This study considers language proficiency test scores achieved by ESL students who subsequently entered a New Zealand university at the undergraduate level. Scores from IELTS and the university's in-house English Proficiency Test are analysed to determine the predictive ability of overall scores on these two tests and scores for each of the four language skills on academic success. The results indicated that language proficiency had a significant effect on undergraduate academic achievement. Furthermore, analyses of the predictive ability of scores for listening, speaking, and reading were remarkably similar between the tests, with non-significant results of similar magnitude for each skill. On the other hand, IELTS writing scores demonstrated a non-significant negative effect on academic achievement, while EPT writing scores were strongly significantly predictive of academic achievement. The results suggest that universities may benefit from measuring ESL students' academic writing proficiency in more authentic university-level writing tasks.