Written By: Forrest Allen, 6-4-3 Charts Data Scientist
In both pre-game and in-game planning, coaches are trying to find the best matchups for their hitters and pitchers to be successful. Traditional approaches like examining a small sample of plate appearances between the two players or an OPS vs. the handedness of the opponent don’t really provide a complete picture. The former will rarely, if ever, have a large enough sample to draw a meaningful conclusion about the matchup, while the latter only shows a fraction of the story, the balls in play. OPS and similar metrics only consider the balls that are put into play. They don’t have any concept of pitches that are not put into play, like whiffs. We wanted to create a tool that provided a complete picture of the strengths and weaknesses of each player and how they interacted with each other. For example, do they cancel each other out, or are they aligned making one’s strength even greater than it may be against an average hitter. The resulting tool is the Matchup Matrix; found in the Synergy tile of the 6-4-3 Charts platform.
Run Values as the Inputs to the Matrix
To measure the effectiveness of all pitches, irrespective of whether they were put into play, we use a metric called Run Value (RV). To understand RV, we first must introduce the concept of the run expectancy (RE) matrix.
RE dates to the 1960s when Branch Rickey’s Dodgers employed a statistician named George Lindsey. What Lindsey did, and what we still do today, is create a state for every possible base/out combination possible in a baseball game. With 3 possible out states (0,1,2) and 8 possible base states (bases empty,1,2,3,12,13,23, and 123), there are 24 base/out state combinations (8 x 3=24). This fact gave rise to another name for the matrix, RE 24. For each state, Lindsey counted the runs scored once the state was entered until the end of the half inning. He then divided this number of times this state occurred. The resulting quotient is the number of runs a team can expect to score from that state. In 2025, with no one on and no one out in Division 1 baseball results in .7858 runs
Because we know the value of each state, we can assign a value to any event that causes a shift in states by taking the difference in the previous and current states. For example, the run value of the bases empty and 1 out is .4079. As such, the first out of the inning is worth -.3779 runs (the difference in the two states).
With only 24 states, only events that end a plate appearance can be assigned a run value. To address this problem, all 12 possible counts were added to all the base/out states to create RE 288 (12 x 24 = 288). With this matrix, we can assign balls and strikes a run value the same way we assign run values to outs and hits. For each event, the differences in the value of the previous and current states are added to produce a cumulative run value.
Large negative values are good for pitchers and bad for hitters as this means their actions are decreasing the expected runs. On the contrary, large positive numbers are good for hitters and bad for pitchers.
An additional benefit to run values is the ability to apply it to a subset of the game. For example, I could calculate a run value for a single pitch type like fastballs. In this case, I don’t add or subtract anything to the run value unless the pitch is a fastball. Similarly, I might want to calculate a run value against a platoon split. For the matchup matrix, we do both; a run value of each pitch group versus lefties and righties for baseball and location based for softball.
The different approaches are based on the different nature of the sports. Platoon splits aren’t as pronounced in softball. In addition, pitch group classification is quite challenging in softball.
The baseball matchup matrix uses 3 different pitch groups: fastballs, breaking balls, and offspeed pitches. Due to uncertainty around pitch classification and sample size concerns, we don’t separate 2-seam from 4-seam fastballs or sweepers, sliders and curveballs. Using 3 pitch groups against lefties and righties results in every player having 6 different run values that can be plugged into the matrix.
On the softball side, we use 6 different locations: inside, outside, high, low, middle vertical, and middle horizontal.
Before including them in the matrix, we need to understand how large the sample is which makes up the run value. For example, Kerrington Cross, a 7th round draft pick by the San Diego Padres, and Ryland Zaborowski, a second-team All-SEC DH, had top 20 run values on fastballs against right-handed pitchers last year, 13.85 and 13.60 respectively. However, Cross accumulated this total, seeing 440 pitches while Zaborowski earned it with 200. Despite similar totals, the per pitch run value is quite different (.031 and .068) In addition to understanding the per pitch value, the sample size also determines the degree to which the run value should be regressed to the mean; large samples will rely much more on what actually happened and less on the league average. Players with smaller samples will rely less on what has actually happened, and more on league average because we don’t have enough data to distinguish them from league average.
For players with large sample sizes like Cross and Zaborowski, we can be confident that what we see is very close to their true talent level, thus requiring little regression to the mean. However, Levi Clark saw only 25 offspeed pitches against right-handed pitchers in 2025 and accumulated a 1.98 run value and a per pitch run value of .0792, a total 16% higher than Zaborowski. Because this total was earned with just 25 pitches, we don’t have enough data to definitely say Clark’s per pitch run value should be that high and need to heavily regress it to the mean. We need a larger sample to determine if this is his true talent. As such, we will take his performance and heavily regress it to the mean.
An Example
In game 2 of the 2025 national championship, LSU head coach Jay Johnson pulled his starter Anthony Eyanson after 6.1 innings and went to Chase Shores. Johnson could have chosen anyone, but he was likely deciding between Shores and his two high leverage relievers who could go multiple innings, Zac Cowan and Casan Evans. His reliever was going to have to face 2, 3, and 4 in the order at least. The matchup matrix can help understand which pitcher would give LSU their best shot at a national championship. Below is a table of the run values of the three pitchers based on pitch group and platoon split.
|
|
Breaking_rv | Fastballs_rv | Offspeed_rv | Breaking | Fastballs | Offspeed | |
| Zac Cowan | vs_lhh | 0.61 | -3.43 | -3.96 | 29 | 178 | 145 |
| Zac Cowan | vs_rhh | 0.68 | -6.55 | -5.39 | 98 | 185 | 133 |
| Casan Evans | vs_lhh | -0.73 | -4.49 | -2.81 | 33 | 215 | 143 |
| Casan Evans | vs_rhh | -1.68 | -1.01 | -1.03 | 158 | 213 | 45 |
| Chase Shores | vs_lhh | -1.77 | 1.21 | -0.58 | 103 | 283 | 64 |
| Chase Shores | vs_rhh | -2.32 | -6.15 | 0.56 | 240 | 358 | 6 |
Table 1: LSU Pitchers Run Values & Pitch Count
This data suggests Cowan and Evans would be very effective irrespective of batter handedness, while Shores’ fastball is very good vs righties. However, we need to determine if these conclusions hold true on a per pitch basis or are due to accumulation. For the most part, our conclusions hold; an expected outcome given we’re evaluating stats for virtually an entire season.
| Br/pitch | Fb/pitch | Off/pitch | ||
| Zac Cowan | vs_lhh | 0.021 | -0.019 | -0.027 |
| Zac Cowan | vs_rhh | 0.007 | -0.035 | -0.041 |
| Casan Evans | vs_lhh | -0.022 | -0.021 | -0.020 |
| Casan Evans | vs_rhh | -0.011 | -0.005 | -0.023 |
| Chase Shores | vs_lhh | -0.017 | 0.004 | -0.009 |
| Chase Shores | vs_rhh | -0.010 | -0.017 | 0.093 |
Table 2: LSU Run Values Per Pitch
|
|
Br_Obs_wt | Fb_Obs_wt | Off_Obs_wt | |
| Zac Cowan | vs_lhh | 94% | 90% | 73% |
| Zac Cowan | vs_rhh | 95% | 86% | 81% |
| Casan Evans | vs_lhh | 76% | 91% | 93% |
| Casan Evans | vs_rhh | 86% | 87% | 88% |
| Chase Shores | vs_lhh | 91% | 86% | 93% |
| Chase Shores | vs_rhh | 93% | 91% | 44% |
Table 3: Weight Given to Observed Per Pitch Run Values
Additionally, we need to determine the level of regression to mean required based on the sample data we have. Again, in Game 2 of the College World Series, we don’t have to regress many of these numbers. In our case, regression to the mean refers to a weighted average where the weight of the observed per pitch run value is in the table below. The Division 1 per pitch run value is included with the percentage required to make 100%. For example, the run value that will go into the matrix for Cason Evans’ breaking ball to right-handed hitters will be 86% his observed value, and 14% league average. With a blended per pitch run value, we multiply by 100 to put everyone on the same playing field and to give the input greater context. We repeat this same process for the hitters we expect to see from Coastal Carolina.
| Breaking_rv | Fastballs_rv | Offspeed_rv | Breaking | Fastballs | Offspeed | ||
| Blake Barthol | vs_lhp | -3.48 | 0.35 | 0.97 | 155 | 249 | 11 |
| Blake Barthol | vs_rhp | 0.18 | 2.01 | 0.06 | 214 | 415 | 120 |
| Sebastian Alexander | vs_lhp | -0.11 | -0.81 | 1.33 | 77 | 166 | 53 |
| Sebastian Alexander | vs_rhp | 2.54 | 3.23 | 0.11 | 273 | 317 | 38 |
| Walker Mitchell | vs_lhp | 4.09 | 1.71 | -0.71 | 79 | 207 | 48 |
| Walker Mitchell | vs_rhp | 0.01 | 0.24 | 0.88 | 285 | 393 | 31 |
| Br/pitch | Fb/pitch | Off/pitch | ||
| Blake Barthol | vs_lhp | -0.022 | 0.001 | 0.088 |
| Blake Barthol | vs_rhp | 0.001 | 0.005 | 0.001 |
| Sebastian Alexander | vs_lhp | -0.001 | -0.005 | 0.025 |
| Sebastian Alexander | vs_rhp | 0.009 | 0.010 | 0.003 |
| Walker Mitchell | vs_lhp | 0.052 | 0.008 | -0.015 |
| Walker Mitchell | vs_rhp | 0.000 | 0.001 | 0.028 |
| Br_Obs_wt | Fb_Obs_wt | Off_Obs_wt | ||
| Blake Barthol | vs_lhp | 93% | 94% | 76% |
| Blake Barthol | vs_rhp | 92% | 91% | 89% |
| Sebastian Alexander | vs_lhp | 92% | 94% | 89% |
| Sebastian Alexander | vs_rhp | 92% | 91% | 86% |
| Walker Mitchell | vs_lhp | 92% | 94% | 89% |
| Walker Mitchell | vs_rhp | 92% | 93% | 83% |
Creating Interaction
The data above shows the effectiveness of each hitter and pitcher by pitch type and platoon split. However, what we’re really after is how they interact with each other. Will the hitter’s talents neutralize a pitcher’s strength, or can the hitter take advantage of weakness?
Mathematically, we create this by adding the appropriate run values of the hitter and pitcher to give the desired effect. If a hitter struggles with a certain pitch type from a certain handed pitcher, he will have a large negative run value. If a pitcher is very successful with that same pitch type against the batter’s handedness, the sum will be a larger negative value suggesting the pitcher’s pitch will play up against that batter. The other side of the coin is also true. If a hitter is very successful, he will have a large positive run value. Large run values will be present for pitchers when they struggle. Thus, the sum will be a large positive value, suggesting a favorable matchup for the hitter.
After adding the regressed and standardized run values, we understand the interplay of the pitchers’ and hitters’ strengths and weaknesses by pitch type and platoon split. To assess the overall matchup, each component is weighted by how often the pitcher uses that pitch to that handed batter. From the pitch totals in Table 1, we derived that Chase Shores throws 23% breaking balls, 63% fastballs and 14% offspeed to left-handed hitters by dividing each number of pitches by the total. When we evaluate the matchup with Blake Barthol (a left-handed hitter), the overall score is the weighted average of the pitch groups where the pitch distribution serves as the weight (overall score = .23 * breaking sum + .63 * fastball sum + .14 * offspeed sum).
Contextualizing the Sums
The goal is to assess the quality of the matchup, and the numbers alone don’t really do that; they need context. The Matchup Matrix contextualizes two sets of numbers:
- The overall matchup between each hitter and each pitcher, and 2.
- The effectiveness of each pitch type for each pitcher against each hitter.
For each of these sets of numbers, the largest number is assigned 100 while the smallest number is assigned 0. The remaining values are scaled based on the maximum and minimum values. As shown in Figure 1 below, the overall column ranks all the matchups on the page from best to worst. Additionally, each pitcher has a best and worst pitch group against the selected hitters.