Grandpa - Wed Oct 29, 2008 7:25 am Post subject: Dynasty Average calculations We know that the members personal average is determined by how many clicks they do each day: ((Current Average - 1) * 9) + Todays Clicks)/10 = New Average I've always thought that the Dynasty Average was based on how many clicks each member did each day - turns out I was wrong. It seems that the Dynasty Average is based on Personal Averages of the members, not how many clicks that were done during the day. Today (10/28) the dynasty average for Positive Credit Dynasty started out at 264. The combined total AVERAGES for each member was 1,887. 1,866 / 7 = 269. At reset the dynasty average went up 2 points to 266. We have 7 members who clicked a combined total of 3,088 clicks on 10/28. 3,088 / 7 = 281.  Does anybody know the algorithm for calculating the ACTUAL Dynasty Average, please??
~Grandpa Roman - Wed Oct 29, 2008 8:12 am Post subject: Re: Dynasty Average calculations It's calcualted this way: New Dyn Ave = Old Dyn Ave + (New Average of all memebrs - Old Dyn Ave) / 10 Grandpa - Wed Oct 29, 2008 8:54 am Post subject: Re: Dynasty Average calculations
So to check this algorithm I would have to individually calculate the new personal averages of each member in the dynasty and subtract the old Dynasty Average -- because those numbers are in parenthesis. I would then divide that total by 10 and add this to the Old_Dynasty_Average. There has to more to it than that though, doesn't there? To make it easier let's assume that every member has a 500 personal average and maintains it at 500 for a period of 10 days. For instance, if I started a new dynasty (not gonna, just saying) with everybody = 500 personal average, and assuming that all members had and maintained a 500 personal average each day: Old Dyn Ave + (New Average of all members - Old Dyn Ave) / 10 = New Dyn Avg
2nd day = 50 + (500 - 50) / 10 = 95 3rd day = 95 + (500 - 95) / 10 = 135.5 4th day = 135 + (500 - 135) / 10 = 171.5 5th day = 172 + (500 - 172) / 10 = 205 6th day = 205 + (500 - 205) / 10 = 234.5 7th day = 234 + (500 - 234) / 10 = 261 8th day = 261 + (500 - 261) / 10 = 285 9th day = 285 + (500 - 285) / 10 = 306.5 10th day = 307 + (500 - 307) / 10 = 326 In other words, Eurul, although I appreciate your answer may I ask "Are you sure?" ~Grandpa  I just noticed that I started this thread in the SUGGESTIONS part of the forum, but should have put it in Questions, sorry this.
Roman - Wed Oct 29, 2008 9:17 am Post subject: Re: Dynasty Average calculations I think, that is is exactly the way you calculated it right now ^^. And exactly because the new Avergaes of every member are needed its hard to calculate the New Dynasty Average before reset. But you can also use the Average of the old Averages of each member. Its not that exactly but still okay, especially when you have many members. (some will fall and some wil rise). Roman P.s. Please anyone correct me if I am wrong with it. Grandpa - Wed Oct 29, 2008 9:29 am I've reviewed a couple of my theories regarding possible algorithms and I'm now thinking that the New_Dyn_Average is calculated as a "derived average" something similar to:
Using my numbers from the original post for example: Old_Dyn_Avg = 264 Total_Member_Click_Average_Today = 281 Therefore New_Dyn_Avg = ((264 * 9) + 281) / 10 == (2376 + 281) / 10 == (2657) / 10 == 265.7 rounded up == 266 (the New Dynasty Average). Still not sure of this but it seems true. I would so much rather use actual averages. It's not that tough. ~Granps Roman - Wed Oct 29, 2008 9:51 am
Yes, thats exactly the same formula like mine only written different 
I think, that we have to wait for Frank or Stand to tell us if this is correct. Grandpa - Wed Oct 29, 2008 9:58 am Thanks again, I wasn't clear in my thoughts until I tried to prove it out. Much appreciated. Yarold - Wed Oct 29, 2008 4:20 pm Both formulas mean the same, and are correct for calculatin new dynasty averages. Tsai - Wed Oct 29, 2008 4:42 pm
If Total_Member_Click_Average_Today means the average of the new personal averages of your members after todays clicking, than your formula is correct. I am already using an excel sheet for a long time now on which I fill in the click results of today 20 minutes before reset. The sheet calculates the new personal averages of my members based on those results. It also calculates the average of the new personal averages. And based on that result it can calculate the new dynasty average: new_dyn_ave = ( (old_dyn_ave * 9) + ave_of_new_pers_ave's) / 10 And although people of course still click in those last 20 minutes before reset, it's usually not that much that it will still have an impact on the new dyn ave calculation. So it makes it possible to predict your new dynasty average and to see the influence of kicking people with low personal averages. That is also why members with low personal averages should be motivated extra to click a lot to get their averages up as soon as possible, since they are the onces that keep your dynasty average from rising. Grandpa - Wed Oct 29, 2008 9:01 pm My thanks to whomever moved this topic into the 'Support - Ask here' thread but... I have a suggestion now. When we calculate PERSONAL averages it would be better (in my opinion) to express a 10 day trendline using simple averages as the base calculation. From there, one could use an "exponentially weighted moving average", similar to a simple moving average, except that more weight is given to the latest data to calculate the DYNASTY Averages. Rewriting the code would take a modest amount of work but the benefit would be true (accurate) personal averages and a method to show trends in dynasty averages as well. The dynasty averages would retain sufficient dynamic change to make it fun to compete but all averages would reflect realtime efforts. The current situation encourages emperors to kick new players (as Tsai pointed out) in order to enhance their numbers. ~Granps Yarold - Wed Oct 29, 2008 11:39 pm Im not sure wich way is better or worse. Current one is there because it operates at 2 numbers, wich was very convinient at time it was introduced. And what others say to exponentiall weighted ave? or not interesting ? Grandpa - Wed Oct 29, 2008 11:56 pm
By way of explanation a weighted average is an average to which each quantity is assigned a weight. The suggestion would involve assigning different degrees of importance according to timeframe where more recent clicks would have greater influence when calculating Dynasty Averages. This could be done over a 10 day time period (or any other). A Simple Moving Average (SMA) could be used to calculate Personal Averages (similar to what is being used today). 
To calculate a basic 10-day moving average you would add up the closing click totals from the past 10 days and then divide the result by 10. As new values become available, the oldest data points must be dropped from the set and new data points must come in to replace them. Thus, the data set is constantly "moving" to account for new data as it becomes available. This method of calculation ensures that only the current information is being accounted for. 
As you can see, a 10 day average method would continue to be used for determining all Personal Averages. In that manner an individual who clicked 500 links per day, every day, for a period of 10 days in a row, would have established a 500 click average, not 326 as it stands currently. Another change that could be considered would come from using a weighted average for determining Dynasty totals. Of course there are other methods that can be used to calculate averages. For instance Yarold could choose the most recent 4 days and give them weighted value while calculating Dynasty Averages. The exponential moving average is a type of moving average that gives more weight to recent changes in click totals to make it more responsive to new information. The proposed changes could be introduced gradually - no need to attempt to do everything at once. There is no "perfect" system but in my opinion these changes would help. ~Granps sebastopol-ca - Thu Oct 30, 2008 4:56 am We also use a google spreadsheet to show the daily dyansty avg, and the new member avg, Purplemkayel set it up with sarged's help on some of the formulas. Maybe she will pop in here and post on it Grandpa. Its a very handy tool to see if you need to cut a deadwood clicker before reset to keep the dynasty avg up. Yarold - Thu Oct 30, 2008 11:52 am And second thing: current one allows one to go for some holidays that are longer than 10 days. Grandpa - Thu Oct 30, 2008 9:23 pm
~Granps |
