Cricket

Cricket was a bat and ball game. Though primarily associated with Britain and her former colonies, (BFA: The Roof of the World) cricket became an Olympic sport by at least 2060. (BFA: Nekromanteia)

The Doctor had a long relationship with the game. Although his first incarnation claimed not to know the sport at all when he landed the TARDIS in the middle of an Australia/England match, (DW: "Volcano") later incarnations seemed to know the game well. (DW: The Ribos Operation, The Horns of Nimon, Black Orchid; Human Nature; NA: Human Nature; Happy Endings; DWM: The Tides of Time; BFA: Autumn)

Indeed, the Doctor's fifth self was particularly keen on the sport, sometimes playing it for months on end. (BFA: Autumn, NA: Happy Endings)

Description
Cricket was played using a flat-faced bat and specially designed cricket balls on a pitch — itself situated on a larger playing field delimited by a boundary line. The offensive object of the game was for the batsmen to score as many runs as possible. The defensive object was to get the batsmen out, either by successful bowling or by running the batsmen out. (NA: Happy Endings, DW: Black Orchid)

The Doctor and cricket
The Doctor appreciated the game in many of his incarnations, but it was his fifth self that seemed the keenest on the game. Not only did the Fifth Doctor regularly wear an outfit that approximated cricket whites, but he took every opportunity to play it, (DW: Black Orchid, BFA: Autumn; MA: Goth Opera) teach his companions its rules (BFA: Phantasmagoria) and attend famous matches, usually called "tests". (BFA: The Roof of the World, Nekromanteia; ST: Graham Dilley Saves the World)

The Doctor sometimes spent long periods of time playing the game. The Fifth Doctor, for instance, spent one whole summer with the local team at Cheldon Bonniface (NA: Happy Endings) and at least one full season with the Stockbridge Cricket Club. (BFA: Autumn) He had probably also intended to spend a similarly long period playing cricket in the Eye of Orion, but Borusa's plan to pluck the Doctor's past selves from the time stream intervened. (DW: The Five Doctors; EDA: The Eight Doctors)

The Doctor's ability to play the game varied depending upon incarnation. While his fifth self was evidently an excellent player who was an asset to every side he joined, (DW: Black Orchid, BFA: Autumn) his seventh incarnation once flatly claimed that he needed to learn the game because he was no longer the same man. Nevertheless, he seemed to retain a knowledge of the strategy behind the game, as he once cunningly called for a batsman on his team to deliberately throw a full toss in order to bring the match to a dramatic conclusion. (NA: Happy Endings)

Regardless of the Seventh Doctor's protestations, there was some evidence that the Doctor retained some instinctual ability to play across incarnations. Even though he had used the Chameleon Arch to turn himself into a human, the Tenth Doctor, as John Smith, expertly bowled a cricket ball in a complicated way that saved the life of a baby and its mother. (DW: Human Nature)

Companions and cricket
The Doctor's companions were almost universally unimpressed with the game and resisted the Doctor's attempts at proselytisation. (BFA: Phantasmagoria, The Roof of the World) Indeed, when Roz innocently asked the Seventh Doctor the question, "What's cricket?", Bernice Summerfield immediately interjected, "I think that's in the top ten of the most dangerous questions in the universe, right up there with 'Excuse me, Mr Dalek, what does that stick do?'" (NA: Happy Endings)

Behind the scenes
Cricket was partially responsible for the first broadcasting delay in Doctor Who history. "Hidden Danger", the third episode of The Sensorites, was bumped from the 4 July 1964 schedule because of an overrunning Australia / England test at and a long tennis match at.