Infield Hit Model, Part 2: Use the Whole Field, Hit Line Drives
This article was written by Donald Slavik
This article was published in Spring 2025 Baseball Research Journal
Bobby Witt Jr. of the Kansas City Royals (Trading Card Database)
Tom Verducci wrote the following in 2023: “From 2015 to 2022, the (infield) shift helped take 2,065 groundball hits out of the game. … Batters saw hit probability on grounders reduced by the shift, so they tried to hit over defensive alignments.”1 Some of the game’s foremost hitters evangelized for that approach, including Josh Donaldson, who said, “If you are 10 years old and your coach says to get on top of the ball, tell them no. Because in the big leagues, these things that they call ground balls are outs. They don’t pay you for ground balls. They pay you for doubles. They pay you for homers.”2
But with infield shift restrictions that began in 2023, does the focus away from groundballs still make sense? Nick Krall, president of baseball operations for the Cincinnati Reds, recently expressed a more traditional mindset, telling reporters, “We want hitters (to take) an approach of using the whole field, hit line drives, and take good at-bats.”3 Pitchers dislike facing hitters who use this approach. “I never liked the guy that was going to use the entire field,” said 21-year veteran LaTroy Hawkins in 2024. “It was tougher when I knew [the batter] had a plan to hit the ball where it was thrown.”4
Many researchers have studied the effect of defensive positioning on hit probability. Jim Albert established a novel iterative approach to determine hit probabilities based on spray angle and launch speeds for the 2017 season.5 Russell Carleton broke down the effect of infield alignment on several offensive statistics during the 2021 season.6 In 2024, Charlie Pavitt studied performance based on batted ball type.7 And this author established a hit model for balls hit to the infield from the 2023 season based on spray angles and launch speed.8 However, none of this research established a comprehensive model for hit probability that assessed balls hit to the outfield and took into account launch angle, exit velocity, and spray angle.
This article describes research to develop hit probabilities for infield and outfield balls in play. Players are not machines, and this is a highly non-linear problem. However, an approach was developed that used hit probabilities to predict hits from spray angles, launch speeds, and launch angles. Simulations were also generated to determine the quantitative benefits of improved launch speed, launch angles, spray angles, and batted ball types. The “model” in this work was the probability functions used to predict hits and quantify good at-bats. This model was used to analyze outcomes of the Cincinnati Reds players, and to compare them to elite left-handed hitter Luis Arráez and elite right-handed hitter Bobby Witt Jr.
INPUT DATA AND DEFINITIONS
This research used Baseball Savant data from the 2023 and 2024 seasons. Note there are some liners below 0 degree launch angles. These should be characterized as ground balls. Balls in-play with incorrect hit types or missing launch angle/speed parameters were rare in the database and therefore will not significantly impact model results. Figure 1 shows hits and outs for different hit types as a function of launch speed and angle.
Figure 1. Hits and Outs by Launch Speed and Angle (2023)
Defensive alignment affects hit probability. Major League Baseball outlawed dramatic infield shifts in 2022, but shade alignments, where a middle infielder is positioned near second base and corner infielders are shifted, are still allowed. The spray angle is the horizontal direction of the ball put in play, with 0 degrees directly toward second base, 45 degrees down the third-base line, and –45 degrees down the first-base line. As in Part 1, the adjusted spray angle is defined as a positive value for pulled balls for both left-handed and right-handed hitters. Upcoming plots will use adjusted spray angles.
Figure 2 shows spray charts for Luis Arráez, courtesy of Baseball Savant.9 His hits were distributed across different spray angle zones, but his outs tended toward groundballs to the pull side and fly balls hit to the opposite field. Adjusted spray angle and infield alignment tags were key parameters in the hit model.
Figure 2. Luis Arráez 2023 Spray Charts
Figure 3. 2023 MLB Line Drive Outs
Table 1. 2023 Outcomes by Batter Handedness
HIT PROBABILITIES WITH LAUNCH SPEED
Equation 1 shows the hit probability model for popups, groundballs and infield line drives. Equation 2 shows the slightly different model for outfield line drives and fly balls.
Equation 1. Model Hit Probability for Popups, Groundballs, and Infield Line Drives
Equation 2. Model Hit Probability for Outfield Line Drives and Fly Balls
The reference speed is the median launch speed for each hit type, reference probability is the hit probability at the reference speed, and m is an optimization parameter. Reference launch speeds for each hit type excluding home runs are provided in Figure 4. Figures 5 and 6 show hit probabilities as a function of adjusted spray angle for left-handed and right-handed hitters, as well as shaded and non-shaded infield alignments. Hit probabilities at reference launch speeds and +/–10 mph from reference launch speeds are plotted to highlight trends. Infield liners and grounders have local hit probability minimums at specific spray angles consistent with infield positions schematically shown with black symbols. Launch speed did not impact popup hit probabilities (m=0). Unique values for m were identified for each hit type in each spray angle zone. Adjusted spray angle zones between –30 and –45 degrees were best for left-handed hitters, with a hit probability of .729 thanks to a lightly defended left side of the infield and the long throw to first. The best spray angles for righties were –20 to –40 degrees, with a hit probability of .383, much lower than those of left-handed hitters.
Figure 4. 2023 Reference Hit Probabilities by Hit Type
Figure 5. Hit Probabilities for Reference and +/–10 MPH Launch Speeds for Left-Handed Hitters
Figure 6. Hit Probabilities for Reference and +/–10 MPH Launch Speeds for Right-Handed Hitters
Figure 7 shows hit probabilities for outfield line drives and fly balls. Local minimums were represented by the three outfield positions shown schematically with black symbols. Because handedness had less effect on hit probabilities, the two groups of hitters are not presented separately. As noted earlier, hit probabilities for outfield balls in play were best characterized by Equation 2. Equation 2 was best for low hit probabilities typical of fly balls, and captured large observed adjustments to hit probabilities with launch speed for outfield liners.
Figure 7. Hit Probabilities for Reference and +/–10 MPH Launch Speeds for Outfield Hits
HIT PROBABILITIES WITH LAUNCH ANGLE
Figure 1 showed the combined effect of launch speeds versus launch angles for each hit type. Launch angles for line drives varied within +/–15 degrees for any given launch speed. Launch angles varied for popups from 20 to 90 degrees. Grounders varied from –90 to above 25 degrees. Fly balls varied from 30 to 70 degrees. In order to calculate the best approach to launch angle, the author assessed different models of increasing complexity, including fully non-linear interactions between spray angles, launch speeds, and launch angles. A non-linear interaction model was developed but required complicated fit terms without obvious physical meaning. A relatively simple launch angle model was eventually established as described in Equation 3.
Equation 3. Launch Angle Adjustment
Hit prob* is an adjustment to the hit probabilities from Equations 1 and 2. The launch angle factor was established from observed and predicted hits at different launch angles for popups, infield line drives, and ground balls as provided in Figures 8, 9, and 10. The launch angle factor is represented with solid lines (main y-axis). The number of observed hits in each launch angle zone is shown with the dashed line (secondary y-axis).
Figure 8. Popup Launch Angle Factor
Figure 9. Infield Line Drive Launch Angle Factor
Figure 10. Groundball Launch Angle Factor
Popup launch angle factors increased significantly for launch angles below 55 degrees, as popups transitioned to line drives. The infield line drive launch angle factor was less than or equal to 1.0 for launch angles below 5 degrees, where liners intermixed with ground balls. It increased as the launch angles approached the optimal level of 25 degrees, then decreased at launch angles above 30 degrees as infield line drives intermixed with popups. The groundball launch angle factor was more complicated. The factor was lowest at a launch angle of –35 degrees, but increased at even lower launch angles, as groundballs turned into high choppers. The factor also increased as launch angle grew closer the maximum near 10 degrees, as grounders intermixed with infield line drives. Grounder launch angle factors slightly decreased below –60 degrees, the few at-bats where batted balls go straight down and catchers make the play, as well as the few grounders above 20 degrees. Baseball Savant categorized some balls with a launch angle above 20 degrees at launch speeds below 60 mph as grounders. These were softly hit balls to an infielder playing back. This rare batted ball type was observed only 189 times.
The launch angle factor was more complicated for outfield liners. These launch angle factors were influenced by launch angle/launch speed interactions. Many different functional forms with varying degrees of complexity were evaluated. Figure 11 shows the best functional form for outfield line drives.
Figure 11. Outfield Line Drive Launch Angle Factor and the Minimum Launch Angle Factor
Separate launch angle factors were required above 100 mph and below 85 mph. Home runs were not included when establishing model constants in this work, as it focused on balls in the field of play. Home runs were added into the hit predictions with a hit probability of 1.0 to predict accurate batting averages and hit totals. There was a minimum launch angle factor where reduced conditions did not reduce hit probabilities, (see Figure 11). Launch angle factors for all hit types and launch speed model constants are provided as an online appendix in the Baseball Research Journal electronic version at SABR.org.
Fly balls were equally complex. The launch angle factor for fly balls is summarized in Figures 12 and 13. The launch angle factors in Figure 12 have a slope provided in Figure 13 used with Equation 5. No Launch angle is permitted to fall below the minimum launch angle factor also provided in Figure 13.
Figure 12. Fly Ball Launch Angle Factor for Low and High Launch Angle Speeds
Figure 13. Fly Ball Launch Angle Slope and Minimum Launch Angle Factor
PREDICTED HITS AND MODEL CHECKS
Hit probabilities were next used to calculate hits from summed hit probabilities with Equation 4.
Equation 4. Total Predicted Hits
In Equation 4, (hit prob) and (hit prob*) were constrained between 0.00 and 1.00 for all at-bats. Home runs are added to predicted hits for proper hit totals. Hit probabilities were summed for all at-bats across different launch speeds, launch angles, players, teams, and seasons. It is worth noting that Equations 1–5 and trends from Figures 4 to 13 are reasonable, but most early attempts to predict hit totals failed spectacularly. Players are not machines, and this is a highly non-linear problem. Early models that did not represent subtle impacts of launch speed, launch angle, and spray angle under-predicted and over-predicted hits in different subgroups by a factor of five.
Equation 5. Launch Angle Factor for Fly Balls
After many model iterations, predicted hits for each hit type from the current model are provided in Figures 14 and 15. Solid lines represent observed hits and the symbols represent predicted hits. Hit predictions for each hit type are well characterized for all launch speed and launch angle regimes. Hit totals for each hit type in each spray angle zone are provided in Figure 16. All data scatter uniformly around the perfect fit 1:1 line. The model accurately represents hit totals for all hit types for different spray angles, launch speeds, and launch angles.
Figure 14. Predicted and Observed Hits With Launch Speed
Figure 15. Predicted and Observed Hits With Launch Angle
Figure 16. Predicted and Observed Hits in Spray Angle Zones
MODEL HIT PREDICTIONS AND SENSITIVITY STUDIES
The model was now ready to predict hits for players and teams. Figure 17 shows observed and predicted hits for MLB players during the 2023 and 2024 seasons. No model adjustments were considered or required to predict hits in the 2024 season. Luis Arráez is highlighted as the top left-handed hitter, with a batting average of .354 in 2023 and .314 in 2024. Bobby Witt Jr. is highlighted as the top right-handed hitter, with a .332 batting average in 2024.
Figure 17. Player Hit Predictions for 2023 and 2024 MLB Seasons
The model provided a quantitative path to assess how individual factors increased hit probabilities. The sensitivity study assessed favorable conditions of a) +10 mph for launch speed; b) +10 degrees of launch angle for grounders; c) –10 degrees of launch angle for popups and fly balls; d) +10 degrees launch angle for infield line drives and –10 degrees of launch angle for outfield liners; e) grounders hit into favorable spray angle zones; and f) different hit types. It was unrealistic for all hits to change to any new condition, so the sensitivity studies assumed that 20% of at-bats were converted to the hitter-favorable condition. Hit probabilities to typical favorable hit types were determined from baseline averages in Table 1. Improved launch angles and launch speeds were determined based on model assessments of each at-bat. The predicted impact of individual favorable conditions toward extra hits and batting average for left-handed hitters and right-handed hitters are given in Tables 2 and 3. The calculations are performed for all at-bats from the 2023 MLB season, then scaled to a hitter with 500 at-bats.
Table 2. Hit Sensitivity Studies for Left-Handed Hitters, 20% Adjustment for Individual Favorable Conditions, 2023
Table 3. Hit Sensitivity Studies for Right-Handed Hitters, 20% Adjustment for Individual Favorable Conditions, 2023
The benefit of improved launch angle or launch speed only was generally low, on the order of zero to six points of batting average. Converting popups to typical grounders also had a small impact, thanks to the low overall rate of popups. There was a more significant benefit of 10 to 15 points in batting average with improved launch speed and launch angle, improved liner launch angles, converting strikeouts to typical grounders, and converting fly balls to typical outfield liners. There was a great benefit of 30 points for lefties with grounders hit into favorable spray angle zones and grounders converted to infield line drives. None of these results is surprising, but this approach offers a unique glimpse into how individual items improved total hits and batting averages.
A hitter does not work to improve only one aspect of their game. Instead, a myriad of factors contributes to boosting batting averages. The cumulative benefits of quality at-bats from reduced strikeouts, hitting grounders at more desirable spray angles, and converting groundballs to infield line drives are provided in Table 4. Improvements in 20% of these at-bats in these three areas can boost batting averages by 52 to 74 points, enough to turn an average hitter into a team leader. Table 5 shows the cumulative benefits of additional quality at-bats. Changing 20% of at-bats to favorable conditions in these areas can boost batting averages by 80 to 100 points, enough to turn an average hitter into a batting champion. Individual players or teams will have unique quantities of balls in play and hits, but predicted trends are consistent for specific players and teams for 2023 and 2024.
Table 4. Hit Sensitivity Study, 20% Adjustment for Cumulative Favorable Conditions, Per 500 Team At-Bats
Table 5. Hit Sensitivity Study, 20% Adjustment for Cumulative Favorable Conditions, Per 500 Team At-Bats
CINCINNATI REDS HITTER TRENDS
Sensitivity studies of increased quality at-bats can also be performed at the team level, for example, comparing Cincinnati Reds players to top hitters Arráez and Witt. How do the Reds compare on balls in play with generally good outcomes, such as line drives and grounders to favorable spray angle zones? And how do they compare on balls in play with poor outcomes, such as grounders to unfavorable spray angle zones? All comparisons were scaled to a reference of 500 at-bats.
Left-handed hitters are compared to both Arráez and the MLB average in Table 6. For switch-hitters Jeimer Candelario and Elly de La Cruz, only left-handed at-bats are considered. Hit probabilities are provided for each hit type in the last row for reference. Players do not control hits in any category, but they have some control over the number of quality at-bats, or the number of balls put in play that are predicted to have good outcomes. Popups were uncommon and similar for all hitters and therefore eliminated in coming tables.
Table 6. Reds LHH Comparisons to Luis Arráez and MLB Average, Per 500 AB
Most Reds lefties scored well on home runs and productive fly balls in Table 6. Although the team had no top-10 home run hitters, overall home run production was acceptable. However, this benefit was offset by a surfeit of strikeouts. It would be unrealistic to expect other players to match Arráez’s elite strikeout avoidance, but reducing strikeouts to at least league-average levels is a reasonable goal. Converting strikeouts to groundballs was shown to have a measurable improvement, adding 13 points of batting average in Table 4. Arráez also excelled in the quantity and quality of liners. Most line drives grade out as quality at-bats, with hit probabilities of .586 to the outfield and .711 to the infield. This highlights the critical importance of launch angles to produce the most productive hit types. Well-struck balls with a launch angle near 20 degrees did not typically end up as home runs, but they were likely to result in hits. Converting grounders to infield liners increased batting averages by 31 points for lefties, so the goal of reaching the league average is another reasonable goal for 2025.
Understanding quality grounders was a bit more complicated. Improved groundball launch speeds and angles results in 12 extra points of batting average, but shifting groundballs to favorable spray angles yielded an increase of 31 points. Reds groundball spray angles are compared to league hitters in Table 7. Quality grounders are a result of: a) many grounders hit the other way; b) some grounders hit up the middle c) few grounders pulled toward first base, and d) grounders hit with good launch speed and launch angle characteristics. Most lefties would benefit from pulling fewer grounders and hitting more the other way. An all-fields approach is key to increasing quality at-bats.
NOTE: For Tables 6 through 9, bold text shows areas where Reds hitters matched Arraez/Witt and the league average. Italic (or shaded/colored) text in the tables show areas where the Reds compared well to Arraez/Witt or the league average. Areas where Reds hitters are below average are shown in plain text.
Table 7. Reds LHH Comparisons to Luis Arráez and MLB Average, Launch Angle, Per 500 AB
Table 8. Reds RHH Comparisons to Bobby Witt Jr. and MLB Average, Per 500 AB
Reds right-handed hitters are compared to Bobby Witt Jr. and the MLB average in Table 8. Observed hits were again scaled to 500 at-bats. Cincinnati’s right-handed hitters had a difficult year at the plate in 2024, with low home run production and high strikeouts. No hitter matched Witt in more than any one single category. Santiago Espinal and Jonathan India had the most quality line drives. Launch angle and line drives stand out as areas for improvement for Cincinnati righties in 2025.
Groundball quality is more difficult to quantify for righties. Improved spray angles can yield improvements of up to eight points of batting average, while improved launch angles can yield up to 11. Table 9 shows right-handed groundball hits and balls in play. Improving the quality of groundballs would help, but right-handed hitters shouldn’t come to the plate trying to hit a better grounder to get on base. A simple message for right-handed hitters could be to focus on launch angle, as the best path to improvement lies on increasing line drives. A secondary message could be that home runs are great, but converting strikeouts even to average groundballs has a dramatic impact.
Table 9. Reds RHH Comparisons to Bobby Witt Jr. and MLB Average, Launch Angle, Per 500 AB
SUMMARY
After reviewing these numbers, the obvious challenge for most batters is to hit more line drives and more groundballs to favorable spray angles without increasing strikeouts or popups. Hitters could improve their offensive production by understanding the tendencies of leading hitters, how the infield defends against these tendencies, and the qualitative benefits of different hitting approaches. However, the author does not think all hitters would benefit from attempting to increase their rates of quality infield liners or grounders. Clean-up hitters need to keep swinging away. Discerning hitters need to take walks. But hitters should consider when balls into poorly defended spray angle zones are possible and warranted.
DONALD SLAVIK is currently an aerospace consultant and an MLB grounds crew member. On the grounds crew, he chalks lines, brooms the infield, repairs bullpen mounds, and fluffs the grass. Don’s first baseball technical paper was published in the Baseball Research Journal (Spring 2024) and presented at SABR 52 (Minneapolis).
Acknowledgments
Davy Andrews did a wonderful job editing this article. The author is grateful to get suggestions from reviewers Jim Donnelley and Cindy Slavik—and all the friends that provided ideas as the work progressed. The anonymous peer reviewers also provided specific and invaluable feedback—I did my best to update the work with the suggestions they provided.
Notes
1. Tom Verducci, “How Banning Infield Shifts Will Change MLB,” Sports Illustrated, November 21, 2022, https://www.si.com/mlb/2022/11/21/banning-infield-shifts-impact.
2. Dave Sheinin, “These days in baseball, every batter is trying to find an angle,” Washington Post, June 1, 2017, https://www.washingtonpost.com/graphics/sports/mlb-launch-angles-story/.
3. C. Trent Rosencrans, “Reds notes: Terry Francona’s coaching staff, front office moves and more,” The Athletic, October 8, 2024, https://www.nytimes.com/athletic/5829237/2024/10/08/reds-terry-francona-coaching-staff-offseason-moves/.
4. “SABR 52: Listen to highlights from Minnesota Twins Pitchers Panel,” SABR.org, https://sabr.org/latest/sabr-52-listen-to-highlights-from-minnesota-twins-pitchers-panel-with-bert-blyleven-jim-kaat-latroy-hawkins-glen-perkins/, last accessed January 10, 2025.
5. Jim Albert, “Chance of Hit as Function of Launch Angle, Exit Velocity, and Spray Angle,” Exploring Baseball Data with R, January 15, 2018, https://baseballwithr.wordpress.com/2018/01/15/chance-of-hit-as-function-of-launch-angle-exit-velocity-and-spray-angle/.
6. Russell A. Carleton, “So You’ve Decided to Ban the Shift,” Baseball Prospectus, March 9, 2022. https://www.baseballprospectus.com/news/article/73029/baseball-therapy-so-youve-decided-to-ban-the-shift/.
7. Charlie Pavitt, “Plummeting Batting Averages Are Due to Far More than Infield Shifting, Part One: Fielding and Batting Strategy,” SABR Baseball Research Journal 53, no. 2 (2024), 91–100, https://sabr.org/journal/article/plummeting-batting-averages-are-due-to-far-more-than-infield-shifting-part-one-fielding-and-batting-strategy/.
8. Don Slavik, “An Infield Hit Model from the 2023 Season: Hit ’em where they ain’t,” SABR Baseball Research Journal 53, no. 1 (2024), 75–85, https://sabr.org/journal/article/an-infield-hit-model-from-the-2023-mlb-season-hit-em-where-they-aint/.
9. Spray charts courtesy of Savant Illustrator on Baseball Savant, https://baseballsavant.mlb.com/illustrator.