Talk:Leprechaun

Possible NS13 formula

Here is a possible formula for the increase in meat rate:

http://sweb.uky.edu/~tjmart1/images/FairyEq.png

See this post for details and data. (Thanks to QNM and greycat for data gathering.) --Starwed 19:20, 8 July 2007 (CDT)

The above post on HCO lists new spading work, including some information on the equation I posted. There is probably a better "pretty" equation that can be found, but the equation I listed is exactly correct for all weights tested (3 pounds to 73 pounds).--QuantumNightmare 17:33, 20 July 2007 (CDT)

am I the only one who sees that the Leprechaun boost is almost exactly twice the fairy boost? The fairy boost can be pretty simply modeled with: (W/10 + 1)/6, so perhaps the Leprechaun boost is (W/10 + 1)/3?--MindlessGames 11:56, 19 March 2008 (CDT)

Keep in mind that fairy formula is only valid above 20 pounds. Even the fairy isn't described by that formula from 1-19 pounds, so using it to describe the leprechaun is inaccurate as well. You're better off using double the leprechaun formula to describe the fairy. Then again, even the leprechaun formula is a simplification of a more complicated exact function, and is accurate to within a few percentage points up to 65 pounds.--QuantumNightmare 12:13, 19 March 2008 (CDT)

• from what I've seen, the fairy formula does line up at lower weight counts, i've only seen a small portion of data on it, but i'll look into it, both are going to be hard to spade though. Especially without like 50 characters with whom to spade. Get 50 people to take data measurements for 1 to 19 pounds of both fairy and lep (fairychaun, anyone?) in a specific known area, and I think we'll see a much more accurate picture of what's happening at lower levels. Unless this data already exists somewhere and I'm just blind.. lol.--MindlessGames 12:21, 19 March 2008 (CDT)

You misunderstood. We already known the exact meat bonuses for low weight leprechauns. There's already a formula that describes it. The data is available. The problem is that the fairy formula isn't accurate at low weights, so please do not use it to describe the leprechaun!

As well, there is no good spading done on low weight fairies. There's no data to compare a possible formula with, although it looks to be non-linear. I'd be interested in the results of a large-scale low weight fairy project, though. Good luck!--QuantumNightmare 12:26, 19 March 2008 (CDT)

advantage of gaining weight?

If this guy gives me +5% meat drops flat-out, then what does gaining weight do?

• "Increases meat drops by 5% per pound" means that you'll get +5% for EACH AND EVERY pound you familiar has, so a 20lb leprechaun would give +100% meat effectively doubling meat drops :P--Dehstil (t|c) 23:44, 6 November 2006 (CST)
  • Ah, I must've overlooked that part. Thanks! --Qhiiyr 22:58, 7 November 2006 (CST)

Was it intentional that his description be a haiku? Just thought that was strange.--InsertNameWhere 16:08, 27 June 2007 (CDT)

• All familiar hatchlings descriptions are haikus. --Hen3ry 16:10, 27 June 2007 (CDT)

Post-NS13 meat drop

Preliminary results: 5% per pound up to 20 pounds; then, a reduced amount (formula still unknown).

I've been spading meat drops with a leprechaun at various weights, a little bit. I only have a modest set of data, so my results are not conclusive yet. Here are the raw data and my conclusions:

darkgreycat, AT

Nimble Fingers, Expert Panhandling, Gnefarious Pickpocketing = +40%

Polka of Plenty running throughout = +50%

JEW hat, Navy Fleece, meatspout, stainless slacks, Baron's money clip, pulled porq pendant, ice skates = +90%

Total base meat = +180%

Adventuring in the Beanbat Chamber

Weight	Meat drops
Baseline (sombero)	106 92 100 98 98 100 95 95 89 100 103 103 84 106 95 100 81 86 86 100 92 95 100 95 89 109 86 89 92 103 92 95 100 86 98 89 103 98 100 106 84 81 109 98
3 lb.	103 113 106 110
4 lb.	105 105 90 96 102
5 lb.	123 114 107 95 101 117 114
6 lb.	93 122 116 106 90 106 116 109 109
7 lb.	94 101 111 111 121 104 101 98 107 117 124
8 lb.	109 132 109 109 119 112 109 112 116 116 119 119 112
9 lb.	121 121 117 117 107 104 121 107 134 111 104 121 117 107 124
10 lb.	109 126 112 119 126 112 122 115 105 132 119 95 126 115 112 119 119
14 lb.	121 110 128 114 128 114 132 114 132 114 132 117 103 103 110 139 135 114 110
15 lb.	122 140 108 122 126 112 122 122 122 115 115 133 140 122 119 119 108 137 137 122 119
16 lb.	135 113 124 109 124 131 120 142 127 124 135 124 135 138 113 116 116 120 142 120 116 135 116
17 lb.	143 136 114 121 132 136 132 136 110 121 121 125 147 121 121 129 125 129 107 132 121 121 125 129 136
18 lb.	115 130 126 134 137 126 130 141 130 126 108 134 134 137 123 137 119 115 137 115 123 111 115 141 126 126 145
19 lb.	135 150 131 105 128 112 116 135 135 150 143 143 135 116 131 131 120 116 139 131 135 143 105 120 128 112 135 131 139
20 lb.	125 148 140 144 133 129 133 133 144 129 110 129 133 140 125 129 144 117 136 121 133 114 129 117 129 125 129 133 121 133 121
26 lb.	160 160 128 136 112 148 132 140 132 116 144 128 144 128 132 148 112 152 136 144 148 140 144 140 116 148 160 144 140 140 152 156 148 120 116 132 136 132 120 144 128 124 144 136 144 152 116 128 144 132 140 148 156 120 132 132 136 148 120 156 128 120 116 144 140 136 124 132 136 124 128 128
27 lb.	137 133 137 137 137 141 129 133 129 141 129 149 141 141 129 145 125 141 157 125 117 129 133 145 137 125 149 121 162 117 129 153 133 137 157 141 149 121 149 145 133 133 137 137 137 149 129 145 153 125 137 149 145 153 153 129
28 lb.	159 130 151 147 155 134 147 151 114 118 163 122 122 138 138 142 138 138 147 122 130 147 134 142 126 134 138 118 134 138 159 147 130 118 114 134 114
30 lb.	128 132 132 124 145 153 166 149 153 149 141 128 153 124 128 145 153 166 128 149 132 149 141 166 128 166 128 132 145 149 128 141 124 137 145 145 166 145 149 128 161 153 145 153 137 153 145 166 153 141 166 128
35 lb.	155 159 142 142 142 155 142 138 129 146 155 146 151 155 133 151 142 125 155 138 168 142 155 138 133 125 164 146 142 146 159 151 138 138 155 155 129 168 151 164 125 138 159 151 168 125 159 151 133 142 142 138 146

• Baseline: consistent with +180% (2.8x) on a base range of 29-39
  • Note: bell-shaped curve? Needs further study.
• 16-pound lep: missing bottom of the range, I think.
  • Roughly 3.6x --> 16 lb. lep = +80% meat. Consistent with +5% per pound.
• 20-pound lep: consistent with +280% meat (2.8x) --> 20 lb. lep = +100% meat
  • Consistent with +5% per pound.
• 26-pound lep: very interesting -- 13 values, instead of 11. This is a better baseline than my baseline. Looks like real baseline is 28-40 instead of 29-39.
  • 4.0x here, very consistent. 26 lb. lep = +120% meat
  • Expected 130% using NS11 formula.
• 27-pound lep: 12 values, missing new bottom.
  • 4.05x --> 27 lb. lep = +125% meat
  • Expected 135%.
• 28-pound lep: 13 values. Mean is a bit low (sample size, no doubt).
  • 4.075x --> 28 lb. lep = +127.5% meat
  • Expected +140%.
• 30-pound lep: Need more data, but roughly 4.24x --> 30 lb. lep = +144% meat
  • Expected +150%.
• 35-pound lep: 4.3x --> 35 lb. lep = +150% meat
  • Expected 175% ... pretty significant deviation here.

I need a lot more data in the 21+ pound ranges. (Especially 21-25 pounds, which are totally missing.)

Oh, it's also worth pointing out that the meat drop values are all discrete points, not continuous over the expanded range. For example, at 26 pounds, the possible values are 112, 116, 120, 124, ..., 160. There are no occurrences of 113, 114, or 115. So, apparently the way this works is: the meat drop value is rolled using the monster's base range (28-40, or whatever the true baseline is). Then, the total meat multiplier is applied to that value, and rounded/truncated to the final integer value. --Greycat 20:23, 4 July 2007 (CDT)

The Best Equipment

When is it better to use "ant equipment" compared to the Meat Detector, Or the Tam o Shanter/shatner? --El taco 04:04, 18 September 2007 (CDT)

The ant tools give a flat bonus amount of meat, rather than boosting your multiplier. They're superior if you're killing fluffy bunnies, but totally inferior if you're meat-farming giants. The meat detector gives +5 pounds of leprechaun, so it's the best when your total familiar weight is very low (because 5 additional pounds at low weight gives a huge multiplier). The Tam gives you a straight multiplier bonus, so it's the best when you're using a heavy familiar (because adding more weight when you're already very heavy gives diminishing returns). --Greycat 17:47, 25 September 2007 (CDT)

Note the leprechaun base equipment is never as good as the Tam o Shanter. Even at low weights, +5 pounds does not give +50%. So the order of familiar equipment on this thing is (from best to worst): Tam o Shanter, Mayflower, Meat detector, Ant hoe.--QuantumNightmare 19:38, 25 September 2007 (CDT)

thank you.--El taco 17:28, 2 November 2007 (CDT)

High precision results

Weight	Range	Estimate
1	10.829% to 10.840%	10.832397%
5	37.157% to 37.169%	37.166248%
17	89.153% to 89.168%	89.155539%
18	92.923% to 92.937%	92.928531%
19	96.640% to 96.656%	96.652920%
20	100.332% to 100.334%	100.332496%
25	118.161% to 118.166%	118.161985%
26	121.621% to 121.633%	121.630682%
30	135.236% to 135.244%	135.240384%
37	158.211% to 158.228%	158.221949%
50	198.853% to 198.889%	198.880885%
65	243.568% to 243.607%	243.582607%

The 20-lb data includes data from 20 turns at the lvl 12 bandits, which is the best place for accurate spading but unfortunately it closes rather quickly. The other data is from the castle with various bonuses, which also produces decent results and can be easily run by anyone with a leprechaun of the appropriate weight.--Eleron 14:06, 26 April 2008 (CDT)

The formula sqrt(220 * x) + 2 * x - 6 fits the high accuracy spading results perfectly. I'm adding it to the main article. --Eleron 02:43, 18 May 2008 (CDT)

How is The Themthar Hills accurate when it doesn't even confidently state the meat drop range, and the bandit page itself has a different meat range listed? --Flargen 02:56, 18 May 2008 (CDT)

They drop 800-1200, this is kinda known but the wiki page meat drops are a bit flaky. Often the correct range is listed at the zone or data pages and the observed drops are listed on the page itself, but this isn't always followed and some people have had Packrat which ruins the range. Anyway, it's not important for determining the results - I've based it on a possible range of 500-1500 for bandits and 100-200 for giants and all the drops only have to be contained within those limits for the algorithm to work. --Eleron 03:11, 18 May 2008 (CDT)

Ah, yes, I forgot that meat drop ranges with +meat effects aren't made to take every possible integer value between the new minimum and maximum. --Flargen 03:23, 18 May 2008 (CDT)

• um, i hate to mention this, but we're back where we started. confidently saying "this exactly matches all my data." exactly? what, to n decimal places where n is a very large number indeed? or does the previous statement only mean "to a tolerable degree of variance?"
• i can pretty much guarantee that the latest formula isn't what jick has typed into the php. there is a strong possibility that the two may be algebraically equivalent, i am (to my undying shame and regret) not enough of a maths geek to see if it simplifies to something sensible.
• since the weights above 20lbs have been shown to be pretty much a straight line, as expected weights from 14lbs upwards are pretty much linear too. modelling these is not tricky. indeed, finding a fit for all weights above five pounds seems not be other than trivial.
• the biggest discrepancies come from trying to model very low weights indeed. how many data points did you take for 1lb of leprechaun? there are eleven lep-type familiars. even if you have ten mr store familiars, given that you can only test them for four turns each at one pound (or is that three, i'm never sure) that's forty tries per ascension. just how long have you been working at this? --Evilkolbot 07:52, 18 May 2008 (CDT)

The ranges have upper and lower bounds which are 100% exact with no variance or uncertainty. More data points can possibly shrink the range of possibilities, but observing the same meat drop a hundred times without improving the bounds does nothing. This is because of how the meat drops work, but I'd rather not repeat that at length here yet again. The straight lines that “pretty much” match are way off at this level of accuracy and don't intersect with the tight ranges at all, not even at high weights. The models you talk about are orders of magnitude less accurate than these results. My formula matches all of them, which shows that if it's not right then it's pretty much indistinguishable from the truth, and then it's mostly a philosophical question. If you have any credible reason at all to believe that the formula isn't feasible, then please tell me. (Also, a rat head balloon is obviously used for low weights. Sorry if the reply might be a little aggressive, but it's a bit tiring to explain over from the very basics every time the edge of meat spading is pushed.) --Eleron 08:21, 18 May 2008 (CDT)

• aggression's fine, i'm partial to a bit of justified tetchy myself. the problem is that since you've not justified the reasoning behind your spading here some of us aren't up to speed. perhaps a summary of your workings (yes, copied from elsewhere if necessary) is in order. especially since you seem so certain.
• i'm still not entirely convinced your sample size can be big enough at the bottom end to justify so many decimal places of accuracy. a rat head balloon cuts your sampling time by what, six which still isn't much. if only i hadn't fallen asleep so many times in stats classes... --Evilkolbot 10:03, 18 May 2008 (CDT)

There is no “accuracy” involved in the ranges, they are exact fractions based on the observed results. I'm adding the spading below.--Eleron 10:45, 18 May 2008 (CDT)

Say you're running more than +200% meat bonus and you get a drop of 456. Then you know that there is an integer x and some bonus y such that floor(x * y) = 456. If you assume that x was actually 100, then you know that 4.56 <= y < 4.57. Those are exact boundaries. If the monster can drop from 100-200 meat, then you end up with 101 such possible ranges for y. If you get another drop of 460 then you get another set of 101 ranges, but the real y has to match both. You'll end up with 69 possible ranges after two drops. If you then get a million more drops and they're all 456, you've learned nothing more and that was completely useless. However, if you then get a drop of 800, you only have 7 possible ranges for y left, because each range now has to fit both something as low as 456 and as high as 800. Add a few more drops and you can reduce it to only one range, and the bounds are exact fractions.

After you get down to one range, you need a drop that helps reduce the range by either increasing the lower bound or reducing the upper bound. When you already have a very good range, it gets more difficult to find drops that help improve the range, and you may need a monster with higher meat drops to be able to narrow it further. However, giants at the castle are sufficient to achieve very good bounds.

The data for 1lb leprechaun vs bandits is:

With +0% from other effects: 914,1170,1041,1147,1089

With +15%: 1248,1215,1252,1292,1258

With +65%: 1877,1958,1564,1438,2030

With +265%: 3803,3288,4028,4111,4175,3457,3352,3897,3942

Now you can do the maths on that or e.g. change QuantumNightmare's simulator to run with a much much higher resolution than the default, and you'll find that only bonuses for the 1lb leprechaun between 10.829145728643219% and 10.839552238805972% can give those results. Now printing it with that many decimals is quite meaningless because only the magnitude of the difference between the numbers is interesting, i.e. the remaining range, but they're exact fractions and can be printed with any accuracy you like. --Eleron 10:45, 18 May 2008 (CDT)

• god this makes me wish i wasn't so old and stupid. well, i say that. but actually, only getting rid of one would probably be enough. and stupid's its own comfort.
• anyway, so this is to do with identifying the set of possible original integers that could have given rise to an individual datapoint, and thereby the multipliers that could have given you that number from those integers. each new datapoint gives a new set, which intersects (or doesn't) with the original set and gives a smaller set for the next run though (euler diagram called for.) by the time you've got ooh, twenty-five or so datapoints well enough spaced you can get the intersections of the sets of multipliers to such a state that there's only one multiplier left.
• what do you know, if you ignore the FLOOR stuff in the original exposition, the numbers work out. do you do this stuff for a living? --Evilkolbot 13:52, 18 May 2008 (CDT)
  • in case anybody missed it, there's a great deal of delicious, delicious crow just for me in the forum, when jick wrote:

Your MOM is a ridiculously inelegant formula.
The actual code is pretty messy, too. I started
with the curve I wanted instead of with pretty math. 

• i'm sorry i doubted you. --Evilkolbot 15:54, 21 May 2008 (CDT)
  • I love that comeback and hope to be able to use it myself some day. Also, link to thread (8th post).—Preceding unsigned comment added by flargen (talk • contribs)

The jalapeño slices grant +10 weight of leprechaun to a pet cheeseling - AvangionQ / February 23rd, 2010