This paper introduces a statistical potential, Discrete Optimized Protein Energy (DOPE), for assessing and predicting protein structures. DOPE is derived from a sample of native protein structures using probability theory, without relying on statistical mechanics. It is based on an improved reference state that accounts for the finite and spherical shape of native structures. DOPE was tested against five other scoring functions using six multiple target decoy sets, and it performed best in all criteria except for one tie. DOPE was incorporated into the modeling package MODELLER-8 for various applications, including model assessment, loop modeling, and fitting into cryo-electron microscopy mass density maps combined with comparative protein structure modeling. DOPE is derived from the negative logarithm of the joint probability density function of a given protein. It is based on the probability theory and does not assume the Boltzmann distribution. The reference state is a finite sphere of uniform density and appropriate size, rather than the distribution of interatomic distances in the sample native structures. This approach allows for a more accurate assessment of protein structures. DOPE was tested on multiple decoy sets and showed high accuracy in identifying the native structure, correlating with model error, and selecting the most accurate non-native model. DOPE outperformed other scoring functions in these tasks. The accuracy of DOPE is influenced by the size of the reference state, and it is less accurate for small structures and low-accuracy models. DOPE is also less accurate for NMR structures due to the difficulty in determining their exact conformation. DOPE is a statistical potential that depends on atomic distances and is used in various applications for protein structure prediction and assessment. It is derived from a sample of native structures and is based on probability theory. DOPE is more accurate than other statistical potentials and is applicable to models of any size. It is also more broadly applicable and can be generalized to other kinds of statistical potentials and future developments. The accuracy of DOPE is influenced by the completeness of the assessed model and the size of the assessed model. DOPE is less accurate for small models and models with low accuracy. It is also less accurate for NMR structures due to the difficulty in determining their exact conformation.This paper introduces a statistical potential, Discrete Optimized Protein Energy (DOPE), for assessing and predicting protein structures. DOPE is derived from a sample of native protein structures using probability theory, without relying on statistical mechanics. It is based on an improved reference state that accounts for the finite and spherical shape of native structures. DOPE was tested against five other scoring functions using six multiple target decoy sets, and it performed best in all criteria except for one tie. DOPE was incorporated into the modeling package MODELLER-8 for various applications, including model assessment, loop modeling, and fitting into cryo-electron microscopy mass density maps combined with comparative protein structure modeling. DOPE is derived from the negative logarithm of the joint probability density function of a given protein. It is based on the probability theory and does not assume the Boltzmann distribution. The reference state is a finite sphere of uniform density and appropriate size, rather than the distribution of interatomic distances in the sample native structures. This approach allows for a more accurate assessment of protein structures. DOPE was tested on multiple decoy sets and showed high accuracy in identifying the native structure, correlating with model error, and selecting the most accurate non-native model. DOPE outperformed other scoring functions in these tasks. The accuracy of DOPE is influenced by the size of the reference state, and it is less accurate for small structures and low-accuracy models. DOPE is also less accurate for NMR structures due to the difficulty in determining their exact conformation. DOPE is a statistical potential that depends on atomic distances and is used in various applications for protein structure prediction and assessment. It is derived from a sample of native structures and is based on probability theory. DOPE is more accurate than other statistical potentials and is applicable to models of any size. It is also more broadly applicable and can be generalized to other kinds of statistical potentials and future developments. The accuracy of DOPE is influenced by the completeness of the assessed model and the size of the assessed model. DOPE is less accurate for small models and models with low accuracy. It is also less accurate for NMR structures due to the difficulty in determining their exact conformation.