TOPIC: Statistical spread of tokens

What with all the new batches of tokens arriving, I'm sure we're all noticing the curious spreads appearing that make random draws so strange. Why, for example, did I get 9 of some new rares, but didn't get a single one of either rare gem? Why, if there have been 47 commons in the last 2 years, have 1 out of every 25 commons I've received in that time been a short bow - nearly double the odds?<br /><br />At any rate, I started this thread to ask what tokens you seem to be on the checklist for.<br /><br />My top three for each type:<br /><br />Commons (out of 840):<br />1) 42 Shortbows<br />2) 38 Small Steel Mirrors<br />3) 37 Longswords<br /><br />Rares (Out of 240):<br />1) 15 Large Shields<br />2) 13 Scrolls of Remove Paralysis<br />3) 11 each of Potion: Detect Secret Doors, Potion: Owl's Wisdom, and Scroll: Bless<br /><br />Very Rares (Out of 120):<br />1) 9 100GP Garnets<br />2) 8 200GP Peridots<br />3) 6 each of Wand: Melf's Acid Arrow, and +2 Cloak<br /><br /><br /><br />Inversely, in this same time period, I have not received a single suit of Banded Armor, a mere 6 5GP gold coins, and only one solitary Darkvision potion, of either type! How about everybody else? <br />

I can't give specific numbers yet, but I received tons of grappling hooks and small shields.  You must have gotten all the shortbows because I didn't get a single one in 30 bags!  In fact, all the weapons were pretty evenly distributed.  Gold and gem wise, Aquamarine was the most plentiful. 

Hey guys,<br /><br />Knowing a little bit about statistics, I was interested in the random spread of token distributions and thought I might share some thoughts about what people are seeing.  Evan, looking only at the VRs, your distribution is consistent with a random selection.<br /><br />Statistically, for a random set of M pulls from N tokens where M is 120 and N is 36, the Standard Deviation is roughly 1.80.  This is confirmed empirically as well.  <br /><br />The mean number of each Token you should expect is 3.33.<br /><br />Therefore for EACH token, you should expect roughly this “spread” to be:<br /><br /><br />For 120 Packs # Tokens with given quantity % of tokens with given quantity<br />Number of 0s     1.16 3%<br />Number of 1s     4.01 11%<br />Number of 2s     5.92 16%<br />Number of 3s     7.32 20%<br />Number of 4s     6.55 18%<br />Number of 5s     4.03 11%<br />Number of 6s     2.33 6%<br />Number of 7s     1.20 3%<br />Number of 8s     0.59 2%<br />Number of 9+     0.24 1%<br /><br />Also note that for 120 packs, there is a 71% chance that you will be missing one or more Very Rares.<br /><br />So 1 in 4 people will get 9 or more of a given token, 1 in 2 will get 8 or more.<br /><br />Here is a similar diagram for 30 packs (which might be slightly more common)<br /><br />For 30 Packs # Tokens with given quantity % of tokens with given quantity<br />Number of 0s   15.40 43%<br />Number of 1s   11.23 31%<br />Number of 2s     5.07 14%<br />Number of 3s     1.48 4%<br />Number of 4s     0.15 0%<br />Number of 5s     0.05 0%<br /><br />So, on average, if you order 30 packs, you should expect to NOT receive 15 tokens.  Of the other 21 tokens possible, you will get 5 to 6 duplicates, 1 to 2 triplicates, and 11 individuals.  One in 5 people will receive 4 or more of one type of token. <br /><br />So given this, it looks like the distributions that people are reporting are consistent with a random distribution of Very Rares in the packs.  Nice work Lori!  =D  But again, this is only for Very Rares.  My head hurts so Im not going to do Commons and Rares.  <br /><br />Hope this sheds some light on what to expect from larger orders.<br />-Douglas<br /><br />

Thanks for taking the time to break that down for us Douglas, you rock!

Yeah...what he said.<br /><br /><br />Jeff<br /><br />:sign5:

So then I got a real statistical oddity with my 30 pack.<br /><br />4's and 2 sets of 3's for the VRs.

<br />Yeah...what he said.<br /><br /><br />Jeff<br /><br />:sign5:<br />

<br />Heehee. That's how I felt. Went WAY over my head.

Math is hard...let's go shopping!

Hehe, thanks for all that legwork Douglas! I know that something like that is to be expected (I'd be very suspicious is I got even numbers of everything), I just thought it was quite fascinating to look at a real life example of statistics in action. <br /><br />So... anybody want to trade some banded armor and a couple 2006 green gems for a large shield? ::Grins::

Sorry, guys... reading through my post, looks like I got a little carried away.  I probably should have just posted the statistics.    :happy6: :happy6:

<br />Sorry, guys... reading through my post, looks like I got a little carried away.  I probably should have just posted the statistics.    :happy6: :happy6:<br />

<br /><br />Don't apologize -- I enjoyed it.  Math geeks unite!

Isn't that...Math geeks stand up and be counted! ???