Skip to main content

Diverging from the shadows: explaining individual deviation from plea bargaining in the “shadow of the trial”



The “shadow of the trial” (SOT) theory posits that plea decisions result from mathematical predictions of probability of conviction (POC) at trial and potential trial sentence (TS). Tests of the SOT model often find support in the aggregate, but not at the individual level. This study examines the factors that account for adherence to, or deviation from, the SOT model, such as mathematical competence, a factor not previously examined in tests of the SOT model.


Participants were randomly assigned to one of nine conditions corresponding to manipulations of probability of conviction (10%, 50%, 90%) and potential trial sentence (5, 15, 25 months). After reading a case description, participants were asked whether they would accept a plea offer and how much time in jail they would be willing to spend; a subset of participants was offered a counter plea offer. Participants then answered questions assessing numeracy and about their legal opinions and personal characteristics.


Results showed that probability of conviction, but not trial sentence, influenced shadow model adherence. Participants assigned to 50% and 90% POC conditions were significantly less likely to deviate from the SOT model than participants assigned to 10% conditions. This effect did not interact with TS. Additionally, the odds of fitting the SOT model increased significantly as participants’ numeracy scores increased.


Our results raise questions about the validity of the SOT model at low POCs and challenge its assumption that defendants are capable of conducting the mathematical calculations required to fit the model.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2


  1. 1.

    This question presented the participant with three options: (1) accept a plea offer if it is the value they specified or lower, (2) accept the plea offer even if it higher than the value they specified, or (3) reject the plea offer regardless of the length of the jail sentence. These categories were subsequently collapsed into a dichotomous measure of whether or not the participant was willing to accept a plea offer versus unwilling to accept any plea deal.

  2. 2.

    Note that participants who indicated that they were unwilling to accept a plea deal of any value were coded as deviating from the shadow model regardless of whether they disagreed with their attorney.

  3. 3.

    A post hoc power analysis indicated that our sample size for logistic regression models 1 and 2 was sufficient to detect an odds ratio of 1.68 (power = 0.92), considered equivalent to a Cohen’s d of 0.2 or higher (see Chen et al. 2010).

  4. 4.

    The results of models 1 and 2 remained unchanged when the invalid responses were included.

  5. 5.

    Estimated statistical power to detect an odds ratio of 1.68 decreased to 0.78 for model 3 due to sample attrition. This is a power level slightly lower than the convention of .80 proposed by Cohen (1992).


  1. Bartlett, J., & Zottoli, T. (in press). The paradox of conviction probability: mock defendants want better deals as risk of conviction goes up. Law and Human Behavior.

  2. Bibas, S. (2004). Plea bargaining outside the shadow of trial. Harvard Law Review, 117(8), 2463–2547.

    Article  Google Scholar 

  3. Bjerk, D. (2008). Glass ceilings or sticky floors? Statistical discrimination in a dynamic model of hiring and promotion. The Economic Journal, 118(530), 961–982.

    Article  Google Scholar 

  4. Bonneau, D., & McCannon, B. C. (2019). Bargaining in the shadow of the trial? Deaths of law enforcement officials and the plea bargaining process.

  5. Bordens, K. S. (1984). The effects of likelihood of conviction, threatened punishment, and assumed role on mock plea bargaining decisions. Basic and Applied Social Psychology, 5(1), 59–74.

    Article  Google Scholar 

  6. Bushway, S. D. (2019). Defendant decision-making in plea bargains. In V. A. Edkins & A. D. Redlich (Eds.). A system of pleas: social sciences contributions to the real legal system (pp. 24–36). Oxford University Press.

  7. Bushway, S. D., & Redlich, A. D. (2012). Is plea bargaining in the “shadow of the trial” a mirage? Journal of Quantitative Criminology, 28(3), 437–454.

    Article  Google Scholar 

  8. Bushway, S. D., Redlich, A. D., & Norris, R. J. (2014). An explicit test of plea bargaining in the “shadow of the trial”. Criminology, 52(4), 723–754.

    Article  Google Scholar 

  9. Chen, H., Cohen, P., & Chen, S. (2010). How big is a big odds ratio? Interpreting the magnitudes of odds ratios in epidemiological studies. Communications in Statistics - Simulation and Computation, 39(4), 860–864.

    Article  Google Scholar 

  10. Cheng, K. K.-y., & Chui, W. H. (2015). Beyond the shadow-of-trial: decision-making behind plea bargaining in Hong Kong. International Journal of Law, Crime and Justice, 43(4), 397–411.

    Article  Google Scholar 

  11. Clatch, L. (2017). Shining a light on the shadow-of-trial model: a bridge between discounting and plea bargaining note. Minnesota Law Review, 102(2), 923–968.

    Google Scholar 

  12. Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155.

    Article  Google Scholar 

  13. Dervan, L. E., & Edkins, V. A. (2013). The innocent defendant’s dilemma: an innovative empirical study of plea bargaining's innocence problem criminal law. Journal of Criminal Law and Criminology, 103, 1–48.

    Google Scholar 

  14. Eckel, C. C., & Grossman, P. J. (2008). Men, women and risk aversion: experimental evidence. Handbook of Experimental Economics Results, 1, 1061–1073.

    Article  Google Scholar 

  15. Fan, A. Z., Grant, B. F., Ruan, W. J., Huang, B., & Chou, S. P. (2019). Drinking and driving among adults in the United States: results from the 2012–2013 national epidemiologic survey on alcohol and related conditions-III. Accident Analysis & Prevention, 125, 49–55.

    Article  Google Scholar 

  16. Federal Bureau of Investigation (2018). Crime in the United States, 2018. Retrieved (September 2020), from (

  17. Garnier-Dykstra, L. M., & Wilson, T. (2019). Behavioral economics and framing effects in guilty pleas: a defendant decision making experiment. Justice Quarterly, 1–25.

  18. Gonzalez, R., & Wu, G. (1999). On the shape of the probability weighting function. Cognitive Psychology, 38(1), 129–166.

    Article  Google Scholar 

  19. Gregory, T. (2013). DUI demographics point to higher mix of women. Chicago tribune. Retrieved from

  20. Gregory, W. L., Mowen, J. C., & Linder, D. E. (1978). Social psychology and plea bargaining: applications, methodology, and theory. Journal of Personality and Social Psychology, 36(12), 1521–1530.

    Article  Google Scholar 

  21. Helm, R. K., Hans, V. P., Reyna, V. F., & Reed, K. (2020). Numeracy in the jury box: numerical ability, meaningful anchors, and damage award decision making. Applied Cognitive Psychology, 34(2), 434–448.

    Article  Google Scholar 

  22. Hill, W. T., & Brase, G. L. (2012). When and for whom do frequencies facilitate performance? On the role of numerical literacy. The Quarterly Journal of Experimental Psychology, 65(12), 2343–2368.

    Article  Google Scholar 

  23. Johnson, B. D. & Richardson, R. (2019). Race and plea bargaining. In V. A. Edkins & A. D. Redlich (Eds.) A system of pleas: social sciences contributions to the real legal system (pp. 83–106). Oxford University Press.

  24. Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2), 263–291.

    Article  Google Scholar 

  25. Kraemer, H. C., & Thiemann, S. (1987). How many subjects? Statistical power analysis in research. Newbury Park, Calif: Sage.

    Google Scholar 

  26. Lipkus, I. M., Samsa, G., & Rimer, B. K. (2001). General performance on a numeracy scale among highly educated samples. Medical Decision Making, 21(1), 37–44.

    Article  Google Scholar 

  27. Mather, M., Mazar, N., Gorlick, M. A., Lighthall, N. R., Burgeno, J., Schoeke, A., & Ariely, D. (2012). Risk preferences and aging: the “certainty effect” in older adults’ decision making. Psychology and Aging, 27(4), 801.

    Article  Google Scholar 

  28. Mnookin, R. H., & Kornhauser, L. (1979). Bargaining in the shadow of the law: the case of divorce. The Yale Law Journal, 88(5), 950–997.

    Article  Google Scholar 

  29. National Center for State Courts (n.d.). Trends in state courts. Retrieved from

  30. Oh, S., Vaughn, M. G., Salas-Wright, C. P., AbiNader, M. A., & Sanchez, M. (2020). Driving under the influence of alcohol: findings from the NSDUH, 2002–2017. Addictive Behaviors, 108, 106439.

    Article  Google Scholar 

  31. Petrova, D. G., Van der Pligt, J., & Garcia-Retamero, R. (2014). Feeling the numbers: on the interplay between risk, affect, and numeracy. Journal of Behavioral Decision Making, 27(3), 191–199.

    Article  Google Scholar 

  32. Pezdek, K., & O'Brien, M. (2014). Plea bargaining and appraisals of eyewitness evidence by prosecutors and defense attorneys. Psychology, Crime & Law, 20(3), 222–241.

    Article  Google Scholar 

  33. Redlich, A. R. & Edkins V. A. (2019). Moving forward in a system of pleas. In V. A. Edkins & A. D. Redlich (Eds.). A system of pleas: social sciences contributions to the real legal system (pp. 187–197). Oxford University Press.

  34. Redlich, A. D., Wilford, M. M., & Bushway, S. (2017). Understanding guilty pleas through the lens of social science. Psychology, Public Policy, and Law, 23(4), 458.

  35. Schneider, R. A., & Zottoli, T. M. (2019). Disentangling the effects of plea discount and potential trial sentence on decisions to plead guilty. Legal and Criminological Psychology, 24(2), 288–304.

    Article  Google Scholar 

  36. Schwartz, L. M., Woloshin, S., Black, W. C., & Welch, H. G. (1997). The role of numeracy in understanding the benefit of screening mammography. Annals of Internal Medicine, 127(11), 966–972.

    Article  Google Scholar 

  37. Tor, A., Gazal-Ayal, O., & Garcia, S. M. (2010). Fairness and the willingness to accept plea bargain offers. Journal of Empirical Legal Studies, 7(1), 97–116

    Article  Google Scholar 

  38. United States Sentencing Commission (2018). 2018 federal sentencing statistics. Retrieved from

  39. Weisburd, D., & Britt, C. (2014). Statistics in criminal justice (4th ed.). New York: Springer.

    Book  Google Scholar 

  40. Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function. Management Science, 42(12), 1676–1690 .

    Article  Google Scholar 

  41. Wright, R. F., Roberts, J., & Wilkinson, B. (2020). The shadow bargainers. Cardozo Law Review, Forthcoming. Available at SSRN:

Download references


We would like to thank Tina Zottoli and Jennifer Bartlett for sharing their work with us and for their continued communication and insight throughout the course of this study.

Author information



Corresponding author

Correspondence to Kevin Petersen.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material


(DOCX 31 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Petersen, K., Redlich, A.D. & Norris, R.J. Diverging from the shadows: explaining individual deviation from plea bargaining in the “shadow of the trial”. J Exp Criminol (2020).

Download citation


  • Shadow of the trial
  • Plea bargaining
  • Guilty pleas
  • Legal decision-making
  • Numeracy
  • Criminal justice