ABA Inside Track – Episode 297: Matching Law (January 8, 2025)

Episode Overview

This episode of ABA Inside Track takes a deep dive into the Matching Law—a fundamental concept in behavior analysis describing how organisms allocate behavior among available reinforcement options. Hosts Robert Perry Crews, Diana Perry Cruz, and Jackie break down key research articles, grapple with the mathematical intricacies, and reflect on the Matching Law’s relevance to practitioners, clients with autism, and even basketball players. Lighthearted banter helps demystify a topic that often intimidates due to its quantitative roots.

Key Discussion Points & Insights

1. What Is the Matching Law? (00:59–07:22)

• The Matching Law explains how individuals (and animals) distribute their responses between two or more behaviors based on the relative rates of reinforcement obtained from each ([06:10]).
• Rob introduces the idea with quirky musical metaphors about song choice and reinforcement bias:
  • Rob: “I have a bias, a reinforcement bias, one might say.” ([01:29])
• Intimidation Factor: Hosts acknowledge the Matching Law’s mathematical reputation. They note many practitioners find the equations daunting, especially the generalized matching law and hyperbola formulas ([07:06-07:21]).

2. Reed & Kaplan (2011): “The Matching Law: A Tutorial for Practitioners” (07:42–30:28)

Purpose & Structure ([07:42])

• Jackie leads a comprehensive and accessible breakdown of this article, which aims to simplify the Matching Law for clinicians.

Main Concepts

• Basic Matching Equation:
  • Allocation of behavior is proportional to the allocation of reinforcement ([14:13]).
  • e.g., Kids playing on the playground: they spend more time where it's more fun—i.e., more reinforcing ([11:18]).
• Historical Roots: Traces back to 1960s pigeon research and variable interval schedules ([12:57]).
• Strict vs. Generalized Law:
  • Strict: Works best with perfect matching; equation is straightforward.
  • Generalized Matching Law: Accounts for biases (e.g., color preference, side preference) and sensitivity (overmatching or undermatching) using logs and extra variables S and B ([17:35]).
  • “What they found is that it happens like that a lot, but not all the time. So not all the time does it match perfectly. … And so this is where they needed to … help the equation along.” – Jackie ([15:53])
• Clinical Relevance:
  • Helps predict preference, informs reinforcement strategies, and can identify biases and confounds when reinforcement doesn’t operate as expected ([20:33], [24:10]).
  • “If clients demonstrate overmatching, they're probably not contacting the programmed reinforcers…” – Jackie ([20:45])

Takeaway

• The tutorial is “kind of a tutorial and kind of complicated for practitioners,” but invaluable for building foundational knowledge ([07:47]).
• Memorable Quote: “There's a reason we didn't pick [the technical primer] for the episode.” – Rob ([28:30])

3. Application 1: Social Preference in Children with Autism (Morris & Vollmer, 2022) (33:42–52:39)

• Diana reviews a study applying the matching law to social preference in children with autism via a “split room assessment” ([34:08]).
  • Procedure: Child can choose either side of a room, one with an experimenter providing social interaction, one without. Analysis quantifies preference and sensitivity to social reinforcement ([37:34]).
• Unique Adaptation: The study uses the matching law to infer preference for or aversion to social interaction, with implications for non-vocal individuals ([40:39]).
• Results Overview:
  • Some children preferred social side (positive slope).
  • Some avoided social interaction (negative slope).
  • Some were indifferent.
  • Noteworthy quote:
    • Diana: “It's not good or bad to like social interaction … It's just a preference.” ([44:48])
• This nuanced view reinforces the need to individualize social reinforcer assessments, especially in clinical settings serving autistic individuals.

4. Application 2: Matching Law in Basketball Shot Selection (Alferink et al., 2009) (52:39–65:14)

• Rob reviews a study using basketball stats to explore the generality of the matching law outside the lab ([53:37]).
• Study Recap:
  • Analysis of shot selection (two vs. three-point field goals) at team and individual player levels.
  • The matching law accounted for much of the shot distribution variance, especially among better-performing players/teams ([61:59]).
  • Persistent bias toward three-point shots, highlighting “quality” of reinforcement ([59:18]).
• Rob’s candid reaction:
  • Rob: “I do think this might be the most pointless article I have ever read in my entire career.” ([53:37])
  • Diana: “Because the data are there...it's very hard...to find places in the ‘natural environment’ where you know pretty clearly what the reinforcers are…” ([53:39], [54:02])
  • Discussion on correlation vs. causation; matching law is descriptive, not necessarily predictive or instructional for game strategy ([62:17]).

5. Big-Picture Conclusions & Dissemination (66:27–69:37)

• Matching Law grants powerful insight into why people (and animals) behave as they do when choices are involved—across basic research and applied settings.
• Quantitative details are helpful, but practitioners can benefit from more general application to understand client preferences, bias, and sensitivity to reinforcement.
• Diana:
  • "We are not special organisms. We behave just as other organisms do, and our behavior is going to follow reinforcement just like other organisms..." ([67:37])
• Jackie: “It's always important to know about it, know that it's out there, and remind ourselves that it's out there. … when we are stuck…we can refer back…” ([69:37])

Notable Quotes & Memorable Moments

• On Daily Relevance:
  “In almost every instance of our lives, choice is always present … There's always multiple behaviors that we could choose from.” – Jackie ([10:08], [11:18])
• On Math Anxiety:
  “I think anything with equations sometimes can be scary...especially...the generalized matching law and the hyperbolas...even me, I'm like, why do they have to log things?” – Jackie ([07:06])
• On the Role of Research:
  “I really appreciate all those cancer researchers doing all that work...but I don't understand what exactly they do...But when they say we have the best tools possible, I trust them.” – Diana ([25:32])
• On Basketball Article Skepticism:
  “I appreciate that they’re being honest that these results are interesting but aren’t necessarily going to change how we bet on basketball in the future.” – Rob ([64:37])
• On Practical Use:
  “If you chase me down with a matching law article, I run to the other side of the room!” – Rob ([66:13])

Timestamps for Key Segments

| Segment | Timestamps | |----------------------------------------|--------------| | Banter/Intro/Theme | 00:13–05:05 | | Definition & Relevance | 05:05–07:22 | | Reed & Kaplan Tutorial Review | 07:42–30:28 | | Morris & Vollmer (Social Allocation) | 33:42–52:39 | | Alferink et al. (Basketball) | 52:39–65:14 | | Dissemination & Reflection | 66:27–69:37 | | Recommended Past Episodes ("Pairings") | 70:10–73:00 | | Lighthearted Close | 73:03–75:49 |

Related Past Episodes Recommended (“Pairings”) (70:12–73:00)

• Basics Series on ABA Inside Track:
  • Episode 126 – Behavioral Economics (with Derek Reed)
  • Episodes 175 & 195 – Token Economies
  • Episode 143 – Stimulus Equivalence
  • Episode 223 – Generality and Generalization
  • Episode 248 – Delayed Discounting
  • Episode 256 – Acceleration Charts Explained
  • Episode 86 – Behavioral Momentum

Episode Tone and Takeaway

Reflective, honest, and playful, the episode demystifies a “scary” topic and encourages practitioners to engage with the Matching Law—not for its equations per se, but for the conceptual richness it adds to understanding choice and reinforcement. Listeners walk away with greater comfort integrating the Matching Law into clinical reasoning, plus a few laughs (and cake-or-cupcake debates) along the way.