Lexicase selection achieves very good solution quality by introducing ordered test cases. However, the computational complexity of lexicase selection can prohibit its use in many applications. In this paper, we introduce Batch Tournament Selection (BTS), a hybrid of tournament and lexicase selection which is approximately one order of magnitude faster than lexicase selection while achieving a competitive quality of solutions. Tests on a number of regression datasets show that BTS compares well with lexicase selection in terms of mean absolute error while having a speed-up of up to 25 times. Surprisingly, BTS and lexicase selection have almost no difference in both diversity and performance. This reveals that batches and ordered test cases are completely different mechanisms which share the same general principle fostering the specialization of individuals. This work introduces an efficient algorithm that sheds light onto the main principles behind the success of lexicase, potentially opening up a new range of possibilities for algorithms to come.