Stoddart originally played for the Eastern Ranges in the TAC Cup. He recorded the second-best running vertical leap at the AFL Draft Combine, at 98 centimetres (39 in).[3] Stoddart was drafted by Sydney with pick 53 in the 2017 AFL draft, and wears number 33.[1] He was touted as a possible round one debutant by Swans captain Josh Kennedy. However, he was overlooked and later injured his back in a practice match against the GWS Giants.[4] Stoddart signed a one-year contract with the club, tying him to the Swans until 2020.[5] Stoddart was delisted at the conclusion of the 2020 AFL season after playing just six games for Sydney.[6]