RuneScape:Grand Exchange Market Watch/Adjustments (20 January 2014)

20 January 2014

Adjusted index: Discontinued Rare Index Adjustment date: 20 January 2014 Affected templates: Template:GE Discontinued Rare Index and Template:GE Discontinued Rare Index/Diff Added item(s): Black Santa hat Removed item(s): None Items before adjustment: 18 Items after adjustment: 19 Divisor before adjustment: 15.2129 Divisor after adjustment: 15.2787 Item Base date Base price Price on adjustment date Comments Christmas cracker 31 December 2008 688,800,000 2,147,483,632 Unchanged Blue partyhat 340,100,000 2,147,483,647 Green partyhat 114,800,000 1,490,829,327 Purple partyhat 83,100,000 1,279,369,134 Red partyhat 129,400,000 1,696,893,747 White partyhat 183,300,000 2,146,833,194 Yellow partyhat 96,300,000 1,335,202,311 Pumpkin 5,300,000 174,290,712 Easter egg 4,300,000 70,272,905 Blue h'ween mask 12,800,000 132,769,255 Green h'ween mask 10,600,000 110,890,723 Red h'ween mask 17,300,000 185,134,793 Santa hat 14,800,000 135,913,306 Disk of returning 4,700,000 223,384,911 Half full wine jug 31,100,000 333,709,743 Fish mask 29 September 2012 4,555,462 944,822 Christmas tree hat 20 January 2013 2,295,576 12,593,302 Crown of Seasons 23 July 2013 8,307,542 3,926,892 Black Santa hat – – 222,967,707 Added item Calculations From the old divisor obtained from the templates: ${div}_{\text{old}}=15.2129$ 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: ${\begin{aligned}\sum \left({\frac {p}{q}}\right)_{\text{old}}&={\text{sum of ratios prior to change}}\\&={\frac {2,147,483,557}{688,800,000}}+{\frac {2,147,483,647}{340,100,000}}+{\frac {1,490,829,327}{114,800,000}}+\dots +{\frac {12,593,302}{2,295,576}}+{\frac {3,926,892}{8,307,542}}\\&=230.87579845{\text{ (up to 8 d.p.)}}\end{aligned}}$ And also: ${\begin{aligned}\sum \left({\frac {p}{q}}\right)_{\text{new}}&={\text{sum of ratios prior to change}}-{\text{sum of removed ratios}}+{\text{sum of added ratios}}\\&=\sum \left({\frac {p}{q}}\right)_{\text{old}}-{\text{sum of removed ratios}}+{\text{number of added items}}\\&=230.87579845-0+1\\&=231.87579845{\text{ (up to 8 d.p.)}}\end{aligned}}$ Thus, the new divisor is: ${\begin{aligned}{div}_{\text{new}}&={div}_{\text{old}}\times {\frac {\sum \left({\frac {p}{q}}\right)_{\text{new}}}{\sum \left({\frac {p}{q}}\right)_{\text{old}}}}\\&=15.2129\times {\frac {231.87579845}{230.87579845}}\\&=15.2787{\text{ (4 d.p.)}}\end{aligned}}$