RuneScape:Grand Exchange Market Watch/Adjustments (20 January 2013)

20 January 2013

Adjusted index: Discontinued Rare Index Adjustment date: 20 January 2013 Affected templates: Template:GE Discontinued Rare Index and Template:GE Discontinued Rare Index/Diff Added item(s): Christmas tree hat Removed item(s): None Items before adjustment: 16 Items after adjustment: 17 Divisor before adjustment: 15.0826 Divisor after adjustment: 15.1547 Item Base date Base price Price on adjustment date Comments Christmas cracker 31 December 2008 688,800,000 2,147,476,523 Unchanged Blue partyhat 340,100,000 2,147,483,647 Green partyhat 114,800,000 1,439,919,758 Purple partyhat 83,100,000 1,194,593,128 Red partyhat 129,400,000 1,588,813,583 White partyhat 183,300,000 2,115,586,339 Yellow partyhat 96,300,000 1,288,308,900 Pumpkin 5,300,000 153,543,323 Easter egg 4,300,000 73,851,614 Blue h'ween mask 12,800,000 130,080,270 Green h'ween mask 10,600,000 107,141,857 Red h'ween mask 17,300,000 168,034,752 Santa hat 14,800,000 130,038,816 Disk of returning 4,700,000 193,631,082 Half full wine jug 31,100,000 282,814,298 Fish mask 29 September 2012 4,555,462 1,778,504 Christmas tree hat – – 2,295,576 Added item Calculations From the old divisor obtained from the templates: ${div}_{\text{old}} = 15.0826$ We need to calculate a new divisor: ${div}_{\text{new}} = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}}$ To calculate the new divisor, we need to find: $\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{old}} & = \text{sum of ratios prior to change} \\ & = \frac{2,146,908,554}{688,800,000} + \frac{2,147,483,647}{340,100,000} + \frac{1,439,919,758}{114,800,000} + \dots + \frac{1,778,504}{4,555,462} \\ & = 209.14534690 \text{ (up to 8 d.p.)} \end{align}$ And also: $\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{new}} & = \text{sum of ratios prior to change} - \text{sum of removed ratios} + \text{sum of added ratios} \\ & = \sum \left ( \frac{p}{q} \right )_{\text{old}} - \text{sum of removed ratios} + \text{number of added items} \\ & = 209.14534690 - 0 + 1 \\ & = 210.14534690 \text{ (up to 8 d.p.)} \end{align}$ Thus, the new divisor is: $\begin{align} {div}_{\text{new}} & = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} \\ & = 15.0826 \times \frac{210.14534690}{209.14534690} \\ & = 15.1547 \text{ (4 d.p.)} \end{align}$