His first-class career lasted only from 1870 to 1872, for he played no more at first-class level after leaving Cambridge. As well as the university, he also appeared for MaryleboneCricket Club. He was a right-arm roundarmfast bowler and a right-handed batsman. In 22 matches he took 65 wickets at an average of 17.20, with best innings figures of 6/35. He took five or more wickets in an innings four times and ten or more wickets in a match once. He made 471 runs at an average of 14.27. He passed fifty only once, when he scored 73 not out. According to Wisden he was a "free and powerful hitter". His brother, Halsted Cobden, also played first-class cricket. Cobden also played county cricket for Herefordshire, Radnorshire, and, between 1868 and 1890, for Shropshire. For the latter he scored a total 926 runs, in 37 two-day matches while playing at club level for Bedstone, Ludlow and Radnor.
The match, scheduled for three days, was finished in two. Cambridge scored 147 in their first innings. Oxford made 175 in reply, with Cobden taking 4/41. Cambridge slumped to 40/5 in their second innings, only 12 runs ahead, with C.K. Francis doing most of the damage. W. Yardley then came in to join J.W. Dale, and they added 116 for the sixth wicket. Yardley made exactly 100, the first hundred ever made in the fixture. Dale scored 67. Cambridge finished with 206, with Francis taking 7/102. Oxford needed 179 to win. Cobden took the wicket of W.H. Hadow for a duck and Oxford were 0/1. However they recovered and reached 153/3 at one point, needing only another 26, thanks to 69 from C.J. Ottaway and 44 from A.T. Fortescue. Though wickets then began to fall, they progressed to 175/6, and their victory seemed assured. At that point E.E. Ward dismissed Francis. Ward had taken six of the seven wickets to fall. He finished with the fine figures of 6/29 from 32 four ball overs. When Cobden began what proved to be the final over, the score was still 175/7, with four runs needed to win. From the first ball, F. H. Hill played a shot which seemed sure to reach the boundary and thus to win the match. However it was brilliantly fielded and the batsmen could only run one. Hill then had to watch the tail-enders try to cope with Cobden in poor light. S. E. Butler was caught off the second ball of the over and T. H. Belcher was bowled by the third. With four-ball overs at that time, Cobden had one ball left. If the batsman, W. A. Stewart, could survive it, then Hill would face the next over and would probably see Oxford home. But Cobden made no mistake and Stewart was bowled. Cobden finished with figures of 4/35, and 8/76 in the match.