Fitness choices: The Matching Law

I really enjoy being active, and I’m sure like many of you, I still wish I could find a way to increase my daily activity. I spend a lot of time travelling to and between clients, and although I spend most of sessions engaging with the clients, some activities like reading or arts and crafts involve sitting. So when I get the opportunity to go for a walk during my lunch break, or to go on the trampoline with one of my clients then I take that opportunity straight away!

The benefits of being regularly active and getting more exercise are limitless; reduced risk of heart related illnesses and diseases, diabetes, stroke and cancer. In addition, regular exercise is related to improved mental health, self-esteem, reduced symptoms of depression and anxiety, etc.. You can learn more about all the health benefits from the NHS Choices webpage. It is recommended that you get “at least 150 minutes of physical activity over a week through a variety of activities”, (NHS Choices, 2018). Unfortunately, the possible punishing consequences (poor health) of not being active or exercising are so far in the future they seem improbable and uncertain, and are not contingent on bad health habits (do not immediately follow and/or impact behaviour).

I had been thinking about the generalised Matching Law in regards to being active last week when I was involved in a step competition on a popular health app. I wear a watch that works as a pedometer and calculates how many steps I take via the health app. There is a variety of challenges on the app I use. These involve going head to head with friends to get the highest number of steps in a day, a week or a weekend.

This week when I was involved in a challenge, I made an effort to engage in behaviours that would allow me to take extra steps. This includes walking to the shop, rather than driving, taking a walk on my lunch break or if I arrived early to a client, using that time to take a short walk.

The Matching Law is a theory that explains how choices are made. Aubrey Daniels states in his book ‘Bringing out the Best in People: How to apply the astonishing power of positive reinforcement’ that “the matching law states that the amount of reinforcement a person receives for a particular behaviour is matched by the time spent engaged in that behaviour” (page 183).

A screenshot of the final results from the fitbit competition


I wondered why I chose to engage in these behaviours. There was reinforcement available to me if I chose to drive to the shops (it’s faster, less effort) or if I chose to sit and relax in my spare time. I could go on social media while on lunch or if I arrived early to my clients (which is a highly valued, and immediate reinforcer for me!). But during this week I placed a higher value on getting the steps, so allocated more time to walking!

It was discovered that pigeons would allocate more time pecking on one of two keys when the two keys represented a concurrent schedule (Herrnstein, 1961). A concurrent schedule is when two ratio (response) or interval (time) schedules are available for different responses/behaviours simultaneously or together. The results of this study demonstrate that organisms will spend more time behaving and responding under the schedule that has the richer reinforcement (reinforcement is delivered more frequently). Myerson & Hale (1984) stated that “the matching law provides a useful approximation of the relation between the distribution of reinforcements and the allocation of behaviour”.

matching law equation
Simplified Matching Law equation


This means when choosing between two behaviours, walking (being active) vs sitting (not active) the behaviour with the densest (most) value will be the behaviour that will be observed. This can change from moment to moment and value of reinforcement may change. If you’re tired, the value of reinforcement from walking is lower. On days when you have more energy, or like me want to win a competition, you may go out for a walk instead of resting at home. The matching law applies to many behaviours, as we are constantly making choices between behaving in a variety of ways.

The Matching Law can help you become more active! Can you change the reinforcement available for being active, so you begin to spend more time being active, whether it’s walking or hitting the gym? Washington et al (2014) investigated the use of a contingency prize (tickets for prizes) for participants who increased the number of steps they took, and found that 80% of the participants increased their daily steps. This research shows that with a denser reinforcer, activity levels can be increased. For me, I’m quite competitive, so bragging rights for winning the step challenge is enough for me (although I came 3rd in the competition I shared above).

Feel free to comment or message me and share your tricks for being active, whether it be a promised reinforcer or an app. Also you can message me if you want an informal chat about your own fitness choices. Contact me via the contact form or via my email address

Also, you can read the November 2016 edition of Busy Analytical Bee Newsletter to learn more about Behavioural interventions that increase exercise. I also discussed fitness and the matching law in a previous blog called ‘The Run’.

Preview of the November edition



Daniels, A. C. (1999). Bringing out the Best in people: How to Apply the Astonishing power of positive reinforcement. New York, NY: McGraw-Hill.

Herrnstein, R. J. (1961). Relative and absolute strength of response as a function of frequency of reinforcement. Journal of Experimental Analysis of Behavior, 13, 243-266.

Myerson, J. & Hale, S. (1984). Practical implications of the Matching Law. Journal of Applied Behavior Analysis, 17, 367-380.

NHS Choices, Exercise, (2018 June, 11). Retrieved from:

Raclin, H. (1971). On the tautology of the Matching Law. Jouranal of Experimental Analysis of Behavior, 15, 249-251.

Washington, W. D., Banna, K. M., & Gibson, A. L. (2014). Preliminary efficacy of prize-based contingency management to increase activity levels in healthy adults. Journal of Applied Behavior Analysis, 47, 1-15.

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