Sports and racing are a huge category for Mario games – and they basically comprise this entire section.
First of all, let's talk about some potential controversy here in terms of lineage. Even though NES Tennis is an earlier program than NES Golf (its original release date was January of 1984 in Japan versus Golf's May of the same year), I've chosen Golf as the main point of lineage for sports games because it was the first game in this genre to feature a playable Mario. Everyone's favorite plumber only made an appearance as an umpire in Tennis, and wasn't playable.
However, even then, there's a potential point of contention. In the Japanese version of NES Golf, the main character is called Ossan – but he was changed to Mario for the US version, which was released on October 18th 1985 as a launch title for the NES alongside Tennis (and 15 other titles). Still, for the reasons outlined above, I'm considering Golf as the first sports title to feature a playable Mario and therefore it takes a critical point of place in the Mario Games Family Tree.
Excitebike: Bun Bun Mario Battle Stadium is a bit of an odd duck. It's basically a remake of Excitebike featuring Mario characters that was made for the Super Famicom and Satellaview. What is it? It's a peripheral that was released only in Japan, and basically sits under the Super Famicom. It was capable of receiving satellite radio signals broadcast by St GIGA during a show called the Super Famicom Hour. While the show aired, Satellaview data was streamed to the device, which it was able to decode into games and demos, many of which were broadcast in installments and parts.
A key title for the racing genre is Famicom Grand Prix F1 Race – a Japan-only release for the Famicom Disk System that's essentially the first racing game to feature Mario. Or is it? During my research, I noticed that on Wikipedia, in its entry for F-1 Race it says that this late 1984 game features appearances by characters including, "Mario, Luigi, Princess Peach, Toad, Bowser, Link, Samus, Pit, and Donkey Kong." I think this must be referring to the later Game Boy version, since Samus didn't appear until 1986, and I can find no other record of any appearances by Mario or any other characters in F1 Race. If anyone can confirm that, please do so in the comments section. What's for sure, however, is that Famicom Grand Prix F1 Race spawned a long line of Mario racing games, including the highly important Kart series. That itself gave rise to three Mario Kart coin-ops, which I've also included in the Family Tree.
What I find interesting is that Mario sports games only covered racing, tennis and golf for many years until the mid 00's, when there was a sudden diversification into other sports – baseball, basketball, and soccer. At the same time, there were also several other sports-type game releases, including Sports Mix, the Mario and Sonic Olympic games series, and Dance Dance Revolution: Mario Mix, which I've put in this category since it runs along the same lines as sports-type games.
The Mario and Sonic Olympic-themed games have gone on to become quite successful in their own right, and the line will continue in 2016 with Mario & Sonic at the Rio 2016 Olympic Games.