Where's George Hit Coolness - Part I

Welcome to the first post in what will likely be a way-too-rambling series of posts about my insane desire to create a metric for how "cool" a Where's George bill hit is. To paraphrase (or perhaps re-quote) a forum post I tried to start on the subject, "all hits are cool, but some hits are definitely cooler than others, so what makes one hit cooler than another?" After getting mostly non-responses and mocking from the other posts on the topic, I took my original thoughts plus some of the better forum suggestions and started my work towards making a program for calculating coolness.

Now that the framework of the program is in place, it makes sense to me to slowly build out the factors that influence a hit's coolness as to not try to digest too much at once. For me, that meant initially focusing on two inputs and seeing if I agreed with the results.

I decided that the coolness factors should be multiplied together with the maximum value for any factor being 1.00 and the minimum would vary based on importances of the factor (lower minimum = more important). The final result would be translated to a 100 point scale with 100.0 representing a product of 1.00 and 0.0 representing the product of all of the minimums.

The obvious place to start was with "bill hit number". The most hits any particular bill I entered has is 4, so the fourth hit on a bill will be worth the 1.00 (once I get a 5 hit bill, this will change dynamcially by the program). Being the first hit on a bill is the least so that will be worth the minimum. As the hits go up, the increase in value will also rise.

The second most obvious factor is State hit. This factor will be graded based on how many hits in that State I have. The minimum number of hits in a State is 1 (South Dakota) so that will translate to the 1.00 value. The most is California (shocking!) with 2175. That will be the minimum. I want this factor to decrease in decay as the number of hits in the State increases.

So what's cooler: a bill's second hit in California or an initial hit in South Dakota? I'd say the hit in SD. What about a second hit in CA versus an initial hit in Nevada (the State where I have the second most hits)? Generically, I'd probably go with the Nevada hit. Generally really doesn't help create a sound formula.

So what would? My thought is that a second hit on a bill that occurred in a State with x hits would be equal in coolness to the first hit on a bill that occurred in a State with x/10 hits. A third hit on a bill that occurred in a State with y hits would be equal in coolness to the second hit on a bill that occurred in a State with y/10 hits and an initial hit that occurred in a State with y/100 hits. A fourth hit on a bill that occurred in a State with z hits would be equal in coolness to the third hit on a bill that occurred in a State with z/10 hits and a second hit on a bill that occurred in a State with z/100 hits and an intial hit that occurred in a State with z/1000 hits.

The easiest way to achieve the above would be to use the following formula:

Coolness = 10^(hit-1) * (max hits in State)/(hits in State)

My biggest problem with that formula is that an initial hit in a State with 1 hit is twice as cool as an initial hit in a State with 2 hits. The coolness hit possible right now is a fourth/fifth hit that is the sole hit in a State. That'd be 100.0 on the scale. The second coolness would be the fourth/fifth hit that was one of two hits in a State. That'd be 50.0 on the scale. It's easy to see that it'll be a very bottom heavy scale (I think that's going to be true with any scale I come up with, but this one even moreso).

So getting back to the original idea (a set minimum for each factor with a maximum of 1.00), I worked to set the numbers to roughly match the concept above. To get the desired effect, I set the minimum value for bill hit number to 0.70 and State hits to 0.85. The bill hit number value increasing exponentially in comparision to minimum input (1). This formula is set up as:

CF = 0.70 + 0.30 * (hit - hit_min)² / (hit_max - hit_min)²

So the first hit on a bill has a factor of 0.70, the second has a factor of 0.73, the third 0.83, and the fourth 1.00.

A similiar forumula will be used for number of hits in the hit State except that will decay as hits in State go up:

CF = 1.00 - 0.15 * (hit - hit_min)^1/3 / (hit_max - hit_min)^1/3

So South Dakota with 1 hit is 1.00, California (2175) is 0.85, and Nevada (second most with 72) is 0.95.

So how does it all work out? Looking at my hits in the first three weeks of the year, coolness scores work out as such:

Bill Hit #	Hit Location	Coolness	#
3rd	OR	50.00	x1
2nd	Italy	34.16	x1
3rd	CA	27.98	x1
2nd	NV	25.46	x1
1st	MI	22.09	x1
1st	NJ	21.34	x2
1st	VA	20.88	x1
1st	PA	20.77	x1
1st	AZ	19.77	x2
1st	FL	19.77	x2
1st	WA	19.19	x2
1st	TX	18.90	x2
1st	HI	17.91	x4
1st	NV	17.63	x1
2nd	CA	7.00	x10
1st	CA	0.00	x55

The ranking of bills in order of coolness seems pretty good. I'm not sure it's quite right, but since there are many more factors to add, I think this is a good starting point.