Paths to the F1 2012 Championship Based on How They Might Finish in the US Grand Prix

If you haven’t already seen it, one of the breakthrough visualisations of the US elections was the New York Times Paths to the Election scenario builder. With the F1 drivers’ championship in the balance this weekend, I wondered what chances were of VET claiming the championship this weekend. The only contender is ALO, who is currently ten points behind.

A quick Python script shows the outcome depending on the relative classification of ALO and VET at the end of today’s race. (If the drivers are 25 points apart, and ALO then wins in Brazil with VET out of the points, I think VET will win on countback based on having won more races.)

#The current points standings
vetPoints=255
aloPoints=245

#The points awarded for each place in the top 10; 0 points otherwise
points=[25,18,15,12,10,8,6,4,2,1,0]

#Print a header row (there's probably a more elegant way of doing this...;-)
for x in ['VET\ALO',1,2,3,4,5,6,7,8,9,10,'11+']: print str(x)+'\t',
print ''

#I'm going to construct a grid, VET's position down the rows, ALO across the columns
for i in range(len(points)):
	#Build up each row - start with VET's classification
	row=[str(i+1)]
	#Now for the columns - that is, ALO's classification
	for j in range(len(points)):
		#Work out the points if VET is placed i+1  and ALO at j+1 (i and j start at 0)
		#Find the difference between the points scores
		#If the difference is >= 25 (the biggest points diff ALO could achieve in Brazil), VET wins
		if ((vetPoints+points[i])-(aloPoints+points[j])>=25):
			row.append("VET")
		else: row.append("?")
	#Print the row a slightly tidier way...
	print '\t'.join(row)

(Now I wonder – how would I write that script in R?)

And the result?

VET\ALO	1	2	3	4	5	6	7	8	9	10	11+	
1	?	?	?	?	VET	VET	VET	VET	VET	VET	VET
2	?	?	?	?	?	?	?	?	VET	VET	VET
3	?	?	?	?	?	?	?	?	?	?	VET
4	?	?	?	?	?	?	?	?	?	?	?
5	?	?	?	?	?	?	?	?	?	?	?
6	?	?	?	?	?	?	?	?	?	?	?
7	?	?	?	?	?	?	?	?	?	?	?
8	?	?	?	?	?	?	?	?	?	?	?
9	?	?	?	?	?	?	?	?	?	?	?
10	?	?	?	?	?	?	?	?	?	?	?
11	?	?	?	?	?	?	?	?	?	?	?

Which is to say, VET wins if:

• VET wins the race and ALO is placed 5th or lower;
• VET is second in the race and ALO is placed 9th or lower;
• VET is third in the race and ALO is out of the points (11th or lower)

We can also look at the points differences (define a row2 as row, then use row2.append(str((vetPoints+points[i])-(aloPoints+points[j])))):

VET\ALO	1	2	3	4	5	6	7	8	9	10	11+	
1	10	17	20	23	25	27	29	31	33	34	35
2	3	10	13	16	18	20	22	24	26	27	28
3	0	7	10	13	15	17	19	21	23	24	25
4	-3	4	7	10	12	14	16	18	20	21	22
5	-5	2	5	8	10	12	14	16	18	19	20
6	-7	0	3	6	8	10	12	14	16	17	18
7	-9	-2	1	4	6	8	10	12	14	15	16
8	-11	-4	-1	2	4	6	8	10	12	13	14
9	-13	-6	-3	0	2	4	6	8	10	11	12
10	-14	-7	-4	-1	1	3	5	7	9	10	11
11	-15	-8	-5	-2	0	2	4	6	8	9	10

We could then do a similar exercise for the Brazil race, and essentially get all the information we need to do a scenario builder like the New York Times election scenario builder… Which I would try to do, but I’ve had enough screen time for the weekend already…:-(

PS FWIW, here’s a quick table showing the awarded points difference between two drivers depending on their relative classification in a race:

A\B	1	2	3	4	5	6	7	8	9	10	11+
1	X	7	10	13	15	17	19	21	23	24	25
2	-7	X	3	6	8	10	12	14	16	17	18
3	-10	-3	X	3	5	7	9	11	13	14	15
4	-13	-6	-3	X	2	4	6	8	10	11	12
5	-15	-8	-5	-2	X	2	4	6	8	9	10
6	-17	-10	-7	-4	-2	X	2	4	6	7	8
7	-19	-12	-9	-6	-4	-2	X	2	4	5	6
8	-21	-14	-11	-8	-6	-4	-2	X	2	3	4
9	-23	-16	-13	-10	-8	-6	-4	-2	X	1	2
10	-24	-17	-14	-11	-9	-7	-5	-3	-1	X	1
11	-25	-18	-15	-12	-10	-8	-6	-4	-2	-1	X

Here’s how to use this chart in association with the previous. Looking at the previous chart, if VET finishes second and ALO third, the points difference is 13 in favour of VET. Looking at the chart immediately above, if we let VET = A and ALO = B, then the columns correspond to ALO’s placement, and the rows to VET. VET (A) needs to lose 14 or more points to lose the championship (that is, we’re looking for values of -14 or less). In particular, ALO (B, columns) needs to finish 1st with VET (A) 5th or worse, 2nd with A 8th or worse, or 3rd with VET 10th or worse.

And the script:

print '\t'.join(['A\B','1','2','3','4','5','6','7','8','9','10','11+'])
for i in range(len(points)):
	row=[str(i+1)]
	for j in range(len(points)):
		if i!=j:row.append(str(points[i]-points[j]))
		else: row.append('X')

And now for the rest of the weekend…