## Desert Bus donation formula analysis

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MarkVI
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Joined: 14 Jul 2008, 19:18
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Location: New Jersey

### 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) Lyinginbedmon Posts: 10808 Joined: 20 Dec 2007, 18:08 First Video: BioShocked Location: Darlington, Co. Durham Contact: ### Re: Desert Bus donation formula analysis This is cool, but I must ask: How bored were you? Morgan wrote:Lyinginbedmon is short, but he makes up for it in awesomeness Jillers Posts: 3006 Joined: 14 Oct 2008, 19:26 First Video: How to Talk LIke a Pirate Location: Somewhere on top of garbage Contact: ### Re: Desert Bus donation formula analysis Nope, still hate math. Team Cybershark [subliminal] visit Geeking Out About [/subliminal] ~End Transmission~ Master Gunner Defending us from The Dutch! Posts: 19383 Joined: 29 Oct 2006, 12:19 First Video: How To Talk Like A Pirate Location: In Limbo. Contact: ### 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. TheRocket wrote:Apparently the crotch area could not contain the badonkadonk area. Twitter | Click here to join the Desert Bus Community Chat. steelfox Posts: 215 Joined: 22 Aug 2008, 10:00 Location: Spokane, WA ### 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. Matt wrote:AND IF SHE'S DEAD SHE CAN'T SAY NO. -M Master Gunner Defending us from The Dutch! Posts: 19383 Joined: 29 Oct 2006, 12:19 First Video: How To Talk Like A Pirate Location: In Limbo. Contact: ### Re: Desert Bus donation formula analysis Well that too. TheRocket wrote:Apparently the crotch area could not contain the badonkadonk area. Twitter | Click here to join the Desert Bus Community Chat. Arius Posts: 7228 Joined: 23 Jun 2009, 03:38 First Video: Max Effect Location: Inside You Contact: ### 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.̘̫̖̮̠͒̔.̝̹̟̳͚̂̆̋͌̐̚.̬͓̰̃̑ Evil Jim Posts: 7265 Joined: 14 Jul 2007, 00:39 First Video: Shake Your Hands Location: R'lyeh, Wisconsin Contact: ### 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? Arius wrote:People were just so awestruck by your awesomeness that they became catatonic. ThrashJazzAssassin wrote:BURN HIM! BURN THE HERETIC! DEATH TO ALL WHO SCORN THE AWESOMENESS OF EVIL JIM! MarkVI Posts: 181 Joined: 14 Jul 2008, 19:18 First Video: iPhone Alternative Location: New Jersey ### 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. Graham Super Moderator Posts: 15038 Joined: 09 Mar 2004, 19:37 Location: Victoria, BC Contact: ### 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. Evil Jim Posts: 7265 Joined: 14 Jul 2007, 00:39 First Video: Shake Your Hands Location: R'lyeh, Wisconsin Contact: ### Re: Desert Bus donation formula analysis Ah, whups. I skipped over the equations in the first post. Arius wrote:People were just so awestruck by your awesomeness that they became catatonic. ThrashJazzAssassin wrote:BURN HIM! BURN THE HERETIC! DEATH TO ALL WHO SCORN THE AWESOMENESS OF EVIL JIM! Lord Chrusher Can't Drink Possible Beers Posts: 8913 Joined: 29 Apr 2005, 22:53 First Video: Door to Door Location: In England. ### 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. We are all made of star dust. However we are also made of nuclear waste. Remember to think before you post. Lord Chrusher Can't Drink Possible Beers Posts: 8913 Joined: 29 Apr 2005, 22:53 First Video: Door to Door Location: In England. ### 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 Hour0 0.00 1.001 1.00 1.072 2.07 1.143 3.21 1.234 4.44 1.315 5.75 1.406 7.15 1.507 8.65 1.618 10.26 1.729 11.98 1.8410 13.82 1.9711 15.78 2.1012 17.89 2.2513 20.14 2.4114 22.55 2.5815 25.13 2.7616 27.89 2.9517 30.84 3.1618 34.00 3.3819 37.38 3.6220 41.00 3.8721 44.87 4.1422 49.01 4.4323 53.44 4.7424 58.18 5.0725 63.25 5.4326 68.68 5.8127 74.48 6.2128 80.70 6.6529 87.35 7.1130 94.46 7.6131 102.07 8.1532 110.22 8.7233 118.93 9.3334 128.26 9.9835 138.24 10.6836 148.91 11.4237 160.34 12.2238 172.56 13.0839 185.64 13.9940 199.64 14.9741 214.61 16.0242 230.63 17.1443 247.78 18.3444 266.12 19.6345 285.75 21.0046 306.75 22.4747 329.22 24.0548 353.27 25.7349 379.00 27.5350 406.53 29.4651 435.99 31.5252 467.50 33.7353 501.23 36.0954 537.32 38.6155 575.93 41.3256 617.24 44.2157 661.45 47.3058 708.75 50.6159 759.36 54.1660 813.52 57.9561 871.47 62.0062 933.47 66.3463 999.81 70.9964 1070.80 75.9665 1146.76 81.2766 1228.03 86.9667 1314.99 93.0568 1408.04 99.5669 1507.60 106.5370 1614.13 113.9971 1728.12 121.9772 1850.09 130.5173 1980.60 139.6474 2120.24 149.4275 2269.66 159.8876 2429.53 171.0777 2600.60 183.0478 2783.64 195.8579 2979.50 209.5680 3189.06 224.2381 3413.30 239.9382 3653.23 256.7383 3909.95 274.7084 4184.65 293.9385 4478.58 314.5086 4793.08 336.5287 5129.59 360.0788 5489.66 385.2889 5874.94 412.2590 6287.19 441.1091 6728.29 471.9892 7200.27 505.0293 7705.29 540.3794 8245.66 578.2095 8823.85 618.6796 9442.52 661.9897 10104.50 708.3198 10812.81 757.9099 11570.71 810.95100 12381.66 867.72101 13249.38 928.46102 14177.83 993.45103 15171.28 1062.99104 16234.27 1137.40105 17371.67 1217.02106 18588.69 1302.21107 19890.90 1393.36108 21284.26 1490.90109 22775.16 1595.26110 24370.42 1706.93111 26077.35 1826.41112 27903.76 1954.26113 29858.03 2091.06114 31949.09 2237.44115 34186.52 2394.06116 36580.58 2561.64117 39142.22 2740.96118 41883.18 2932.82119 44816.00 3138.12120 47954.12 3357.79121 51311.91 3592.83122 54904.74 3844.33123 58749.07 4113.44124 62862.51 4401.38125 67263.88 4709.47126 71973.36 5039.13127 77012.49 5391.87128 82404.37 5769.31129 88173.67 6173.16130 94346.83 6605.28131 100952.11 7067.65132 108019.75 7562.38133 115582.14 8091.75134 123673.89 8658.17135 132332.06 9264.24136 141596.30 9912.74137 151509.04 10606.63138 162115.68 11349.10139 173464.77 12143.53140 185608.31 12993.58141 198601.89 13903.13142 212505.02 14876.35143 227381.37 15917.70144 243299.07 17031.93145 260331.00 18224.17146 278555.17 19499.86147 298055.04 20864.85148 318919.89 22325.39149 341245.28 23888.17150 365133.45 25560.34151 390693.79 27349.57152 418043.36 29264.04153 447307.39 31312.52154 478619.91 33504.39155 512124.30 35849.70156 547974.01 38359.18157 586333.19 41044.32158 627377.51 43917.43159 671294.93 46991.65160 718286.58 50281.06161 768567.64 53800.73162 822368.37 57566.79163 879935.16 61596.46164 941531.62 65908.21165 1007439.84 70521.79166 1077961.62 75458.31167 1153419.94 80740.40168 1234160.33 86392.22 We are all made of star dust. However we are also made of nuclear waste. Remember to think before you post. Iqy Posts: 6 Joined: 25 Nov 2010, 03:04 First Video: Le Cafe ### 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 Posts: 3325 Joined: 08 Aug 2011, 13:59 First Video: Killer Instinct Location: Somewhat nearish Vancouver. Kind of. Contact: ### Re: Desert Bus donation formula analysis It would mean a lot of entertainment. "Jamfalcon's a super weird name" - Graham I wrote a book! MarkVI Posts: 181 Joined: 14 Jul 2008, 19:18 First Video: iPhone Alternative Location: New Jersey ### 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) JackSlack Posts: 4572 Joined: 15 Oct 2010, 19:46 First Video: ENN, but I forget which. Location: Sydney, Australia ### 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. Master Gunner Defending us from The Dutch! Posts: 19383 Joined: 29 Oct 2006, 12:19 First Video: How To Talk Like A Pirate Location: In Limbo. Contact: ### 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.
Lord Hosk
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### Re: Desert Bus donation formula analysis

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
Can't Drink Possible Beers
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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).

We are all made of star dust. However we are also made of nuclear waste.
Remember to think before you post.
the amativeness
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Joined: 31 Jul 2008, 19:53
Location: America, where everyone sues everyone, always, for everything.

### 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.
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Lord Chrusher
Can't Drink Possible Beers
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Joined: 29 Apr 2005, 22:53
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Location: In England.

### 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.

We are all made of star dust. However we are also made of nuclear waste.
Remember to think before you post.
Keab42
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Location: In England

### Re: Desert Bus donation formula analysis

Unless your study is designed to show that homoeopathy actually works.
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Dave-O_Boy
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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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Yaxley
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Joined: 02 Nov 2008, 14:38
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### 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.