Creating a Measure of Plate Discipline

Author: Connor Courtright – Computer Science and Data Science Major at the University of Alabama

1. Introduction

Plate discipline is one of the most important traits in a hitter, yet also one of the more elusive. Hitters are often described as ‘having a good eye’ or ‘knowing the zone’, but there aren’t many in-depth statistics that provide a solid, at-a-glance understanding of whether batters actually exhibit disciplined swing behavior. There are metrics like ZSwing% and OSwing%, which track how often a batter swings at pitches inside and outside of the strike zone, respectively, but these are surface level and require context to understand. Because of this, I set out to make a number that identifies hitters with real plate discipline, which I have named ‘DISC+’.

2. Deriving DISC+

The key component when assessing plate discipline is the swing decision: what pitches a hitter swings at, and which ones they don’t. Pitch location, naturally, should be a significant component in swing decisions. So, the goal of DISC+ is to measure how closely a hitter’s swing decisions align with an empirically derived estimate of the optimal decision at every pitch location.

To begin, I modeled swing behavior as a continuous spatial process. The strike zone is divided into a 15×15 grid, creating 225 evaluation points. With the bottom-left corner of the strike zone being placed at (0, 0), the grid covers horizontal locations from -15 to 33 inches and vertical locations from -15 to 41 inches. These points serve as locations at which local estimates of league and hitter behavior are calculated. Every pitch contributes to every grid point, with nearby pitches contributing significantly more than ones further away. To estimate local behavior, DISC+ employs a two-dimensional Gaussian kernel. For a pitch located at $(x_i, y_i)$ with some grid point $g_k = (x_k, y_k)$, then the contribution of that pitch to $g_k$ is determined by:

The bandwidth parameter, $\sigma$, is fixed at $\sigma = 4$ in. The Gaussian kernel assigns a weight close to one for pitches located near the evaluation point and progressively smaller weights as the distance increases. Consequently, estimates vary smoothly across space, creating a mapping that reflects the continuous nature of pitch location.

Three league-wide quantities are estimated independently at every grid point using the kernel-weighted averages. First, there is the local swing rate $s_{lg}$, which estimates the probability that a hitter swings at a pitch located near $g_k$:

The next is the called-strike probability, the chances that a pitch taken by the batter is called a strike by the umpire:

Lastly, the probability of swinging and missing on a pitch at the given location:

Unlike traditional plate discipline metrics, DISC+ does not assume that every strike should be swung at or that every ball should always be taken. Instead, the optimal decision at each location is anchored to observable outcomes. The target swing rate is defined as:

This formula combines two complementary probabilities. The called-strike probability represents the cost of taking a pitch, while the whiff probability represents the likelihood that a swing results in contact rather than a miss. Multiplying these terms produces a quantity that is large only when both conditions favor swinging. Locations that are frequently called strikes but also produce many whiffs receive lower target values than they would under a purely zone-based approach, and pitches that are easy to hit but rarely called strikes likewise remain poor swing candidates. As a result, the target reflects the expected value of the swing decision.

Next, I weighted each grid point by $p_ꓘ(g_k)$. This is because not every pitch location provides equal information about a hitter’s discipline – pitches that are almost always called balls or almost always called strikes require little decision-making, and thus should not be counted equally as more borderline points. Each grid point, then, is assigned a weight:

This weighting function reaches its maximum when the called-strike probability is 0.5, and decreases towards zero as the probability approaches either extreme (0 or 1). Consequently, borderline pitches contribute most heavily to the final metric, whereas obvious balls and obvious strikes contribute relatively little.

Using these weights, the league’s average deviation from the target swing rate is calculated as:

This value represents the weighted average difference between actual league behavior and the estimated optimal behavior across all evaluate locations. It is calculated using the entire league dataset, so it serves as a fixed reference point against which every hitter is compared.

For an individual, the local swing rate is estimated using the exact same kernel smoothing procedure, except that only pitches faced by that hitter are included:

Unlike the league dataset, however, an individual hitter (especially in the Prospect League, in which teams play only ~60 games) has observed a very limited number of pitches. Consequently, some evaluation points may have very little nearby information, making local estimates unreliable. To prevent sparse data from skewing the results, I excluded all evaluation points whose total kernel weight is less than three. This threshold represents an effective sample size rather than a simple raw pitch count, allowing several nearby pitches or many moderately close pitches to provide sufficient information. Locations that fail to meet this requirement are omitted for an individual hitter’s calculation.

From this point, the hitter’s weighted deviation from the target swing rate is found:

Then, at long last, a hitter’s final score is calculated:

A score of 100 corresponds to league-average plate discipline. Values above 100 indicate that a hitter’s swing decisions more closely match the empirically derived target than those of the average hitter, while values below 100 indicate larger deviations from the target. Because the statistic is normalized by the league baseline, DISC+ functions as a plus metric, allowing intuitive comparisons across players while preserving a league average of 100. For example, a hitter with a DISC+ of 135 is 35% better than league average; similarly, a hitter with a DISC+ of 65 is 35% worse than league average.

Using this methodology, DISC+ values for all qualified hitters were calculated. Figure 1 shows the distribution of DISC+ values among Prospect League hitters, and Table 1 lists the top 10 hitters in DISC+. Worth noting are the highest ranked CornBelters: Charlie Vercruysse (157 DISC+, ranked 7th overall), Ben Voegele (132, 25th), and Dylan Coty (127, 29th).

Batter	Team	DISC+
Kriss Sydlowski	JOH	202
Adrian Nina	SPR	199
Jude Clough	CHI	173
Joseph Gutierrez	TER	172
Sam Meyer	CHI	162
Dean Hannah	LAF	161
Charlie Vercruysse	NOR	157
Nik Nelson	DAN	153
Brady Grabowski	DEC	151
Caleb Crider	DEC	150

3. Is DISC+ Worthwhile?

DISC+ on its own is nice enough. As with any statistic, though, it is important not to take the numbers at face value. In order to determine whether DISC+ is useful in any way, additional analysis needs to be performed. To assess the usefulness of DISC+, I ran three tests: a principal component analysis, to determine whether what DISC+ was measuring was distinct from pre-existing discipline statistics; a reliability test, to assess whether the construction of DISC+ was sound; and a predictive-validity test, to see whether DISC+ had any use as a predictor of future success.

A principal component analysis (PCA) was conducted to determine whether DISC+ measures a distinct aspect of plate discipline or simply repackages information already contained in existing statistics. The analysis included DISC+, Swing%, ZSwing%, OSwing%, Whiff%, Contact%, K%, and BB%, as well as Hard% and Barrel% as controls for quality of contact. DISC+ loaded primarily against overall swing tendency on the first principal component, while exhibiting only minimal loadings on the components dominated by contact ability and batted ball quality. This is a meaningful result, showing that DISC+ is capturing minimal amounts bat-to-ball or power signal.

That same result, however, raises a separate question, because loading heavily on the swing-tendency component is not the same as being independent of it. To assess this directly, DISC+ was correlated against the first principal component of a second PCA run on the pre-existing discipline statistics alone, with DISC+ withheld entirely. DISC+ correlated with this component at $r = -0.790$, and a regression of DISC+ onto the first three components of the reduced model produced $R^2 = 0.666$. This means that roughly two-thirds of DISC+’s variance can be accounted for using the existing discipline statistics alone. This indicates a non-negligible degree of redundancy between DISC+ and the group of statistics that describe how often a hitter swings the bat, even though its separation from contact quality and power still holds.

A communality analysis added further detail to this picture. Using the components retained from the original PCA, DISC+ had a communality of 0.208, meaning that only 21% of its total variance is explained by structure shared with the other nine variables. Taken alone, a figure this low might suggest a largely independent statistic; however, nearly all of that shared portion (roughly 95%) loads onto the same swing-tendency component identified above, rather than being spread across several metrics. What limited overlap DISC+ does have with existing statistics, then, is concentrated in exactly the place the correlation result already pointed to. The remaining variance, unexplained by any retained component, may reflect information not captured by traditional discipline statistics, though communality analysis cannot confirm this, and some portion of it may simply be noise. Altogether, these results suggest that DISC+ is cleanly separated from contact ability and power, but overlaps with existing measures of swing frequency rather than resting on a fully independent dimension of plate discipline.

Next, to evaluate the stability of DISC+, a split-half reliability analysis was performed by dividing each hitter’s season into two equal samples and comparing their resulting DISC+ values. DISC+ produced a split-half correlation of 0.547, placing it firmly in the middle of the other selected statistics. It remained reasonably close to established plate discipline statistics. Applying the Spearman-Brown prophecy formula yielded a projected full-season reliability of approximately 0.71, indicating that DISC+ maintains a level of consistency comparable to widely used discipline metrics despite its more complex construction. Overall, these results suggest that DISC+ is sufficiently reliable for player evaluation. While no plate discipline statistic is perfectly stable due to the inherent variability of swing decisions, DISC+ demonstrated repeatability comparable to existing metrics, supporting its underlying methodology.

Lastly, the predictive validity of DISC+ was evaluated by testing whether it explained future offensive performance beyond traditional plate discipline statistics. DISC+ showed the strongest positive correlation with future BB% ($r = 0.391$) of any statistic tested, exceeding the predictive ability of BB% itself ($r = 0.320$). It exhibited little relationship, however, with future K% or OPS. Multiple regression analyses produced similar results: adding DISC+ to a baseline model containing the conventional discipline statistics increased the explained variance for future BB% from 0.181 to 0.219, a 0.038 increase, while providing essentially no additional predictive value for K% or OPS. These findings are broadly consistent with the intended purpose of DISC+. Because it is designed to measure swing decision making rather than contact ability or quality of contact, its strongest predictive relationship should be with a hitter’s ability to draw walks. The absence of meaningful improvement in predicting strikeout rate or overall offensive production further suggests that DISC+ captures a specific aspect of plate discipline rather than acting as a general proxy for hitting ability.

4. Limitations

Like any statistic, DISC+ should not be interpreted as a complete measure of offensive ability, or even plate discipline itself. By design, it evaluates only a hitter’s swing decisions and intentionally ignores the outcome of balls put into play. As a result, hitters with exceptional bat-to-ball skills or elite power will probably succeed even while making relatively poor swing decisions, while hitters who are more disciplined but lack the offensive tools may receive high DISC+ scores without producing as much offensive value. DISC+ is therefore best viewed as a measure of process rather than overall performance.

The PCA results discussed above are also worth keeping in mind as a limitation of DISC+. It overlaps with existing swing-rate statistics, which means that some of its value, such as its predictive relationship with future BB%, may be attributable in part to information those statistics already provide rather than to something wholly new. This does not undermine the metric, since it still adds incremental predictive value beyond the existing toolkit, but it does mean DISC+ should be understood as a refinement of how swing-rate information is combined and evaluated rather than as an entirely separate signal.

Additionally, the construction of DISC+ relies on kernel smoothing, making the metric more data-intensive than traditional plate discipline statistics. Although the smoothing procedure improves stability by borrowing information from nearby pitch locations, reliable estimates still require a substantial number of observed pitches. The metric is consequently better suited for long-term performance evaluation than for drawing conclusions from small samples. Finally, the target swing rate is derived from league-average outcomes and therefore reflects the average run environment rather than player-specific characteristics. Different hitters may (and probably should) rationally adopt different swing strategies based on their individual strengths, meaning that deviations from the league-derived target are not necessarily suboptimal in every case,

5. Conclusion

DISC+ was developed to provide a more comprehensive measure of plate discipline than traditional swing metrics by evaluating hitter decision-making across pitch location and anchoring the ‘correct’ decision to observed outcomes. Validation analyses indicated that the statistic is cleanly separated from contact ability and power, demonstrated reliability comparable to established discipline metrics, and provides meaningful predictive value for future walk rate, even though it shares a non-negligible relationship with existing measures of swing frequency rather than standing entirely apart from them.

No single statistic can fully describe a hitter, and DISC+ is not intended to replace any existing metrics. Instead, it is best understood as a way of combining and refining information that swing-rate statistics already partially capture, applied specifically to the question of whether a hitter’s decisions predict future outcomes. As more data becomes available and the underlying model is refined, DISC+ has the potential to become a useful tool for player evaluation and projection as well as the study of a hitter’s approach.

6. Acknowledgments

I would like to take a moment to thank everyone who helped me throughout this project and all of this summer. I appreciate the CornBelters front office staff, players, and coaches, as well as my fellow interns for all their support over the past few months. Also, thank you to the owners, staff, coaches, players, and all others who have contributed to rebuilding the Houston Texans into the contender they are today. In particular, I am indebted to Nick Caserio and Demeco Ryans, for their impeccable decision making and leadership; Will Anderson Jr., for leading the best defense in the NFL; and CJ Stroud, for lifting the Texans to the upper echelon of football. CJ, don’t listen to the haters – Houston still believes in you.