Desert Bus donation formula analysis
Desert Bus donation formula analysis
For those who are interested, I decided to put up a short summary of how to compute the total donations required to achieve k hours of game play. Conversely, I've derived the formula to compute how many hours of Desert Bus would have to be played given C dollars of total donations.
The basic idea: Hour 1 costs $1 and subsequent hours cost 1.07 times the previous hour.
Let H(k) be the cost of hour k. Then
H(k) = (1.07)^(k-1).
Moreover, the total cost C(k) of hours 1 through k will be
C(k) = H(1) + H(2) + ... + H(k) = \sum_{j=1}^{k} H(j) = \sum_{j=1}^{k} (1.07)^(j-1) = \sum_{j=0}^{k-1} (1.07)^j.
This simplifies to:
C(k) = (1.07^(k) - 1)*(100/7)
Now to find the total hours achieved for a given donation amount C. It turns out that
k = ln( 7C/100 + 1) / ln(1.07) = log_{1.07}(7C/100 + 1)
The basic idea: Hour 1 costs $1 and subsequent hours cost 1.07 times the previous hour.
Let H(k) be the cost of hour k. Then
H(k) = (1.07)^(k-1).
Moreover, the total cost C(k) of hours 1 through k will be
C(k) = H(1) + H(2) + ... + H(k) = \sum_{j=1}^{k} H(j) = \sum_{j=1}^{k} (1.07)^(j-1) = \sum_{j=0}^{k-1} (1.07)^j.
This simplifies to:
C(k) = (1.07^(k) - 1)*(100/7)
Now to find the total hours achieved for a given donation amount C. It turns out that
k = ln( 7C/100 + 1) / ln(1.07) = log_{1.07}(7C/100 + 1)
- Lyinginbedmon
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Re: Desert Bus donation formula analysis
This is cool, but I must ask:
How bored were you?
How bored were you?
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Re: Desert Bus donation formula analysis
Nope, still hate math.
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Re: Desert Bus donation formula analysis
Lyinginbedmon wrote:This is cool, but I must ask:
How bored were you?
Probably not that bored, the formulas are standard, you just need to plug in the numbers that apply here. I did that last year to calculate for the last few hours. Crusher did it the first year to come up with his list of the first 120 hours.
As well, last year somebody came up with a few charts to show how different increases would work out. Its not hard, and the formulas are easy to look up.
Twitter | Click here to join the Desert Bus Community Chat.TheRocket wrote:Apparently the crotch area could not contain the badonkadonk area.
Re: Desert Bus donation formula analysis
I thought the formula was:
Give money until they all go mad from driving... Also ask for ridiculous things.
Give money until they all go mad from driving... Also ask for ridiculous things.
Matt wrote:AND IF SHE'S DEAD SHE CAN'T SAY NO.
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Re: Desert Bus donation formula analysis
Well that too.
Twitter | Click here to join the Desert Bus Community Chat.TheRocket wrote:Apparently the crotch area could not contain the badonkadonk area.
Re: Desert Bus donation formula analysis
steelfox wrote:I thought the formula was:
Give money until they all go mad from driving... Also ask for ridiculous things.
Don't forget to compensate for when they have time away from DB, gotta make sure to break their willpower when they get back. Otherwise they resist.
H̼̮̖͓̻ͮ̀ͬ̓e̟̦͉̾̔̀ͣ͆̄ ͚̤̈̉ͦ̎ͭ̚c̰̠͚̜̹ͪ̐̎̃ͅo̗͌͛ͥ͑m̍ͬͥ̚e͍̱̲̤͚̹͔͛s͚̱̤͚̲̭̗̃̎ͭ̚.̘̫̖̮̠͒̔.̝̹̟̳͚̂̆̋͌̐̚.̬͓̰̃̑
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Re: Desert Bus donation formula analysis
Isn't it, each hour costs seven or eight percent more than the previous one, with the first hour costing a dollar?
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Re: Desert Bus donation formula analysis
I didn't have to look anything up other than the 1.07 multiplier. Everything else is easy to derive from scratch in 5 min.
Re: Desert Bus donation formula analysis
Evil Jim wrote:Isn't it, each hour costs seven or eight percent more than the previous one, with the first hour costing a dollar?
That's what multiplying by 1.07 will do—a 7% increase.
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Re: Desert Bus donation formula analysis
Ah, whups. I skipped over the equations in the first post.
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Re: Desert Bus donation formula analysis
Master Gunner wrote:Lyinginbedmon wrote:This is cool, but I must ask:
How bored were you?
Probably not that bored, the formulas are standard, you just need to plug in the numbers that apply here. I did that last year to calculate for the last few hours. Crusher did it the first year to come up with his list of the first 120 hours.
As well, last year somebody came up with a few charts to show how different increases would work out. Its not hard, and the formulas are easy to look up.
I will have to post a bigger table for this year.
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Re: Desert Bus donation formula analysis
Ok here is this year's version of the donation table. It goes for seven days - over a million dollars would have to be raised for Desert Bus for it to go that long, roughly the total amount of money Child's Play raised in total last year.
Code: Select all
Hours Total To Next Hour
0 0.00 1.00
1 1.00 1.07
2 2.07 1.14
3 3.21 1.23
4 4.44 1.31
5 5.75 1.40
6 7.15 1.50
7 8.65 1.61
8 10.26 1.72
9 11.98 1.84
10 13.82 1.97
11 15.78 2.10
12 17.89 2.25
13 20.14 2.41
14 22.55 2.58
15 25.13 2.76
16 27.89 2.95
17 30.84 3.16
18 34.00 3.38
19 37.38 3.62
20 41.00 3.87
21 44.87 4.14
22 49.01 4.43
23 53.44 4.74
24 58.18 5.07
25 63.25 5.43
26 68.68 5.81
27 74.48 6.21
28 80.70 6.65
29 87.35 7.11
30 94.46 7.61
31 102.07 8.15
32 110.22 8.72
33 118.93 9.33
34 128.26 9.98
35 138.24 10.68
36 148.91 11.42
37 160.34 12.22
38 172.56 13.08
39 185.64 13.99
40 199.64 14.97
41 214.61 16.02
42 230.63 17.14
43 247.78 18.34
44 266.12 19.63
45 285.75 21.00
46 306.75 22.47
47 329.22 24.05
48 353.27 25.73
49 379.00 27.53
50 406.53 29.46
51 435.99 31.52
52 467.50 33.73
53 501.23 36.09
54 537.32 38.61
55 575.93 41.32
56 617.24 44.21
57 661.45 47.30
58 708.75 50.61
59 759.36 54.16
60 813.52 57.95
61 871.47 62.00
62 933.47 66.34
63 999.81 70.99
64 1070.80 75.96
65 1146.76 81.27
66 1228.03 86.96
67 1314.99 93.05
68 1408.04 99.56
69 1507.60 106.53
70 1614.13 113.99
71 1728.12 121.97
72 1850.09 130.51
73 1980.60 139.64
74 2120.24 149.42
75 2269.66 159.88
76 2429.53 171.07
77 2600.60 183.04
78 2783.64 195.85
79 2979.50 209.56
80 3189.06 224.23
81 3413.30 239.93
82 3653.23 256.73
83 3909.95 274.70
84 4184.65 293.93
85 4478.58 314.50
86 4793.08 336.52
87 5129.59 360.07
88 5489.66 385.28
89 5874.94 412.25
90 6287.19 441.10
91 6728.29 471.98
92 7200.27 505.02
93 7705.29 540.37
94 8245.66 578.20
95 8823.85 618.67
96 9442.52 661.98
97 10104.50 708.31
98 10812.81 757.90
99 11570.71 810.95
100 12381.66 867.72
101 13249.38 928.46
102 14177.83 993.45
103 15171.28 1062.99
104 16234.27 1137.40
105 17371.67 1217.02
106 18588.69 1302.21
107 19890.90 1393.36
108 21284.26 1490.90
109 22775.16 1595.26
110 24370.42 1706.93
111 26077.35 1826.41
112 27903.76 1954.26
113 29858.03 2091.06
114 31949.09 2237.44
115 34186.52 2394.06
116 36580.58 2561.64
117 39142.22 2740.96
118 41883.18 2932.82
119 44816.00 3138.12
120 47954.12 3357.79
121 51311.91 3592.83
122 54904.74 3844.33
123 58749.07 4113.44
124 62862.51 4401.38
125 67263.88 4709.47
126 71973.36 5039.13
127 77012.49 5391.87
128 82404.37 5769.31
129 88173.67 6173.16
130 94346.83 6605.28
131 100952.11 7067.65
132 108019.75 7562.38
133 115582.14 8091.75
134 123673.89 8658.17
135 132332.06 9264.24
136 141596.30 9912.74
137 151509.04 10606.63
138 162115.68 11349.10
139 173464.77 12143.53
140 185608.31 12993.58
141 198601.89 13903.13
142 212505.02 14876.35
143 227381.37 15917.70
144 243299.07 17031.93
145 260331.00 18224.17
146 278555.17 19499.86
147 298055.04 20864.85
148 318919.89 22325.39
149 341245.28 23888.17
150 365133.45 25560.34
151 390693.79 27349.57
152 418043.36 29264.04
153 447307.39 31312.52
154 478619.91 33504.39
155 512124.30 35849.70
156 547974.01 38359.18
157 586333.19 41044.32
158 627377.51 43917.43
159 671294.93 46991.65
160 718286.58 50281.06
161 768567.64 53800.73
162 822368.37 57566.79
163 879935.16 61596.46
164 941531.62 65908.21
165 1007439.84 70521.79
166 1077961.62 75458.31
167 1153419.94 80740.40
168 1234160.33 86392.22
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Re: Desert Bus donation formula analysis
What would that mean if someone donated a billion dollars? I make it about 230 years.
Last edited by Iqy on 28 Feb 2013, 11:33, edited 1 time in total.
- Jamfalcon
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Re: Desert Bus donation formula analysis
It would mean a lot of entertainment.
Re: Desert Bus donation formula analysis
Not too bad actually. It would be just 267 hours.
And to make the team bus even for 1 year (8760 hours) would cost in the range of 3.6*10^(258) dollars (many orders of magnitude more than the number of elementary particles in the universe)
And to make the team bus even for 1 year (8760 hours) would cost in the range of 3.6*10^(258) dollars (many orders of magnitude more than the number of elementary particles in the universe)
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Re: Desert Bus donation formula analysis
Now a better question would be: What's the best formula for predicting a new year's DBfH donation total? I remember Fugiman and I had a go at it last year, only to way, way undershoot.
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Re: Desert Bus donation formula analysis
I have in the past tried it with software that uses genetic algorithms to try and derive the best equation to describe a data set. The problem is that there anywhere near enough data points to get a reliable result. It was a few years ago the last time I tried it, and the range between the best-fitting equations was around $100,000.
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Re: Desert Bus donation formula analysis
Lord Chrusher made this graph.
He predicted based on the power law that they would raise $536 917.
Based on a linear progression taking DB5 as a aberration in the math I predicted $422,550. I was off by less than one desert buck.
Desert Bus 6 total $443,630
I will predict right now that DB7 will raise $512,560 and run for 155 hours They will not have purchased the 155th hour yet but will run over because "they are so close".
He predicted based on the power law that they would raise $536 917.
Based on a linear progression taking DB5 as a aberration in the math I predicted $422,550. I was off by less than one desert buck.
Desert Bus 6 total $443,630
I will predict right now that DB7 will raise $512,560 and run for 155 hours They will not have purchased the 155th hour yet but will run over because "they are so close".
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- Lord Chrusher
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Re: Desert Bus donation formula analysis
I ran my analysis again with the DBFH total and I got this:
The linear model predicts that they will raise $522 450 (155 hours).
The power law model predicts that they will raise $599 864 (157 hours).
The linear model predicts that they will raise $522 450 (155 hours).
The power law model predicts that they will raise $599 864 (157 hours).
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Re: Desert Bus donation formula analysis
Now, random thought:
If you subtract 100,000 from both DB5 and DB6, you end up with what looks like a perfectly straight line. Based on this line, what is the DB7 prediction (adding back in that 100K that we removed)?
y=66.0008(7)+-52.8888 (+100)
Based on these numbers, I predict $509,116.60. This means that they will bus for 154 hours, and possibly push to 155.
If you subtract 100,000 from both DB5 and DB6, you end up with what looks like a perfectly straight line. Based on this line, what is the DB7 prediction (adding back in that 100K that we removed)?
y=66.0008(7)+-52.8888 (+100)
Based on these numbers, I predict $509,116.60. This means that they will bus for 154 hours, and possibly push to 155.
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Re: Desert Bus donation formula analysis
<GIF of Kate shaking her head>Nope</GIF>
When you are making projections you can not just modify data to fit a trend.
When you are making projections you can not just modify data to fit a trend.
We are all made of star dust. However we are also made of nuclear waste.
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Re: Desert Bus donation formula analysis
Unless your study is designed to show that homoeopathy actually works.
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Re: Desert Bus donation formula analysis
MarkVI wrote:Not too bad actually. It would be just 267 hours.
And to make the team bus even for 1 year (8760 hours) would cost in the range of 3.6*10^(258) dollars (many orders of magnitude more than the number of elementary particles in the universe)
So you're saying it's probably an unrealistic goal for next year then?
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Oh and you can just call me Dave.
No need for the whole screen name.
Oh and you can just call me Dave.
No need for the whole screen name.
Re: Desert Bus donation formula analysis
Lord Chrusher wrote:<GIF of Kate shaking her head>Nope</GIF>
I didn't have that saved, and for some reason I tried to google it. I got as far as "kate nop" before Google suggested "kate stark nope gif". I'm a little scared that it knew that.
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