The model I used was to calculate the following quantity:

*sum of (gridPosition-racePosition)/racePosition) over all races*

The numerator (top term),

`gridPosition-racePosition`, gives the number of positions gained (positive), or lost (negative).

These values are scaled by dividing through by the final racePosition in each corresponding race, which means that position changes at the head of the field count for more than those at the back of the field. (There is a certain balancing effect going on here though, because cars that start at the back of the field may gain several places through non-finishers amongst the cars that started ahead of them). Here are the resulting rankings...

I then tweaked the model to add in a term that accounted for holding position, equal to 1/racePosition (so the equation became

`sum of ( (gridPosition==racePosition)/racePosition + (gridPosition-racePosition)/racePosition) over all races`. Here's the result this time:

A problem with that approach is that there is no differentiation between gaining a a place and holding position. We can account for this using the following refinement:

`sum of ( (gridPosition>=racePosition)/racePosition + (gridPosition-racePosition)/racePosition) over all races`

Here's a final chart, this time using the product of the grid and final positions as the denominator (that is, calculating

`sum of ( (gridPosition==racePosition)/(racePosition*gridPosition) + (gridPosition-racePosition)/(racePosition*gridPosition) ) over all races`).

So do any of these charts make (non)sense? (And if so, which make most (or least) sense and why?)

Interesting graphs.

ReplyDeleteThe first three produce a ranking that I would generally agree with. But, although few would argue that Alonso was the best driver of 2012, I think the margin he has over Vettel is excessive.

The final graph does mediate that Alonso-Vettel difference but it also gives some big changes.

For example, Maldonado was consistently ranked at or near the bottom, but leaps up in the final graph.

And Michael Schumacher goes from poor to worst by a long way. Ok, he didn't have a great season, but this seems an unfair representation.

How did you treat retirements?

It all comes down to what you value personally. Hence to even out the "weight" of results with the one of overtaking or even position keeping is just one approach. I'd say you cannot find an objective measure for it, without a prior definition of the hierarchy of the single variables you bring into play (results, overtaking, pos. holding). So is it like results >= overtaking >= grid holding or maybe they are equal or maybe you calculate some additional variables like the post above me proposes -> retirement or what the call "unforced errors" in Tennis :)

ReplyDeleteBut still, cool approach