You need to look at several attributes when choosing a central defensive midfielder: defending, to be able to support the back line; strength, to win possession more times; heading, to win the ball in aerial moves like goal kicks; pace, to cover as many spaces as possible; stamina, so he can equally participate in offensive and defensive plays (especially useful for players with high/high work rates); passing and possession, so that he can properly start attacks. In our opinion, the two first are the most important ones.
Usually, defensive midfielders are chosen to help the defence. So, it makes sense that they have high defensive stats. The area of the field occupied by CDMs is the one where most ball disputes happen. Strong players will have highest probabilities of winning the ball.