Some recently proposed robust methods for time domain timing and frequency synchronization in OFDM systems incorporate the use of cross-correlation based threshold detection in their timing adjustment and joint time-frequency algorithms. In this paper, we analyze the threshold criterion used and derive its theoretical performance. This translates into a better characterization of these OFDM synchronization algorithms, leading to a closer match between design expectations and practical performance. Computer simulations show a strong agreement between theoretical predictions and numerical results.