Assessing the Accuracy of Runs Created: Comparing Outside and Inside Aggregation Methods

Any accuracy assessment of Bill James’s Runs Created (RC) requires aggregating the individual batters’ RCs and then comparing that total to the team’s actual runs scored.1 This seems simple enough until one realizes that the RCs of the individual batters can be aggregated in two different ways. We can apply the RC formula for each individual, then simply sum those stand-alone RCs to arrive at an aggregated team RC. I will call this aggregation method the Outside Aggregation Method. On the other hand, we can apply the RC formula to the team’s combined statistics. I will call this second method of aggregation the Inside Aggregation Method.

In this article, I assess the accuracy of both the inside and outside aggregation methods for four Runs Created measures: Basic Runs Created (BRC), Stolen Bases Runs Created (SBRC), the First Version of Technical Runs Created (TechRC), and the Second Version of Technical Runs Created, which accounts for strikeouts (TechKRC).2 For all four RC measures, I find that inside aggregation is always more accurate than outside aggregation. This is probably not surprising for two reasons in particular. First, each batter’s productivity depends on the performance of the batters who come before and after him. As Bill James wrote, “players’ individual totals do not occur in an individual context.”3 Second, players who don’t play much may have to be neglected from outside aggregation because their stand-alone RC cannot be defined. For example, a player whose only plate appearance produced an RBI on a sacrifice fly earned neither an at-bat nor a walk. This players’ stand-alone BRC/SBRC is not calculable because the denominator is zero. Thus, his batting stats cannot be incorporated into his team’s seasonal outside-aggregated Runs Created, but it can be incorporated into inside-aggregated Runs Created.

Additionally, this study finds that, for a given aggregation method, the BRC formula is the most accurate while the TechRC formula is the least accurate. Thus, of the eight aggregated RC formulas assessed (two for each aggregation method), the inside-aggregated BRC is the most accurate while the outside-aggregated TechRC is the least accurate. This is a curious finding, since it suggests that RC formulas with more inputs are not necessarily more accurate. However, including strikeouts does seem to improve accuracy—since the strikeout version of technical runs created, or TechKRC, is more accurate than the first TechRC—although TechKRC is still less accurate than BRC and SBRC.

WHAT IS RUNS CREATED?

a. Runs Created Versus Runs Produced

At its core, Runs Created is a formula that measures how many runs a given batter’s offensive performance contributed to his team’s run total.4 Specifically, it tells us how many scored runs can be attributed to a specific batter. The best way to explain Runs Created is to compare it to its predecessor, Runs Produced. Runs Produced was first developed by Bob Creamer and came to public attention in Sports Illustrated.5 Runs Produced (or RP) is a simple formula that adds a batter’s RBIs to his Runs Scored (RS) and subtracts his Home Runs (HR).

RP=RBI+RS–HR

Home runs are subtracted to prevent double counting, since a home run necessarily gives a batter both an RBI and a run scored. However, this measure can greatly underestimate or overestimate the contribution of a batter because it fails to recognize that runs are often the product of multiple contributors. For instance, consider Jorge Mateo’s 2022 season, shown in Table 1.

 

Table 1. Jorge Mateo’s 2022 Batting Line

 

Mateo scored 63 runs and drove in 50, 13 of them on home runs, so he produced 100 runs.

RP=50+63–13 = 100

Because Mateo only hit 13 home runs, a later batter’s performance contributed towards 50 of the runs he scored, and an earlier batter’s performance contributed towards 37 of the RBIs he earned. Runs Created overcomes this misattribution issue by considering only those batting stats that a given batter can control. Bill James’s original Runs Created formula was:

This formulation is often called Basic Runs Created, or BRC, where (H + BB) is the “on-base factor,” TB is known as the “base-advancement factor,” and (AB + BB) is the “opportunities factor.” Thus, Mateo had 494 + 27 = 521 opportunities, out of which he got on base 109 + 27 = 136 times. Additionally, Mateo advanced to 187 total bases.

Thus, Mateo may have “produced” 100 runs in 2022, but he only “created” approximately 49 runs.

B. Why Is Runs Created Better Than Runs Produced?

While Runs Produced may be an immediately intuitive measure of a batter’s contribution, it fails to acknowledge the contributions of other batters. As Bill James argues, Runs Produced does NOT give any credit to a batter whose plate appearance does not result in a run or an RBI but nonetheless facilitates the base advancement necessary for another batter to score.6 A hypothetical can better illustrate this point. It’s the start of a new inning for the Orioles. Austin Hays is first up to bat and Mateo is on deck.

The Hypothetical Inning

1. Hays bats first and strikes out. There’s one out and nobody on base.
2. Mateo walks. There’s one out and a runner on first. See Sub-figure A in Figure 1.
3. Ramón Urías doubles, advancing Mateo to third base. There’s one out with runners on second and third. See sub-figure B.
4. Anthony Santander flies out and both runners tag up. Mateo scores and Urías advances to third. There are two outs and a runner on third. See Sub-figure C.
5. Adley Rutschman strikes out. The inning ends with a runner stranded at third. See Sub-figure D.

 

Mateo earns a run for scoring, while Santander gets an RBI for driving in the run with his sacrifice fly ball, but what about Urías? Does he receive any credit for this run? According to the Runs Produced formula, Urías does NOT, even though it was his double that advanced Mateo from first to third. What’s more, we can see that although only one run actually scored, two runs were “produced,” one for Mateo and one for Santander. Despite the home run correction, Runs Produced continues to double count while underestimating some contributions, because every time a batter scores a run, one of his teammates must earn an RBI (except in the case of an error or double play). Runs Created overcomes this issue by using only stats that are uninfluenced by other batters.

C. Runs Created Conceptually

Bill James eventually generalized Runs Created to include other batting stats, such as stolen bases (SB), caught stealing (CS), and hit-by-pitches (HBP). All formulations of Runs Created have the general structure shown in Equation (1) below.

“A” is the on-base factor, “B” is the base-advancement factor, and “C” is the opportunities factor. For Basic Runs Created, the ABC factors are defined below.

A later iteration included the effects of stolen bases and caught stealing. This Stolen Bases Runs Created version (or SBRC) has the following ABC factors.

Notice that a batter’s on-base factor is reduced by one each time he gets caught stealing, while his base-advancement factor increases by 0.55 for each base successfully stolen.

More “technical” versions of RC were later developed. The first of these, denoted as TechRC, accounts for sacrifice flies (SF), bunts (SH), double plays (GIDP), hit-by-pitches (HBP), and intentional walks (IBB). The TechRC version has the following factors.

A subsequent technical version of Runs Created accounts for strikeouts (K). This version is called TechKRC and is calculated using the same on-base and opportunities factors as TechRC, but a different base-advancement factor that is calculated as follows.

Using the data in Table 1 and the fact that Mateo struck out 147 times in 2022, Table 2 displays four measures of his Runs Created during the 2022 MLB season. Mateo created between 49 and 50 runs, depending on the measure used. Regardless, his Runs Created were roughly half of his Runs Produced.

 

D. What Basis Is There for Runs Created?

The crucial argument of Runs Created is that scoring is the result of two interacting effects: an on-base effect and a base-advancement effect. As Eric Walker writes, there is a mathematical identity within a team’s total plate appearances in a season, a game, or even just an inning.7 This identity states that in any timeframe as broad or broader than an inning, total plate appearances must always equal the sum of outs, stranded runners, and runs. This is shown in Equation (2) below.

Recall the hypothetical Orioles inning in which there were three outs, one runner left on base, and one run scored. According to Equation (2), this must mean there were 5 = 3+1+1 PAs, which is indeed true. Equation 2 can be solved to isolate R by itself as Equation (2’) shows.

The first term on the right-hand side of Equation (2’) is the difference between plate appearances and outs, which might be called “excess plate appearances,” since there must always be at least as many plate appearances as outs. Equation (2’) essentially says that a team scores runs by earning more excess plate appearances and stranding fewer runners.

Excess plate appearances are directly related to reaching base, since a team earns one additional plate appearance every time a batter gets on base. Recall the hypothetical inning where Mateo and Urías reached base, creating two excess plate appearances. The second term on the right-side of (2’), runners left on base, is inversely related to base advancement because base advancement necessarily reduces the number of men left stranded on base at the conclusion of an inning. A team that reaches base more often will earn more PAs, and when base advancement prevents fewer of those runners from being left on base, the team must necessarily score more runs. Although Equation (2’) does not specify how the batters reach base or advance, it nonetheless shows that those two actions combine to create runs. As a result, it validates the crucial argument of Runs Created.

AGGREGATING RUNS CREATED AT THE TEAM LEVEL

A. Outside Aggregation Versus Inside Aggregation

Runs Created can be aggregated from the individual level to the team level through two different methods: outside aggregation and inside aggregation. To provide the clearest explanation possible, it is best to first differentiate between Stand-Alone RC and Team-Season RC. Stand-alone RC pertains to the runs created by a particular batter. For instance, consider Table 3, which lists the batting stats for the Atlanta Braves during the 2022 season.

 

Using the BRC version, Dansby Swanson created 93.81 runs.

Swanson’s on-base factor was 226, since he earned 177 hits and 49 walks from balls. His base-advancement factor was 286, and his opportunities factor was 689.

The right-hand column of Table 3 shows the stand-alone BRC for each batter. The outside aggregation method simply adds all the stand-alone RCs of all the batters. Notice that the outside aggregated BRC, or BRCOut, is 771.44, off by approximately 18 runs from the Braves’ actual run total of 789.

The inside aggregation method, on the other hand, adds the individual RC factors first, and then calculates Runs Created using Equation (1). For instance, finding the team-season BRC for the Braves in 2022 requires one to first add all the A factors for each batter to get the team on-base factor, or A_team, as shown below.

As a team, the Braves got on base 1,864 times during the 2022 season. The same must be done for the B and C factors to find the team base-advancement factor, or B_team, and the team opportunities factor, or C_team. The Braves advanced through 2,443 bases, and they had a total of 5,979 opportunities. The inside aggregation method simply applies Equation (1) using the factors A_team, B_team and C_team.9 Thus, the Braves inside-aggregated Basic Runs Created, or BRCIn was 761.62.

The crucial difference between outside aggregation and inside aggregation lies in the sequence of calculations. Outside aggregation applies Equation (1) first then takes the sum, whereas inside aggregation takes the sum of individual factors first then applies Equation (1).

B. Marginal Runs Created

The inside aggregation method allows for an alternative measure of individual batter runs contributions. Recall that Swanson had a stand-alone BRC of 93.81 runs in his 2022 season with the Braves. If Swanson had the same hitting stats in 2022 but had instead played for the Cubs (his current team), his stand-alone BRC would still be 93.81, but the marginal runs created due to his batting would be different. In other words, a batter’s performance as measured by stand-alone RC potentially implies different inside-aggregated Runs Created for different teams. This leads to an alternative measure called Marginal Runs Created, or MRC. An individual batter’s MRC for a particular season essentially imagines what his team’s inside-aggregated Runs Created would be if the batter did not play that season. The difference between his team’s actual inside-aggregated RC and the inside-aggregated RC without his batting performance is the marginal runs contributed by the batter to his team in that season.

For instance, let’s consider what would have happened to the Braves’ 2022 total inside-aggregated Basic Runs Created if Swanson had not batted at all. Their on-base factor would fall to 1,638, since the Braves got on base 1,864 times, while Swanson himself got on base 226 times. Additionally, the Braves would have advanced 2,157 bases and would have had only 5,290 opportunities. Thus, their inside-aggregated BRC would fall from 761.62 to 667.90. meaning Swanson’s Marginal Basic Runs Created was 93.72.

In other words, the Braves would have 93.72 fewer BRC without Swanson’s batting performance. Swanson’s Marginal BRC is within a tenth of a run of his stand-alone BRC. However, as section five will show, on rare occasions, the MRC and stand-alone RC can differ by as much as 27 runs.10

ASSESSING THE ACCURACY OF RUNS CREATED

A. Data and Procedures

Two sets of batting data were downloaded from FanGraphs, covering 30 franchises over the 21-season period from 1999 to 2019.11 Let j denote a given team-season. The first data set consisted of franchise-level stats, while the second consisted of player-level stats. To ensure that all measures would be calculable (that is, no zero in the denominator), player-team-seasons with zero opportunities (i.e., the C factor) were eliminated. Using these refined data sets, the four RC measures (BRC, SBRC, TechRC, TechKRC) were then calculated for each player-team-season. Afterwards, the outside-aggregated values of BRC, SBRC, TechRC, and TechKRC were calculated for each of the 630 team-seasons by summing all the relevant stand-alone RCs. Players who changed franchises in the midst of a regular season had their RCs split among their respective franchises.

B. Accuracy Assessment Methodology and Results

I calibrated the data to assess the accuracy of the inside and outside Runs Created measures.12 Intuitively, a given RC’s accuracy is judged by how well a scatter plot of runs created versus runs scored fits around the 45-degree line. An accurate RC metric will have a scatter plot that aligns evenly around the 45-degree line, with a tighter scatter indicating greater precision. This means that a simple regression between a given RC measure and actual runs scored (or R for short), should have a slope coefficient equal to one and an intercept equal to zero.

Consider the unrestricted regression shown in Equation (3), where ê_ju is the regression’s residual. The chosen RC measure of RC_j would be considered an accurate measure of runs scored R_j if the estimated slope coefficient is indistinguishable from one and the estimated intercept coefficient β is indistinguishable from zero. Consider Figure 2, which shows a scatterplot of actual runs scored for a given team-season on the vertical axis and the inside-aggregated stolen-bases form of RC, or SBRC, on the horizontal axis.

 

Figure 2. Inside Aggregated SBRC and Actual Runs Scored

 

The dots are fairly evenly distributed around the dashed 45-degree line, indicating that the inside-aggregated SBRC is fairly accurate. However, notice that the regression line, denoted by the solid line, begins to lie slightly below the 45-degree line for team-season observations where 700 or more runs are scored or created. For team-seasons below 700, the regression line largely overlaps with the 45-degree line. The estimated regression equation for the solid regression line in Figure 2 is:

R_j=21.3783+0.96113 • SBRC_j + ê_ju

SBRC_j is the inside-aggregated SBRC for the jth team-season. As the regression line and regression equation both confirm, the inside-aggregated SBRC measure is accurate, but it slightly over-predicts the actual runs scored in seasons when more than 700 runs are score.

It turns out that Basic Runs Created, or BRC, is the most accurate of the Runs Created measures. Figure 3 shows the scatter plots of aggregated BRC against actual runs scored. The scatterplot at the top uses the inside-aggregation method while the scatterplot at the bottom uses the outside-aggregation method. The solid regression line for the inside-aggregated BRC measure overlaps with the 45-degree line entirely until around 800 runs. The outside-aggregated BRC is clearly less accurate. Its regression line never overlaps with the 45-degree line, consistently overpredicting the actual runs scored.

 

 

The technical version of Runs Created, or TechRC, is the least accurate. Figure 4 shows the calibration scatterplots, in which neither regression line ever overlaps with the 45-degree line. Similar to BRC, inside aggregation is more accurate than outside aggregation.

 

Figure 4. Technical Runs Created Calibration

 

Regardless of the RC measure under examination, the outside-aggregation method is always less accurate. Figure 5 shows the regression lines for all eight aggregated measures of Runs Created.13 The left-hand side shows the inside-aggregated measures and the right-hand side shows their outside-aggregated counterparts. Notice that the regression lines for the inside-aggregated measures are always much closer to the 45-degree line. None of the regression lines for the outside-aggregated RCs overlap with the 45-degree line, while three (BRC, SBRC, and TechKRC) of the inside-aggregated RCs do overlap with the 45-degree line at some point.

 

 

Figure 5 clearly shows that the inside-aggregation method of Runs Created is always more accurate than the outside-aggregation method of Runs Created. This makes intuitive sense because the inside-aggregation method still allows for each batter’s performance to interact with his teammates’ batting performance. However, any Runs Created measure is more accurate than a Runs Produced measure. Even after adjusting for the inherent double-counting, the aggregated Runs Produced always underpredicts actual runs scored. Runs Created tends to slightly overpredict actual runs scored regardless of aggregation method, but one-half Runs Produced tends to greatly underpredict the actual runs scored, while the full Runs Produced overpredicts. This inaccuracy is presumably due to the definition of an RBI, which excludes runs scored thanks to an error. If errors never occurred, then a team’s RBIs would nearly always equal its runs scored (after accounting for double plays). Excluding errors creates a lot of noise because there is always human judgment involved in determining errors.

Comparing the regression lines for the inside-aggregated BRC and SBRC measures, it is difficult to immediately determine which measure is closest to the 45-degree line, and therefore more accurate. A more quantitative criterion for accuracy is needed. We can do this by comparing each RC measure’s respective unrestricted regression equation, like that in Equation (3), to a restricted regression equation that describes the 45-degree line where ê_jr is the residual of the restricted regression equation:

Notice that Equation (4) restricts the coefficients of Equation (3) so that ß = 1 and α = 0. Let MSE_u be the mean squared error of the unrestricted regression.

And let MSE_r be the mean squared error of the restricted regression.

Generally, the restricted MSE, or MSE_r, can assess the accuracy of a given metric, but if the more accurate metric is also much less precise, then the simple restricted MSE may not properly discern which metric is more accurate. For this reason, MSE_u will be compared to MSE_r to make a final determination of accuracy. Specifically, a certain RC measure is deemed more accurate if its MSE increases by a smaller percentage as a result of restricting its regression to the 45-degree line. Let %ΔMSE denote this percentage.

Thus, a smaller value for %ΔMSE indicates greater accuracy, so one might think of %ΔMSE as a measure of inaccuracy.

Consider the inside-aggregated SBRC as analyzed in Figure 2. The MSE for the unrestricted regression is MSE_u = 573.9972, while the MSE for the restricted regression is MSE_r = 646.7579. Thus, restricting the inside-aggregated SBRC regression equation to the 45-degree line raises the MSE by 12.68%.

Now consider the inside-aggregated BRC analyzed at the top of the graph of Figure 3. With an MSE_u of 590.1641 and an MSE_r of 632.8687, restricting the inside-aggregated BRC regression to the 45-degree line raises the MSE by 7.24%.

The inside-aggregated measure of BRC is more accurate than the inside-aggregated measure of SBRC because its regression has a lower percentage-deviation from the 45-degree line. Note that this is in spite of the fact that the SBRC regression has a slightly larger R-squared value (92%) than that of BRC regression (91.78%).13

Figure 6 shows a bar chart of the percent increase in MSE for each of the eight aggregated Runs Created measures under consideration. Inside-aggregated RCs are represented by a lighter bar while outside aggregated RCs are represented by a darker bar. Two general insights can be immediately gleaned from Figure 6.

 

 

First, the less complex measures of Runs Created are more accurate, regardless of the aggregation method used. For a given aggregation method, the BRC and SBRC formulas are always more accurate than the TechRC and TechKRC formulas. Second, the inside-aggregation method is always more accurate than the outside-aggregation method, regardless of the RC formula examined. The inaccuracy of the outside-aggregation method is anywhere from three to 10 times greater than that of the inside-aggregation method. Overall, the inside-aggregated measure of BRC is the most accurate, while the outside-aggregated measure of TechRC is the least accurate.

The accuracy statistic %ΔMSE is essentially the F-statistic for testing the hypothesis of whether the unrestricted regression in Equation (3) is statistically different from the 45-degree line regression in Equation (4), but without accounting for the degrees of freedom ratio

Because the regression in Equation (3) has two estimated coefficients, α and ß and the regression in Equation (4) has two restrictions, α = 0 and ß = 1, the degrees of freedom are df₂ = 628 and df₁ = 2. Thus, the degrees of freedom ratio is

Multiplying each %ΔMSE by this ratio will give the F-statistic for testing whether the regression Equation (3) is statistically different from the 45-degree line, such that:

The F-statistic for the inside-aggregated BRC is 22.734, while the F-statistic for the inside-aggregated SBRC is 39.815. For either of these RC measures, the probability of finding such a large F value under the assumption that the regression equals the 45-degree line is effectively zero. This means the regression equations for the inside-aggregated BRC and SBRC are statistically different from the 45-degree line under any usual significant level (i.e., 10%, 5%, 1%, and so on). The same is true for the two other inside-aggregated RCs, as well as all the outside-aggregated RCs. Thus, while the Runs Created measure is significantly more accurate than Runs Produced, Runs Created is still inaccurate in terms of statistical significance. Nonetheless, Runs Created, especially inside-aggregated BRC, is still an accurate runs contribution measure for most practical purposes.

PLAYER-LEVEL RUNS CREATED: MARGINAL VERSUS STAND-ALONE

Stand-alone Runs Created is generally larger than Marginal Runs Created. Figure 7 compares the average player-level MRC to the average player-level stand-alone RC. The left-hand side of Figure 7 shows the median player-level runs created. Notice that the median major-league batter created 4.7 marginal runs and 5.3 stand-alone runs. On the other hand, mean player-level Runs Created is approximately four times larger than the median player-level Runs Created. As the right-hand side of Figure 7 shows, the average batter earned around 22 marginal Runs Created and around 23 stand-alone Runs Created. Figure 7 thus demonstrates that the average stand-alone RC is larger than the average MRC regardless of the RC formula or the type of average.

Because inside aggregation is more accurate than the corresponding outside aggregation, it stands to reason that marginal Runs Created (MRC) is a more accurate measure of a given batter’s runs contribution than stand-alone RC. That said, stand-alone RC does not deviate substantially from marginal RC. To assess how MRC differs from stand-alone RC, statistical estimates were evaluated for the absolute deviation between MRC and Stand-Alone RC, which will be simply called the Absolute Deviation, or AD for short. The Absolute Deviation for a given player-team-season p, or AD_p, is thus defined as:

MRCp is the marginal runs created for player-team-season p and saRCp is the stand-alone Runs Created measure for player-team-season p. Figure 8 below shows the 90th percentile, the 75th percentile, mean, and median absolute deviations of the player-team-seasons using the BRC and TechRC formulations.

 

Figure 8. Absolute Deviation Between Marginal and Stand-Alone Runs Created

 

The median absolute deviation is about 0.3 runs, while the mean absolute deviation is about 0.67. According to the 75th percentile, the absolute deviation between MRC and saRC differs by less than one run 75% of the time. Likewise, the 90th percentile shows that the absolute deviation between MRC and saRC differs by less than two runs 90% of the time.

That said, there are some outlier players whose stand-alone BRC exceeds their marginal BRC by more than 13 runs. The left-hand side of Table 4 shows the top 10 player-team-seasons for which stand-alone BRC exceeded Marginal BRC. Notice that the table consists of well-known sluggers like Barry Bonds, Sammy Sosa, Albert Pujols, and Bryce Harper. Bonds in particular is on the table for four different seasons and holds the top three spots. In 2001, his stand-alone RC exceeded his MRC by nearly 27 runs. For all the sluggers listed, stand-alone BRC exceeds Marginal BRC by at least 13 runs.

 

Table 4. Top Differentials Between Stand-Alone BRC and Marginal BRC

 

The right-hand side of Table 4 shows the top ten player-team-seasons for which stand-alone BRC falls short of Marginal BRC. Notice that the overall runs created for these players are generally less than those for the players on the left-hand side. What’s more, the deviations between stand-alone and marginal BRC are not nearly as substantial. Although all the deviations on the right-hand side of Table 4 exceed two runs, none of them exceeds three. The greatest deviation came from Alfonso Soriano’s 2002 season with the Yankees, when his marginal BRC exceeded his stand-alone BRC by 2.63 runs.

Finally, notice that the player-team-seasons on each side of Table 4 are creating far more runs than average, but those batters on the left-hand side of Table 4 have a substantially larger slugging percentage (.726) than those on the right-hand side (.426). This suggests that stand-alone RC tends to overestimate the runs contribution of big sluggers, since marginal Runs Created is likely the more accurate measure of individual batter runs contribution. Since the inter-quartile range of teams actually score 98 runs in a given regular season, an inaccuracy of 27 runs could potentially impact a team’s seasonal winning percentage.

PRACTICAL APPLICATIONS AND ISSUES

A. Benefits and Drawbacks: MRC Versus Stand-Alone RC

Compared to stand-alone Runs Created, marginal Runs Created provides a more accurate measure of a batter’s contribution to their team in a given season, but this is conditional on the performance of the batter’s teammates. Suppose Swanson’s individual BRC factors remain the same, but rather than playing for the Braves (his 2022 team), he plays for the Cubs (his 2023 team). His marginal BRC might very well be different due to differences in aggregate teammate batting performance. In the 2022 season, the Cubs had an on-base factor of 1,800, a base-advancement factor of 2,097, and an opportunities factor of 5,932. All three factors were lower than Atlanta’s, which means the Cubs generated a lower inside-aggregated Runs Created.

If Swanson had played for the Cubs, his 2022 batting performance would have created 92.63 runs, or about 1.1 fewer runs than it created for the Braves.

However, regardless of which team Swanson plays for, his stand-alone BRC would be 93.81. Thus, both marginal Runs Created and stand-alone Runs Created have their own drawbacks and benefits. Because outside-aggregated Runs Created is less accurate than inside-aggregated Runs Created, it stands to reason that stand-alone Runs Created will generally be less accurate than marginal Runs Created, since marginal Runs Created is a result of inside-aggregated RC. However, given an individual batter’s performance in a particular season, his MRC is sensitive to the team he is playing for, which is not true of stand-alone RC. As a result, stand-alone Runs Created could be better described as a measure of an individual batter’s capacity for run creation, which is independent of the team he plays for, while marginal Runs Created is a measure of the actual runs an individual batter created for his team in the given season.

Thus, Dansby Swanson’s 2022 batting performance had the capacity of creating 93.81 runs for a given ball club. It actually created 93.72 runs for the Atlanta Braves, and it would have created 92.63 runs for the Chicago Cubs.

B. Implications for Non-Pitcher Trades

The difference between an individual batter’s stand-alone Runs Created and his marginal Runs Created nonetheless provides insights for non-pitcher trades between MLB teams. It is rare for two MLB teams to trade one player for another player based on offensive abilities alone. A fundamental concept of economics holds that no trade between two rational, well-informed parties would occur if it were not mutually beneficial. It would thus seem that most MLB teams do not often find purely offensive trades, or batter-for-batter transactions, to be mutually beneficial.

This is not surprising if one considers outside-aggregated Runs Created as the only measure of a team’s runs scoring. Were two teams to trade one batter for another batter based on batting characteristics alone, the trade would not benefit both teams without other considerations, such as cash, a pitcher, a draft pick, or significant differences in the players’ defensive capabilities. If there were such a trade based purely on the player’s offensive contribution, the best-case scenario would be a wash. More likely than not, one team’s Runs Created would benefit while the other team’s Runs Created would suffer. Of course, this is true only if one assumes outside aggregation to be the only team-season Runs Created measure, which it’s not.

For instance, consider a hypothetical trade that occurs right before the beginning of the 2025 season. Suppose the Royals trade their current shortstop, Bobby Witt Jr,. in exchange for Giants shortstop Willy Adames. Assume a straight trade with no cash, with defense not taken into consideration.

Table 6 shows the hypothetical 2025 batting performance of both Witt and Adames, as well as the hypothetical overall batting performance of the Giants and Royals.

 

Table 6. Hypothetical Season

 

Witt has a stand-alone RC of 152.83 while Adames has a stand-alone RC of 165.31. This means the Giants are effectively hurt by the trade because they are trading 165.31 stand-alone Runs Created to the Royals but receiving only 152.83 stand-alone RC in return, reducing their outside-aggregated Runs Created by 12.48 runs (and increasing Kansas City’s by the same amount). If outside-aggregated Runs Created is the only accurate team-season RC measure and both parties are rational, the trade would never go through, since it would hurt the Giants.

Yet, as section 4 demonstrates, inside-aggregated RC is more than twice as accurate as outside-aggregated RC. So, one cannot definitively say the trade is not mutually beneficial without also seeing how the trade affects both teams’ inside-aggregated Runs Created. If the Giants had kept Adames, their inside-aggregated Runs Created would have been 669.86:

That is lower than the 672.91 inside-aggregated runs the Giants created as a result of the trade:

Thus, unlike with outside-aggregated RC, the Giants do benefit from the trade through an increase in their inside-aggregated RC. What’s more, if the trade had not occurred, then the Royals would have had an inside-aggregated RC of 615.70:

That is lower than the 622.65 inside-aggregated RC earned with the trade:

Thus, using the inside-aggregation method, the trade is actually mutually beneficial to both teams. As a result, the Giants increase their inside-aggregated BRC by 672.91 – 669.86 = 3.05 runs while the Royals increase their inside-aggregated BRC by 622.65–615.70 = 6.95 runs. In the language of economics, the Giants had an absolute advantage in base advancement prior to the Adames-Witt trade; 2,319, compared to the Royals’ 1,773. On the other hand, the Royals had an absolute advantage in getting on base; 2,152, compared to the Giants’ 1,719. The Giants struggle to get on base, so they benefit from the trade because of Witt’s superior 257 on-base factor. The Royals benefit because the 314 base-advancement factor Adames provides meets their needs.

CONCLUSION

This study shows that the inside aggregation of Runs Created is a more accurate measure of the team’s actual runs scored than the outside aggregation of Runs Created. This is true regardless of whether one uses the basic Runs Created formula (BRC), the stolen bases Runs Created formula (SBRC), the first version of technical Runs Created (TechRC), or the second version of technical Runs Created that accounts for strikeouts (TechKRC). However, the inside aggregation of a team-season’s Runs Created is still inaccurate to the extent that it overpredicts actual runs scored.

For a given aggregation method, the basic Runs Created formula is the most accurate measure of a team-season’s actual runs scored. Of all eight aggregated RC formulas assessed in the study, the inside-aggregated basic Runs Created formula is the most accurate, while the first technical Runs Created formula using the outside-aggregation method is the least accurate. Additional batting statistics do not always improve an RC formula’s accuracy.

Finally, it stands to reason that the marginal Runs Created measure (MRC) more accurately reflects a batter’s runs contribution to his team-season than the stand-alone measure does. This is because MRC is based on the more accurate inside-aggregated RC whereas the stand-alone measure is based on the less accurate outside-aggregated RC. That said, the deviation between the two measures of individual batter runs contribution is minimal; over 90 percent of the time, the deviation is less than just two runs. 

JOEY de SOUZA WHITE is currently an adjunct instructional assistant professor of economics at the University of Mississippi. Previously, he taught business and economics at Bethel University for five years. A Cubs fan since childhood, his 2016 pride was rivaled in 2022 when Ole Miss won the College World Series.

 

Notes

1. Bill James, The New Bill James Historical Abstract (New York: Free Press, 2003), 329–31.

2. Gabriel B. Costa, Michael R. Huber, and John T. Saccoman, Understanding Sabermetrics: An Introduction to the Science of Baseball Statistics (Jefferson, NC: McFarland & Co., 2008).

3. Jim Furtado with G. Jay Walker and Don Malcolm, “Deciphering the New Runs Created,” Baseball Think Factory, https://www.baseballthinkfactory.org/btf/scholars/furtado/articles/NewRC.html.

4. Frank M. Chimkin, “Another Look at Runs Created,” SABR Baseball Research Journal 32 (2003).

5. Herm Krabbenhoft, “Who Invented Runs Produced?” SABR Baseball Research Journal 38, no. 1 (Summer 2009), 135–138.

6. “Runs produced,” Baseball Reference, https://www.baseball-reference.com/bullpen/Runs_produced.

7. Eric Walker, “Common Run-Production Formulae Evaluated,” Baseball Analysts, November 23, 2009, https://baseballanalysts.com/archives/2009/11/common_runprodu.php.

8. “2022 Atlanta Braves Statistics,” Baseball-Reference, https://www.baseball-reference.com/teams/ATL/2022.shtml.

9. Given batter p playing for team t, inside-aggregated Runs Created can be formally defined as:

10. The marginal Runs Created that player p created for his team is formally defined as:

11. Major League Leaders,” FanGraphs, https://www.fangraphs.com/leaders/major-league?pos=all&stats=bat&lg=all&qual=0&type=0&month=0&ind=1&rost=&age=&filter=&players=0&startdate=&enddate=&season1=1999&season=2019&team=0%2Cto.

12. Nate Silver describes the idea behind these calibrations. Nate Silver, The Signal and the Noise (New York: Penguin Books, 2020), 128–41. Nate Silver, “When We Say 70 Percent, It Really Means 70 Percent,” FiveThirtyEight, April 4, 2019, https://fivethirtyeight.com/features/when-we-say-70-percent-it-really-means-70-percent/.

13. The table below shows the regression output for all the regression line in Figure 5.