Gesture and signature passwords are two-dimensional figures created by drawing on the surface of a touchscreen with one or more fingers. Prior results about their security have used resilience to either shoulder surfing, a human observation attack, or dictionary attacks. These evaluations restrict generalizability since the results are: non-comparable to other password systems (e.g. PINs), harder to reproduce, and attacker-dependent. Strong statements about the security of a password system use an analysis of the statistical distribution of the password space, which models a best-case attacker who guesses passwords in order of most likely to least likely. Estimating the distribution of recognition passwords is challenging because many different trials need to map to one password. In this paper, we solve this difficult problem by: (1) representing a recognition password of continuous data as a discrete alphabet set, and (2) estimating the password distribution through modeling the unseen passwords. We use Symbolic Aggregate approXimation (SAX) to represent time series data as symbols and develop Markov chains to model recognition passwords. We use a partial guessing metric, which demonstrates how many guesses an attacker needs to crack a percentage of the entire space, to compare the security of the distributions for gestures, signatures, and Android unlock patterns. We found the lower bounds of the partial guessing metric of gestures and signatures are much higher than the upper bound of the partial guessing metric of Android unlock patterns.