通过时间反事实分析，量化飞盘运动中球员启动时机的优劣。

Ultimate is a sport where points are scored by passing a disc and catching it in the opposing team's end zone. In Ultimate, the player holding the disc cannot move, making field dynamics primarily driven by other players' movements. However, current literature in team sports has ignored quantitative evaluations of when players initiate such unlabeled movements in game situations. In this paper, we propose a quantitative evaluation method for movement initiation timing in Ultimate Frisbee. First, game footage was recorded using a drone camera, and players' positional data was obtained, which will be published as UltimateTrack dataset. Next, players' movement initiations were detected, and temporal counterfactual scenarios were generated by shifting the timing of movements using rule-based approaches. These scenarios were analyzed using a space evaluation metric based on soccer's pitch control reflecting the unique rules of Ultimate. By comparing the spatial evaluation values across scenarios, the difference between actual play and the most favorable counterfactual scenario was used to quantitatively assess the impact of movement timing. We validated our method and show that sequences in which the disc was actually thrown to the receiver received higher evaluation scores than the sequences without a throw. In practical verifications, the higher-skill group displays a broader distribution of time offsets from the model's optimal initiation point. These findings demonstrate that the proposed metric provides an objective means of assessing movement initiation timing, which has been difficult to quantify in unlabeled team sport plays.