nobody out a runner will advance from second to third 43% of the time when the ball is fielded by the shortstop but 97% of the time when handled by the second baseman) and translating those percentages to runs using the Run Expectancy matrix we can credit or debit a runner for each and every opportunity they have on the bases.

    Totaling the credit assigned to each opportunity (and not crediting the runner for advancing the minimum number of bases) for players allows us to assign a number of theoretical runs above and beyond what a typical player would have contributed given the same opportunities. Yes, theoretical since these metrics, being based on models like the RE matrix, don't actually measure the precise number of runs contributed by a runner but rather can be thought of as an accounting of the decisions made by runners and coaches, that put their teams in more or less advantageous situations throughout the course of a season. That accounting is performed in terms of runs. As mentioned above we then adjust for park effects where necessary. For example the spacious Coors Field outfield allows for easier advancement than the smaller Fenway Park.

    Already many of you can see where this is going. EqHAR, by measuring runner advancement on hits, may be an appropriate methodology to apply to third base coaches since it measures an aspect of the game in which third base coaches are directly involved. Looking more closely, EqHAR is composed of three basic scenarios.

  • Runner on first, second not occupied, and the batter singles

  • Runner on first, second not occupied, and the batter doubles

  • Runner on second, third not occupied, and the batter singles
  • A third base coach may be active in each of these scenarios but as will be obvious it typically depends on where the ball is hit. When a batter singles or doubles with a runner on first base, the runner typically makes his own decision about whether to advance if the ball is hit to left field or within his field of view in center field. On the other hand he'll usually pick up his third base coach if the ball lands in right field. Likewise when on second base ball hit to the outfield typically results in the runner typically taking matters into his own hands only if the ball is hit to left, but rely on the coach if the ball is hit to center or right. By using these general rules as a guide the analysis can be restricted in this sense to plays that fall only into these categories but also include scenarios when multiple baserunners are on base.

  • Runner on first and the batter singles and the ball is fielded by the right fielder. Other bases may be occupied.

  • Runner on first and the batter doubles and the ball is fielded by the right fielder. Other bases may be occupied.

  • Runner on second and the batter singles and the ball is fielded by the center or right fielder. Other bases may be occupied.
  • One might argue that these categories are either too restrictive or not restrictive enough and we have sympathy with both arguments.

    For example, with the runner on first on a single fielded by the centerfielder there are certainly occasions when the runner picks up the coach. Conversely, with a runner on second and the batter singling to left there are definitely times when the runner knows the ball will be difficult to handle or is running with the pitch and so heads home without consulting the coach. This analysis will not include those events. And these events of course do not include runners attempting to advance on ground ball and fly ball outs nor does it include runners attempting to stretch doubles into triples or triples into inside the park homeruns. The thought was to error on the side of caution and include only those events where it seems the third base coach would be most likely to have influence. Further, these scenarios will include times when runners run right through the stop sign given by their frantic coach only to get thrown out. Through no fault of his own, the coach will be still be debited for plays like these.

    Surely this is far from a perfect system but given the granularity of the play by play data available and absent video inspection of each play, this seems like a reasonable approach for a first pass at creating this kind of metric.

    The primary advantage to using the methodology described above as opposed to simply counting the number of runners that were thrown out on each coach's watch is that this system also gives appropriate credit when a runner advances successfully. The system also takes into consideration how difficult the advancement event was and gives more credit when a runner takes a base in a higher reward situation. While keeping runners from getting thrown out is clearly a major component of the job, knowing when to take risks based on game situation is a secondary component and one that this metric captures.

    Given the above caveats we ran the EqHAR framework for third base coaches for 2006 with the following results.

    Table 1: Third Base Coaches 2006 Ordered by Rate

    Team   Name                 Opp     OA  EqHAR   Rate
    ANA    Dino Ebel            238      3   10.3   1.19
    PHI    Bill Dancy           262      5    7.8   1.15
    HOU    Doug Mansolino       214      1    5.6   1.11
    TBA    Tom Foley            163      1    5.3   1.15
    DET    Gene Lamont          240      5    5.0   1.10
    FLO    Bobby Meacham        199      4    2.3   1.05
    NYN    Manny Acta           228      3    2.3   1.05
    KCA    Luis Silverio        237      4    2.0   1.04
    WAS    Tony Beasley         239      6    1.5   1.03
    COL    Mike Gallego         247      3    1.5   1.03
    ARI    Carlos Tosca         275      6    0.5   1.01
    MIN    Scott Ullger         222      3    0.5   1.01
    BAL    Tom Trebelhorn       296      3    0.3   1.01
    MIL    Dale Sveum           214      5    0.3   1.01
    SDN    Glenn Hoffman        231      4   -0.2   1.00
    TOR    Brian Butterfield    237      6   -0.4   0.99
    CLE    Jeff Datz            274      5   -0.7   0.99
    CIN    Mark Berry           217      5   -0.8   0.98
    SLN    Jose Oquendo         230      5   -1.1   0.98
    PIT    Jeff Cox             230      3   -1.2   0.98
    SEA    Carlos Garcia        226      6   -1.5   0.97
    SFN    Gene Glynn           220      3   -2.2   0.95
    TEX    Steve Smith          234      5   -2.5   0.95
    CHN    Chris Speier         199      6   -2.9   0.94
    ATL    Fredi Gonzalez       231      6   -3.3   0.94
    NYA    Larry Bowa           289      5   -4.1   0.93
    OAK    Ron Washington       245      7   -4.9   0.89
    LAN    Rich Donnelly        260      9   -6.0   0.90
    BOS    DeMarlo Hale         248      5   -7.6   0.86
    CHA    Joey Cora            234      9   -7.7   0.86

    This table includes the number of hit advancement opportunities (Opp), the number of times runners were thrown out advancing (OA), the EqHAR for those opportunities, and a Rate statistic that is the ratio of EqHAR to the expected number of advancement runs given both the quantity and the quality of opportunities along the axes mentioned above. This is important since you'll notice that while Baltimore and Tom Trebelhorn had 296 opportunities, Tom Foley in Tampa Bay had just 163 and all other things being equal, more opportunities means a higher EqHAR.

    It should be noted that the coach was assigned all plays for the 2006 season for his team since there is no easily accessible record of when a third base coach was not on the field for his team. For example, although Chris Speier took a several day leave of absence beginning July 20th after being arrested for DUI earlier that week, the opportunities during that time are credited to Speier. Through this analysis the coaches were assigned opportunities based on their team's media guides for the respective seasons.

    So under this measure Dino Ebel of the Angels played a part in helping his runners to the tune of just over 10 additional theoretical runs (the second highest of any single season from 2000 through 2006) while Joey Cora was complicit in costing the White Sox the equivalent of almost 8 runs. Intuitively, this range seems to be within the bounds of believability. Interestingly, newly minted managers Ron Washington (-4.9) and Fredi Gonzalez (-3.3) don't come out very well although Manny Acta (+2.3) does.

    But is this really a fair gauge of a third base coach's influence? We'll answer that question along with the two we started this article tomorrow.

    Dan Fox is an author for Baseball Prospectus where he writes the weekly Schrodinger's Bat column. He also writes about baseball and other topics on his blog Dan Agonistes.

    Neal Williams is the president of the Rocky Mountain chapter of the Society for American Baseball Research.


    Schrodinger's Bat: Hit the Ground Running
    Schrodinger's Bat: An Air of Advancement
    Schrodinger's Bat: Advancing in Context
    Schrodinger's Bat: Using The House Advantage
    Schrodinger's Bat: The Running Man
    Schrodinger's Bat: The Whole, the Sum, and the Parts


    It would be nice if the defensive and baserunning gurus provide us with home and away splits. seeing is believing and I am not believing the adjustments made for park effect are accurate, especially where Fenway is concerned. So how bad are Manny or Demarlo Hale? I think Manny is an average defensive LFer except last year when he was bothered with his knees, and Demarlo Hale is an above average 3rd base coach (and well above average in holding runners at 3B to prevent them getting thrown out at home). The home and away splits may prove me wrong, but until I see them, I am not buying into any of these stats where Fenway is involved.

    Also, the Red Sox had some of the worst base runners in the league last year and some players like Manny do not even pay attention to the 3rd base coach, so I will be interested in your answers rommorow. The run environment of a team and park, not to mention lineup position, are also factors in deciding to risk advancing players an extra base. A lead of batter for the Red Sox is unlikely to risk advancing a base with Papi and Manny up next unless it is a sure thing, while teams like the Tampa Bay Devil Rays have no such constraints.

    Theres the numbers verifying what i knew to be true last year(and probably voiced here on occassion).

    CHA Joey Cora 234 9 -7.7 0.86

    Thank God his 'promotion' by his hetero-life partner Ozzie takes him off of that bag.

    and it was more that 8 runs for sure.
    more like 20

    Thanks for the itneresting history on coaches. I suspect the propensity to send runners home has much to do with 1.) The speed of the player 2.) Game situation 3.) Throwing ability of the outfielder and cutoff man and 4.) Who's up next and overall team offense.

    But is this really a fair gauge of a third base coach's influence?

    I hope the answer to that is no. If the algorithm put Ron Washington is at the bottom of the list, the algorithm isn't passing my smell test.

    Washington was fabulous at gauging the four things Al Doyle listed above. I've watched the A's closely for years, and there aren't many times the A's have had a runner thrown out that I thought Washington made the wrong decision given the context. I'm sure my fellow A's fans agree, and how often do fans think their team's third base coach is good?

    Paul, for Hale his rate was .86 on the road and .86 at home and so there was essentially no difference. But your point about what he had to work with is good one. Tomorrow's article will correct for this (as it will for Ron Washington and even Joey Cora).

    I love the idea.

    It seems to me that you'd want to regress on the non-3B-coach-influenced baserunning measures onto the 3B-coach-influenced measure, to account for the player's speed.

    For example, the 80s Cardinals probably did well, and the 3B coach gets a bonus because of that. However, using a speed-factor, as I describe above, should handle part of that.

    I agree about the home/away: I just don't trust any analyst, on any of this, be it my favorites like Dan or MGL or anyone else. Even myself.

    I am curious as to why you chose to assign responsibility to the coach with a runner on 2nd (and a single) only on hits in the players view?

    Conventional wisdom, which is basically true (from playing, coaching and watching thousands of games), is that the third base coach is ALWAYS responsible for sending runners home or not, regardless of where the ball is hit.

    Yes, it is true that a player is more likely to disregard or oppose the coach when he can see the ball, but doing so is rare, regardless of where the ball is hit.

    I think your results will be more reliable (larger sample size) if you used ALL batted balls when a runner is sent home or not, regardless of where the ball is hit in the OF.

    Tango, I'm not sure I understand your comment on regressing the non coach side. Since both coach and non coach opportunities use the same baserunners, isn't the speed factor accounted for?

    I'll publish the park factors I used on my blog.

    MGL, I did *not* assign responsbility to the coach for that scenario (runner on 2nd and the ball hit to left) since the ball is in view which is what I think you meant. I was thinking anecdotally about players running through their coaches signs but I didn't run the numbers the other way but will to see how it turns out.



    I didn't see your part 2 until now, and you in fact addressed my issue in part 2.



    What I meant is that the coach is ALWAYS responsible for sending the runner HOME or not, regardless of where the ball is hit in the OF.

    First to third is another story. In general the coach is responsible on a ball hit out of the runner's view, but many players look over their shoulders and make their own decisions.

    MGL, thanks for clarifying and I'll see who changing the assignment works.

    While I thought the whole thing was a great idea and great work, the fact that there are weak y-t-y correlations suggests that all we are seeing are random flucs anyway.

    To address the year-to-year correlations, use an AR1 covariance matrix to see what the intra-class correlation is (as you have multiple years). That'll give you a better idea of how much this is an endogenous skill and how much it's just random fluctuation.

    Methodological concern: not all "extra bases" and potential throw-outs are created equally. Suppose that the RF finally picks the ball up in the corner with the runner already 20 feet to home plate. Even Victor Martinez himself could score from there. Should the third base coach get credit for that? In theory, it should all even out in the end, and yes to test this, you'd need to video inspect all such plays over a season...

    Agreed Pizza Cutter. Or alternatively use zone information (which we don't have at this point).