I have thought about this for a long time and could never really think of a way to make it work. It either becomes a tedious game of dice and stats or it goes nowhere. There's just no way to effectively make racing the centerpiece of an interactive story- at least not one that I found appealing as someone who follows a lot of racing.

Judging by the replies and the system you have in mind, it seems like you are looking for something maybe closer to car combat which may work with what you have put together. Depending on what you want in your story, racing has a lot of variables: the weather, track temp, driver ability/fatigue, tire performance, car type. The list goes on and on and that is what always kept me from really considering it. Once you start putting stats on one thing, it just leads to another.  

The best advice I could give is that you'd have to be fairly discerning in your recruiting and then see how much dice the players are interested in before you invest more time. Depending on the interest you get, go from there. Some people are going to want to write more and some are going to want to roll more. The only thing that ever really felt "fair" to me was to roll for the true variables in any race: the weather, caution flags and mechanical failures. There are others, but those apply no matter the discipline. To determine a "winner" and assuming most drivers/cars are somewhat evenly balanced you could let the players just roll maybe three times (race start, halfway point and finish) for who has position and then let the writing take it up from there.

It's a rabbit hole for sure, so good luck to you.

-P