This article, and the research supporting it, grew out of a Twitter discussion before the trade deadline, when I was periodically deriding the notion that Andrew Benintendi would be a valuable addition to a contending team.   At the time he was traded from the Royals to the Yankees, KC had played 98 games; Benintendi had scored 40 runs and driven in 39.  He was on pace to score 66 runs by season’s end and drive in 64.  Those are not good numbers.  He had a .320 batting average, yes, but with a secondary average of .202.  Secondary average is a summation of power, walks and stolen bases.  Benintendi’s then-teammate M. J. Melendez at that time was hitting .228, but with a secondary average over .300.  He was driving in and scoring runs at a more rapid pace than Benintendi was, with the same team.  A Twitterspat developed in which others were arguing that Benintendi was only driving in and scoring two runs a week because he was playing on a weak offensive team, and I was arguing that he was only driving in and scoring two runs a week because his .320 batting average was an empty shell. 

            I was being hoisted here upon my own petard.  It would help me out if I actually knew what a petard was, or is.  Do you have any petards in your house?  How about a hoist?  The expression "hoisted on your own petard", which may be archaic, means that you have become the victim of your own argument, or your own weapon. Decades ago, I was the one telling people to stop paying attention to Runs Scored and RBI, but to focus instead on what the batter himself has done. At one time I was virtually the ONLY person in the baseball writing universe who would make that argument.  Now, that position is SO dominant that if you site runs scored and RBI—even appropriately—somebody will ridicule you for it.

            In the midst of this twitterspat, someone—actually a very nice person who was simply trying to have a fair discussion—wrote to me "but isn’t it true that Runs Scored and RBI are mostly a creation of the players hitting around you?"  I responded instinctively, "Well, no, that’s not remotely true."  But then it occurred to me:  I don’t really know, do I?

            I had spotted a gap in my understanding of the game.   This is what I live for. My life’s work has been to spot gaps in my understanding of the game or my understanding of something else, and figure out how to fix those gaps, how to plaster some actual knowledge into that gap. That’s what I do, that’s who I am, that’s why you know who I am.  I have never actually studied the relationship between a player’s runs scored/RBI and his run creation.  As far as I know, no one has ever studied it.  It’s a gopher hole in our putting green, a pot hole on our highway, a rip in our underwear.   Somebody needs to fix it.

            For the rest of this article I will often refer to Runs + RBI as "Run Participation".  

            My first effort to study the issue was to do a matched-set comparison.  Essentially, I was trying to identify sets of players who hit the same number of singles, the same number of doubles, triples, homers, drew the same number of walks and stole the same number of bases, but one of whom played for a good team and the other of whom played for some bunch of losers.  I love doing matched-set studies, because it is just fun to see who turns up matched with who.  It has probably never occurred to you, I am guessing, to pair up Ken McMullen, 1969, with Hector Lopez in 1956, but McMullen in 1969 was 153-for-562, and Lopez in 1956 was 153-for-561.   McMullen had 25 doubles, 2 triples and 19 homers, whereas Lopez had 27-3-18, which is pretty much the same.  McMullen had 239 total bases, Lopez had 240.  There’s a small difference in walks (70-63), but both players stole 4 bases and were caught stealing 5 times.  They’re a match.  

            After working on this problem for two or three days, I had identified 300 matches like this—Patsy Tebeau in 1894 with Homer Smoot in 1904, for example.   Tommy Harper in 1971 and Jason Kipnis in 2012.   My assumption was that if you took two players who had almost exactly the same numbers of singles, doubles, triples and everything, then you could identify those who played for strong offensive teams and those who played for the Wimps and the  Weenies, and you could measure the extent to which playing for a good team increases a player’s run participation rate.  

            That was what I was trying to do, but I didn’t know exactly HOW I was going to do it.  I was in "I’ll cross that bridge when I come to it" mode, but when I actually came to that point. . . no bridge.  I couldn’t figure out a good way to complete the study.  I had just wasted two or three days, although, you know, when you meet Homer Smoot in your research, it is never truly a wasted day. 

            Then it occurred to me that there was a better way to study it.  One of the implicated issues here is the effect of batting third, let’s say, as opposed to the effect of batting leadoff, or batting eighth.  What I did next, then, was to go to Retrosheet and copy out teams’ "splits" for hitters who hit first, second, third, fourth. . . .ninth, etc.  I did that for every major league team in the years 2010 to 2021 except 2020.  It’s a total of 330 teams, or 2,970 batting lines.   (11 seasons, 30 teams per season, 9 batting lines per team, 11 X 30 X 9 = 2970.) 

            We’re no longer dealing with individual players now, we’re now dealing with batting lines compiled somewhat by a mix of players, but that’s actually a littles better for what we are studying.  We’re studying what the effects of the OTHER players are on the focus player’s runs and RBI.  Any peculiarities of the individual player, such as for example if he is an exceptionally good or exceptionally bad baserunner.. ..anything like that is a screen obscuring what we are really trying to measure.  Using mixes of players, rather than individual players, gives a slightly cleaner look at the issue—plus, each line of the study now represents 162 complete games, rather than sometimes 155 games and sometimes 109, which is also better for the study. 

            Then I figured the Runs Created by the batting stats at each position.   For example, the leadoff men for the Houston Astros in 2019 hit .276, but with 50 homers, 89 walks, 134 Runs Scored, 122 RBI.  133 Runs Created.  I think that was mostly George Springer.  The key numbers there are 133 Runs Created, 134 Runs Scored, 122 RBI. 

            The first thing we have to establish here is the normal relationship of Runs Participated In to Runs Created.   For every 100 Runs Created there are 100 Runs Scored and 95 RBI, so the overall ratio is 1.95 to 1. 

            This ratio, however, is not the same for cleanup hitters as it is for 8^th place hitters, for example.  Well, actually it pretty much is.

            The ratio of Runs Created to Run Participation is essentially the same for the 2^nd through the 8^th spots in the batting order.   The ratio of Runs/RBI to Runs Created for cleanup hitters is 1.98 to 1. For 8^th place hitters, it is 1.98 to 1. Third-place hitters have a 4% disadvantage in terms of run participation, a little bit less than 4%; second-place hitters are at a 3% disadvantage.  No other position, 4 through 8, has an advantage or disadvantage as large as 2%. 

            Leadoff hitters, however, are at a small but meaningful disadvantage.  The 330 leadoff "hitters"—actually the leadoff positions for the 330 teams.  Anyway, the leadoff men created an average of 93 runs, based on their individual batting stats.  They scored an average of 102 runs but, for reasons you can figure out yourself unless you are secretly Dan Shaughnessy, they drove in an average of only 65.   That’s a ratio of 1.80 Runs Participated in for each Run Created, which is 8% below the norm of 1.95. Leadoff hitters are at an 8% disadvantage in the RBI/Runs Scored categories, all of which is in the RBI portion, of course. 

              And ninth place hitters have a 24% advantage in Run Participation, actually 11% in the American League and 42% in the National League.

            Very weak hitters have somewhat non-representative runs scored and RBI, because it IS a shared activity.  A hard worker and a lazy man go into business together and split the income, the lazy man will be overpaid and the hard worker will be underpaid.  Same thing.  When a good hitter and a bad hitter combine to create runs, the bad hitter gets more than his share of Run Participation. I will refer to that as the good hitter/weak hitter effect. 

            OK, we’re creeping toward a better understanding of this, but what we are trying to get to is discrepancy vs. expectation.  A player, by his own production, creates an expectation for how many runs he should participate in.  That expectation is 1.95 times his runs created.   But, because of his circumstances, his teammates and his batting order position and other things, he won’t exactly meet expectation.  That’s the discrepancy.  What we are asking here is, to what extent are the player’s run participation totals created by expectation, and to what extent are they created by the discrepancy?   You can call it expectation and discrepancy, or you can call it production and context; in this discussion it means broadly the same thing.  Did Andrew Benintendi not participate in very many runs mostly because of expectation (his production), or because of discrepancy (context) ?   If it is 70/30 discrepancy, then we should barely glance at runs scored and RBI totals as we are on the way to the hotdog stand.   But if it is 20/80 toward expectation, then the people who say we shouldn’t pay any attention to Runs and RBI are missing out on valuable information.  

            I’ll give you a temporary, first-hit answer to that question.  Of the variance in run participation between different hitters, 65% is created by the variance in productivity (that is, created by expectation) and 35% is created by all other factors.  How do we know that? 

            Well, the 2,970 "players" created an average of 79 runs, and the variation between expected runs and actual run participation (discrepancy) is an average of 16 runs, so that would suggest that the answer is 83% expectation, 17% discrepancy.  That, however, is the wrong way to look at the data.   What we need to look at is not how many of the runs are created this way or that way, but how much of the difference between one hitter and another hitter is explained in this way (expectation or performance) or that way (discrepancy or context.)   What we need to look at is not the average of runs, but the standard deviation. 

            The average is 79 runs created (per batting order slot), but with a standard deviation of 23.65.   The average discrepancy from expected run participation is 20.49, but that has been "stretched out" by the fact that we have multiplied runs created by 1.95 in order to create that figure, so it’s no longer on the same scale as runs created.   Adjusting for that problem, the standard deviation of the discrepancy is 12.79. . . .I don’t know if this is making any sense to you anymore, but if you read it three or four times it should.   So the relevant figures are:

            Standard deviation of expectation (productivity):            23.65

            Standard deviation of discrepancy (context):             12.79

            So our estimate, at this point, is the split is 65/35.  We would currently estimate that 65% of a player’s run production is based on his own productivity, and 35% is based on other factors.   But we’re not to the end of the road yet.  As a parenthetical aside, the discrepancy does not INCREASE the standard deviation of Runs Participated In; it decreases it.   It decreases it because of the good hitter/weak hitter effect.   A great hitter will have a lower ratio of RPI to runs created than a weak hitter, which pushes everybody toward the center, which decreases the standard deviation of runs participated in. 

            But as I said, we’re not at the end of the road yet.  What we have here is the discrepancy—in other words, the difference between the number of runs we would expect the player to participate in vs. the number he actually participated in.  But there are many different things that contribute to that discrepancy.   There are really three categories of things that can cause a player to participate in more runs than expected or fewer runs than expected:

1)     Special characteristics of the player, such as baserunning or performance with runners in scoring position,

2)     Luck, or

3)     Playing for a good hitting or weak hitting team. 

We are only interested in Category 3.  Did Andrew Benintendi not participate in very many runs with Kansas City because the KC offense was poor, or was it something else?   

            Here’s how we can study that.   Suppose that we divide the candidates into a 7 by 6 matrix—seven layers of hitters, and six layers of teams.   Group 1 A is the best hitters (that is, the strongest batting slots) who created the most runs by their own actions, and who play for the teams that score the most runs.  Group 1 B is the best hitters, who play for good-hitting teams but not THE BEST hitting teams.  Group 1 F is really good hitters playing for really weak-hitting teams, while Group 6 A is very weak hitters playing for good hitting teams.  These are the charts that were used:

            So a hitter in Study Group 3A would be a "hitter" (actually a batting order position) who created 85 to 92 runs, playing on a team that scored 785 or more runs, whereas a hitter in group 3F would be a hitter who created 85 to 92 runs, but playing on a team that scored 634 or fewer runs.  The question is, what is the effect on the player’s Run Participation of playing on a good-hitting team, as opposed to a weak-hitting team? 

            Since we are talking 3A and 3F. . . .3A is somewhat above-average hitter who plays for a team that scores lots of runs, and 3F is a somewhat above-average hitter who plays for a team which scores very few runs.   There are 66 players in the study in group 3A, and 59 players in group 3F.  This chart gives the number of players (positional batting lines) represented in each of the 42 cadres of the study:

            That will show you that there are more good hitters on teams that score more runs, but you probably could have figured that out on your own. 

            The real work here is to compare the Run Participation Numbers for players of essentially the same offensive quality.   We’ll start with 3A and 3F:

            The 66 players in Group 3A created an average of 88.5 runs, and participated in an average of 178.6 runs, which we could say would be 92 runs scored and 87 RBI.  The 59 players in Group 3F created an average of 88.4 runs, and participated in average of 157 runs, which we could say was 80 and 77.  

            So that’s what playing for a great hitting team as opposed to a weak-hitting team means; you get 92 runs scored and 87 RBI, as opposed to 80 and 77.  An extra 12 runs and 10 RBI.

            This little slice of the data—that is, the data for players in the "3" group—would suggest that a player playing on a very weak offensive team is working at a 7% disadvantage in terms of Run Participation (7% compared to the average), and a hitter playing for a really good hitting team has a 6% advantage, compared to the average.  This chart summarizes the data for all 42 player groups in the data, and for all seven levels of hitters:

            Combining the data from all seven groups, we reach the conclusion that a hitter playing in a very strong offensive lineup (785 runs scored or more) has a 7% advantage in Runs Scored and RBI, as opposed to a player on an average team.   A player on a very weak offensive team (634 runs scored or less) has a 6% disadvantage in terms of runs scored and RBI, as opposed to a player on an average team.   A player on a very strong team has a 14% advantage in terms of runs scored and RBI, as opposed to a player on a weak offensive team. 

            I think the data shows that I was basically right about Benintendi, but there’s no gloating in science; just take it for what it is.  The split between expectation and discrepancy is 65-35, but a relatively small portion of the discrepancy is actually attributable to team context.  Therefore, it is unwise to ignore run participation in evaluating a player, because the team context issue is only about a 14% distraction in the extreme case. 

            There is another issue that came up in the course of the Twitter discussion. One guy, joining in the discussion, wrote that. . . .well, it’s Twitter, so I had a little bit of trouble understanding EXACTLY what he was saying.  But I think what he was saying was that, comparing two players who create the same number of runs, but one of whom hits more home runs than the other, then the player who hits more home runs will drive in/score more runs, because, of course, the Home Run is guaranteed to be attached to at least one run scored and one RBI.

            I did not comment on that thread of the discussion, because I did know at that time whether what the man was saying was or was not true.  Having now studied the issue (as a part of this research), I can confirm that the gentleman’s claim is quite certainly true. 

            That part of the study was done by creating matched sets of players—that is, players who "created" exactly the same number of runs, but one of whom hit significantly more home runs than the other.  For example, the second place hitters for the 2017 Milwaukee Brewers and the leadoff hitters for the 2011 New York Mets are each credited with creating 124 runs.   However, the second place hitters for the 2017 Brewers (mostly Eric Thames and Domingo Santana) hit 40 home runs; they hit .271 with 2 triples and 11 stolen bases, but they did hit 40 home runs.  The leadoff hitters for the 2011 New York Mets (mostly Jose Reyes) hit .318 with 16 triples and 49 stolen bases, but only 11 home runs.  The 2011 Mets had 228 hits from their leadoff men, as Jose Reyes won the batting championship; the 2017 Braves had 168 hits from their #2 hitters, although they did walk a lot.

            A second example, to illustrate the point with less productive hitters, the 8^th place hitters for the 2021 Texas Rangers and the 8^th place hitters for the 2012 San Francisco Giants are each credited with creating 50 runs in 162 games, which is a very low number.   But the 8^th place hitters for the 2021 Rangers hit just .216, but with 16 homers.  The 8^th place hitters for the 2012 Giants hit for a little bit better average (.232), hit more singles (101-75), hit more triples, drew more walks, and grounded into half as many double plays (9 vs. 18), but hit only 3 home runs.  The 26 singles and 9 double plays, etc., offset the 13 home runs, so they created just as many runs. 

            There were 442 players in each part of the study; it is really easy to find matched sets of players when you are only matching them on two parameters, actually matching them on one parameter (runs created) and dividing them on the other (home runs.)  But in that study, the home run hitters hit an average of 28 home runs.   The non-home run hitters, although they were better at almost everything else, hit an average of only 10 home runs. 

            The singles hitters scored an average of 80 runs; the power hitters scored an average of 79.  But the singles hitters drove in an average of only 61 runs; the home run hitters drove in an average of 85.  The 18 extra homers of the power-hitting group led to an increase of 23 extra Runs Participated In.  

            That number was exaggerated somewhat because the singles-hitting group had far, far more leadoff men than the power-hitting group, and (as demonstrated earlier in the article) leadoff men are at a competitive disadvantage when it comes to driving in and scoring runs.  Of the 442 power-hitting positions in the study, less than 10% were leadoff men or #2 hitters.  Of the 442 singles hitters, just barely short of half were leadoff men or #2 hitters.  That emphasized the run participation advantage of the power hitters, but certainly did not create it.  

            Thank you all for reading.