Following the trends established in psychology and emerging in L2 research, we explain our support for an Open Science approach in this paper (i.e., developing, analyzing and sharing datasets) as a way to answer controversial and complex questions in applied linguistics. We illustrate this with a focus on a frequently debated question, what underlies individual differences in the dynamic system of post-pubertal L2 speech learning? We provide a detailed description of our dataset which consists of spontaneous speech samples, elicited from 110 late L2 speakers in the UK with diverse linguistic, experiential and sociopsychological backgrounds, rated by ten L1 English listeners for comprehensibility and nativelikeness. We explain how we examined the source of individual differences by linking different levels of L2 speech performance to a range of learner-extrinsic and intrinsic variables related to first language backgrounds, age, experience, motivation, awareness, and attitudes using a series of factor and Bayesian mixed-effects ordinal regression analyses. We conclude with a range of suggestions for the fields of applied linguistics and SLA, including the use of Bayesian methods in analyzing multivariate, multifactorial data of this kind, and advocating for publicly available datasets. In keeping with recommendations for increasing openness of the field, we invite readers to rethink and redo our analyses and interpretations from multiple angles by making our dataset and coding publicly available as part of our 40th anniversary ARAL article.