How Do You Quantify Happiness?

Hey there Internet!! It's Guido with another Scoring Indy update. I was prepared to bring you all a scorecard this week for the Firestone 600 at Texas Motor Speedway. However, Texas has had ALL THE RAIN, and so the conclusion of the race won't be til August. By the way, that racing was fantastic. I'll have to re-watch the race from last year to see if it was equivalent, but dang if that wasn't Indy 500 level battling out there. It wasn't just a mindless pack. It wasn't Tire Fest '16. It was racing. Awesome, awesome racing.

Ok, now that I've gushed, let me say how scary the Daly/Newgarden wreck was. That was a nasty, nasty incident. But, it could have been much worse. The cars stayed on the ground. The SAFER barriers did their job. Even Newgarden's roll bar was instrumental in minimizing the injuries that he sustained. I'm glad that IndyCar officials are looking into ways to improve driver safety (especially in the cranium department), and I commend all twelve of you to go and read David Malsher's article on motorsport.com today where Bryan Herta and Ryan Hunter-Reay discuss (in a reasonable and nuanced way) how to go forward in terms of cockpit safety.

That's all I have for Texas for now. I'm sure there will be fore when I finally score the race once it's done. For now, on to our main topic:

Why am I here?

Now, I'm no Admiral James Stockdale. (For those of you, who miss the historical reference, watch this gem from the 1992 Vice-Presidential debate.) I've got a pretty solid idea of why I'm writing this little blog. Years ago, I wondered if there were a better way of objectively looking at IndyCar performance than just looking at race finishes. That quest led me to produce the Race Score, and (with some sporadic interruptions) I've been producing those here at Scoring Indy ever since.

My Race Scores are the product of a mathematical formula that I devised ("devised" is a nice way of saying "made up." There's not a ton of mathematical rigor here. I'm a clergyman after all. They don't exactly bombard us with math at seminary). Anyway, I devised the formula to account for the following performance factors:

• Race Finish
• Positions Gained/Lost from grid to checkers
• Average (or Representative) Running Position
• Laps Led
• and, Laps Completed

And, as an arbitrary touchpoint, I set the formula so that if a driver started on pole, led every lap, and won, that driver would receive a Race Score of 100. So, a Race Score is an objective description of the quality of a drive. You can use this to compare drives. Let's just look at a couple of performances from the second race from the Chevrolet Dual in Detroit a couple weeks ago. You can watch it here if you'd like a refresher.

So, let's compare the drives of Ryan Hunter-Reay and Sebastien Bourdais. Here's what their lines looked like on my Race 2 Scorecard:

Finish	Driver	Grid	Led	Completed	A.R.P.	Race Score
3	Hunter-Reay	2	0	70	3.76	57.94
8	Bourdais	12	8	70	7.33	56.34

Hunter-Reay started second, finished third, and ran between the third and fourth position on track. He stayed on strategy with the leaders, pitting on exactly the same laps as Power and Pagenaud (laps 1, 24, and 49).

Bourdais, on the other hand, started farther back: P12. He employed an alternate pit stop strategy (pitting earlier on his second stop, and coming in on laps 1, 12, 33, and 59). This strategy allowed him to run up front for several laps toward the end of the race, that might have allowed him to compete for a win if cautions had fallen differently.

These two drives, in my opinion, are pretty equivalent. And, the Race Scores bear this out. The difference between the two is just 1.6 points. But, I've started to wonder if there isn't more to the story.

The Question

Let's look at the full Race 2 Scorecard again.

Finish	Driver	Grid	Led	Completed	A.R.P.	Race Score
1	Power	8	10	70	5.09	75.84
2	Pagenaud	1	40	70	2.01	81.15
3	Hunter-Reay	2	0	70	3.76	57.94
4	Newgarden	17	0	70	8.34	70.69
5	Dixon	4	0	70	7.36	49.46
6	Daly	21	0	70	11.13	66.47
7	Kanaan	6	0	70	7.97	45.50
8	Bourdais	12	8	70	7.33	56.34
9	Andretti	22	0	70	15.2	52.73
10	Sato	16	0	70	14.14	42.21
11	Rahal	7	1	70	12.04	29.20
12	Rossi	18	1	70	14.26	39.48
13	Chaves	13	0	70	15.53	26.47
14	Castroneves	3	10	70	6.20	27.19
15	Munoz	13	0	70	12.66	24.76
16	Kimball	11	0	70	9.13	24.05
17	Aleshin	5	0	70	11.99	7.60
18	Pigot	20	0	67	14.72	22.49
19	Hawksworth	9	0	48	15.75	3.20
20	Montoya	10	0	33	7.94	8.16
21	Hinchcliffe	14	0	0	21.00	3.03
22	Chilton	19	0	0	22.00	1.52

Look at the Race Scores of the drivers around Hunter-Reay. He's the low man of the group. Power, Pagenaud, and Newgarden (get well soon) all outperformed him. Now, on the other hand, Bourdias is the best scorer in his immediate neighborhood. So, I began to ask myself, "How happy should a driver be with a given score at a given position?"

The Answer

The problem with answering this question is that there would need to be some sort of benchmark for how happy a driver should be at every point on the standings. And, that benchmark would have to be variable. For those of you who read my Detroit Mega-Post you saw that I was rolling the idea of a "par score" for each position around in my mind. Well, I think I've worked out how to make that happen. The way my arbitrary formula works, some fraction of 33.33 points are awarded for how a driver finishes, another fraction of 33.33 are awarded based on average running position, and then "bonus points" (which can be negative) are awarded based on gaining/losing positions as well as leading laps. Those bonus points are then multiplied by percentage of race finished, and you've got a Race Score.

So, to create a par score at each position, I simply took the fractions of 33.33 that a driver would earn by finishing and running in exactly the position where a driver finished. Bonus points are thrown out. So, this is what the Scorecard would look like with "par scores" for each position from Race 2 of the Chevrolet Dual in Detroit, since we've been looking at that one so closely:

Finish	Driver	Grid	Led	Completed	A.R.P.	Race Score	Par Score
1	Power	8	10	70	5.09	75.84	66.67
2	Pagenaud	1	40	70	2.01	81.15	63.64
3	Hunter-Reay	2	0	70	3.76	57.94	60.61
4	Newgarden	17	0	70	8.34	70.69	57.58
5	Dixon	4	0	70	7.36	49.46	54.55
6	Daly	21	0	70	11.13	66.47	51.52
7	Kanaan	6	0	70	7.97	45.50	48.48
8	Bourdais	12	8	70	7.33	56.34	45.45
9	Andretti	22	0	70	15.2	52.73	42.42
10	Sato	16	0	70	14.14	42.21	39.39
11	Rahal	7	1	70	12.04	29.20	36.36
12	Rossi	18	1	70	14.26	39.48	33.33
13	Chaves	13	0	70	15.53	26.47	30.30
14	Castroneves	3	10	70	6.20	27.19	27.27
15	Munoz	13	0	70	12.66	24.76	24.24
16	Kimball	11	0	70	9.13	24.05	21.21
17	Aleshin	5	0	70	11.99	7.60	18.18
18	Pigot	20	0	67	14.72	22.49	15.15
19	Hawksworth	9	0	48	15.75	3.20	12.12
20	Montoya	10	0	33	7.94	8.16	9.09
21	Hinchcliffe	14	0	0	21.00	3.03	6.06
22	Chilton	19	0	0	22.00	1.52	3.03

Now, I should note that the "par scores" are variable. They vary based on the number of cars in any given race. But, I think it is interesting that (on the whole) they seem to validate the sort of intuitive benchmarks that have served us well here at Scoring Indy: the most famous of these being that "45.00 is the floor for a good Race Score."

So, we can compare Race Scores to par now, and see how good/bad a driver should feel about a given drive at a given position. But, instead of publishing the par scores and making you do math, I'm going to do something a little different. I'll be adding a column onto the scorecard, and including each driver's "Happiness Index" (we'll shorten it to "Index") which is Race Score minus Par. So now, the Scorecard for Chevrolet Dual in Detroit Race 2 looks like this:

Finish	Driver	Grid	Led	Completed	A.R.P.	Race Score	Index
1	Power	8	10	70	5.09	75.84	9.18
2	Pagenaud	1	40	70	2.01	81.15	17.51
3	Hunter-Reay	2	0	70	3.76	57.94	-2.66
4	Newgarden	17	0	70	8.34	70.69	13.12
5	Dixon	4	0	70	7.36	49.46	-5.09
6	Daly	21	0	70	11.13	66.47	14.96
7	Kanaan	6	0	70	7.97	45.50	-2.99
8	Bourdais	12	8	70	7.33	56.34	10.89
9	Andretti	22	0	70	15.2	52.73	10.30
10	Sato	16	0	70	14.14	42.21	2.81
11	Rahal	7	1	70	12.04	29.20	-7.16
12	Rossi	18	1	70	14.26	39.48	6.15
13	Chaves	13	0	70	15.53	26.47	-3.83
14	Castroneves	3	10	70	6.20	27.19	-0.09
15	Munoz	13	0	70	12.66	24.76	0.52
16	Kimball	11	0	70	9.13	24.05	2.84
17	Aleshin	5	0	70	11.99	7.60	-10.58
18	Pigot	20	0	67	14.72	22.49	7.34
19	Hawksworth	9	0	48	15.75	3.20	-8.92
20	Montoya	10	0	33	7.94	8.16	-0.93
21	Hinchcliffe	14	0	0	21.00	3.03	-3.03
22	Chilton	19	0	0	22.00	1.52	-1.52

I'll probably continue tweaking the presentation on this, and devising ways to incorporate it into my analysis, but for now, here it is. We have a new tool. Let the people rejoice.

Stay Tuned

So, now we have a fun shiny new toy. We will undoubtedly learn to make use of it. What do you think about our new Index tool? Do you like it? Do you have questions? Sound off here or on Twitter. You can follow me @ScoringIndy. Until next time, enjoy the nerdiness!

I'll see you out there!

-- Guido