Monday, July 27, 2009

Montoya's Team Math is wrong

If you saw the race on ESPN this week, they mentioned Montoya's team calculation that he needed to average a 14th place finish to make into the chase.

That sounds *VERY* similar to the post I made on March 11 of this year, suggesting that you need about 120 Points Per Race to make 12th place after 26 races. The post is here

The *mistake* however that Montoya's team is making, is comparing the 120 Points average to an average of 14th place finishes. Yes, we know that 14th place earns you 121 points, but....

The Average of Finishes DOES NOT EQUAL The Average of Points.

Montoya's team is making a big mistake, and we'll go through some examples why.

This is because of the non-linearity of the way points are awarded. Let's consider a few examples:

14th place is 121 points. So after 2 races if you got 14th and 14th, you'd have 242 points, and an average finish of 14.0

But what other ways can you have a 2-race average of 14.0? And how many points would that earn you?

Look at the table below:

Do you see the pattern here? If you average a 14.0 with mediocre finishes, you only get 242 points. But if you can average a 14.0 with one really good finish (like a win) then you can actually score a lot more than 242 points.

And look at this graph below, showing the total points after two races. Again you see the big advantage when one of your races is good - much better than two mediocre finishes:

The point here is that you don't just want to race for a 14th place, but for higher spots - since it will serve you better on your bad days, giving you more cushion.

From my previous posting on March 11 and my visualizations from May, we already know that you need to average 120 (or call it 121 in this case) points per race over the course of the season, so the more you win, the worse you can do in other races and still be okay. This year we have a perfect example: Montoya has an average finish better than Mark Martin's, but because Mark has scored 4 wins, he has more points than Montoya. Mark's DNFs have been balanced out by his wins. Montoya does not have this luxury, because with ZERO top fives all year, he's relied on a bunch of finishes between 6-15. He hasn't the same cushion to save a bad day as the other Chase drivers.

Maybe it's because their math is all wrong, and they are focused too much on Top 15s instead of the Top 5s you need to really make a move up in points.

Finally, consider this perspective. What possible sets of two finishes would earn a minimum of 242 points.

Notice again, that when you have a really good finish in there, you can balance it with a bad finish, have a lower average finish than 14.0, but still have more than 121 points per race. Look at what happens if you finish 31st to 35th in the first race. If you win the next race, your average finish is in the 16-18 area, but you always earned more than 242 points.


And the best way to race for points, is to go out there and RACE FOR WINS.

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