Talk:Hovering Sombrero
The Formula
This formula (in general, round all numbers down):
NORMAL MONSTER EXPERIENCE (NME) * SOMBRERO LEVEL * (0.015 - (NME / 11350)) + NME
Will give you an approximate value for the experience a sombrero is worth at any given monster level with any given level of sombrero. The formula is NOT the correct one, but it is +/- 1 point (when rounded) vs. actual values, which is reasonably close.
For example, The Hooded Warrior is normally worth 33 stat points. With a 30 pound sombrero, the formula would calculate:
33 * 30 * (0.015 - (33 / 11350)) + 33 = 44.97 rounded to 44
This jives with Grignr's actual value, as seen here. Factoring in the error, the critical point at which a 30 lb sombrero begins to outclass a 30 lb volleyball is about 21-22 stat points.
Obviously, this calculation is completely wrong, but somewhat accurate nonetheless. I have a feeling that my method of flattening the high end of the curve is not correct. Does anyone have any ideas as to how this formula may work? For raw data, check out Grignr's repository, found in the linked forum post. --Snickles 19:59, 22 Jul 2005 (Central Daylight Time)
This calculation seems to be close at lower levels, but stat gains skyrocket somewhere between monster levels of 180 (topiary golem) and 200 (Sorceress' Tower monsters). --Poochy 23:57, 20 Sep 2005 (Central Daylight Time)
According to Snickles's formula above, a heavy sombrero should be better than a heavy volleyball much sooner than the Icy Peak -- as soon as the 8-bit realm! [ made using OpenOffice Calc, where XP = ROUNDDOWN(MonsterPower/5), VolleyballXP = XP + ROUNDDOWN(30/4), SombreroXP = XP + ROUNDDOWN(XP * 30 * (0.015 - (XP / 11350)) + XP)
http://img168.imageshack.us/img168/7366/sombrerochartmozaivv5.png
The word on the forums is to use Muefigilo's forumla, which jives with data observed by Strangerer:
Bonus Substat Gain = rounddown( sqrt(creature power) * sombrero weight ) / 33
This would make a heavy (30lbs) Sombrero as effective equivalent Volleyball at Cobb's Knob Menagerie Level 2 / Pirate Cove, and better than the Volleyball from the Orc Chasm and beyond. --Mozai 18:20, 28 January 2006 (Central Standard Time)
--Mozai 18:20, 28 January 2006 (Central Standard Time)
I put together a table comparing the sombrero and volleyball stat gains at given monster levels and lbs. Blue is for when the volleyball is superior, red is for when the sombrero is superior. Purple is when it is the same.--Blibbler 23:59, 23 April 2006 (CDT) Comparison graph.
Observations
If it helps, I have attempted to collect some data on this run up the tower:
| Sombrero effective weight | Mind Control setting | Stat gain | |
| Topiary Golem | 0 | 1 | 36 |
| Topiary Golem | 30 | 1 | 47 |
| Topiary Golem | 40 | 1 | 51 |
| Sorceress' Tower monsters | 0 | 1 | 40 |
| Sorceress' Tower monsters | 25 | 1 | 260 |
| Sorceress' Tower monsters | 25 | 11 | 260 |
| Sorceress' Tower monsters | 30 | 1 | 304 |
| Sorceress' Tower monsters | 32 | 1 | 321 |
| Sorceress' Tower monsters | 33 | 1 | 330 |
| Sorceress' Tower monsters | 40 | 1 | 392 |
| Sorceress' Tower monsters | 41 | 1 | 401 |
| Sorceress' Tower monsters | 42 | 1 | 410 |
| Sorceress' Tower monsters | 43 | 1 | 418 |
From what I can tell, the top end of the curve does not flatten out at all as the normal monster experience increases. Quite the contrary; it only gets steeper. And Mind Control didn't have any effect when I changed that, so we can probably throw out that column. --Poochy 23:57, 20 Sep 2005 (Central Daylight Time)
The Tower Monsters are not level 200. The stat gain recieved from them is capped, however, so if you calculate level based on that, they appear to be level 200. --Snickles 11:32, 1 Oct 2005 (MDT)
Yeah, further observation tells me that you're right. One more piece of data, though: My friend decided to try fighting the NS with her 21-pound Hovering Sombrero, and got 685 substat points upon winning, which is a bonus of 185 points, or 37%. Does this help any? --Poochy 14:49, 8 Oct 2005 (MDT)
The best known approximation of the formula for the hovering sombrero's stat gain is Floor (Sqrt (monster level) * sombrero weight / 33). This formula gives the observed value just over 90% of the time, and is one point high the other 10%.
Wouldn't the calculation be more or less 100% accurate if you wrote it as (Sqrt (monster level) * sombrero weight / 33.3), or, even better, (Sqrt (monster level) * sombrero weight * 3 / 100)?--LoopyChew 10:11, 23 February 2006 (Central Standard Time)
Arena Message
Is the Ultimate Cage Match message another reference to They Might Be Giants's Hovering Sombrero, with the lines "But the old sombrero just keep hovering on/Hovering sombrero hover on"? --Drab Emordnilap 14:40, 14 February 2007 (CST)
New formula
My best approximation of the new, post-NS13 formula is:
sqrt(weight * monsterLevel)/10
I'm putting this in the article for now, until someone else finds a more accurate formula. --Poochy 02:31, 8 August 2007 (CDT)
If that is correct, the Sombrero is just as good as a volleyball (with the same weight), exactly at monsterlevel 100. Right? --Mercantilia 10:07, 18 August 2007 (CDT)
- If the formula currently on the volleyball page is also correct, I reckon you've done your algebra correctly. --Bagatelle 12:39, 18 August 2007 (CDT)
The NS13 formula is floor(sqrt(lb) * (1 + sqrt(ML - 4)) / 10). MLs below 4 give no stats (for known weights, it might give stats above 100lb).
The data used to determine this new, accurate formula was added to a separate spading log page.--Eleron 20:23, 7 July 2008 (CDT)
Spading Log
Below is the spading data the new formula is based on. For each weight, it lists a known range of ML values that give a certain number of stats.
(Some entries were entered incorrectly and detected by the new formula. These have been re-spaded and corrected in the log below, but it is possible that some areas around (159 ML, 45 lb) and (110 ML, 7 lb) may still be incorrect.)
1 lb: 1 - 36: 0
2 lb: 1 - 36: 0
3 lb: 1 - 20: 0 28 - 76: 1 116 - 116: 2
4 lb: 1 - 18: 0 20 - 84: 1 92 - 116: 2
5 lb: 1 - 16: 0 18 - 54: 1 68 - 116: 2
6 lb: 1 - 13: 0 14 - 54: 1 56 - 124: 2 136 - 136: 3
7 lb: 1 - 10: 0 12 - 44: 1 48 - 110: 2 111 - 124: 3
8 lb: 1 - 6: 0 12 - 36: 1
9 lb: 1 - 6: 0 12 - 36: 1
10 lb: 1 - 6: 0 12 - 32: 1 36 - 36: 2
11 lb: 1 - 6: 0 12 - 20: 1 36 - 36: 2
12 lb: 1 - 6: 0 12 - 20: 1 36 - 36: 2
13 lb: 1 - 6: 0 12 - 20: 1 36 - 36: 2
14 lb: 1 - 6: 0 12 - 20: 1 36 - 36: 2
15 lb: 1 - 6: 0 8 - 20: 1 24 - 36: 2
16 lb: 1 - 6: 0 8 - 18: 1 20 - 36: 2
17 lb: 1 - 6: 0 7 - 18: 1 19 - 43: 2 44 - 79: 3 80 - 126: 4 128 - 128: 5
18 lb: 1 - 5: 0 7 - 16: 1 19 - 38: 2 44 - 67: 3 76 - 120: 4 121 - 124: 5
19 lb: 1 - 5: 0 7 - 16: 1 17 - 38: 2 39 - 67: 3 76 - 84: 4
20 lb: 1 - 5: 0 6 - 16: 1 17 - 36: 2 37 - 67: 3 68 - 84: 4
21 lb: 1 - 5: 0 6 - 15: 1 16 - 34: 2 35 - 63: 3 64 - 84: 4 144 - 148: 5
22 lb: 1 - 5: 0 6 - 14: 1 15 - 33: 2 34 - 60: 3 61 - 84: 4 140 - 140: 5 144 - 148: 6
23 lb: 1 - 5: 0 6 - 14: 1 15 - 31: 2 32 - 57: 3 58 - 84: 4 140 - 140: 6
24 lb: 1 - 5: 0 6 - 13: 1 14 - 30: 2 31 - 52: 3 58 - 84: 4
25 lb: 1 - 4: 0 5 - 12: 1 13 - 28: 2 29 - 52: 3 53 - 84: 4 85 - 104: 5
26 lb: 1 - 4: 0 5 - 12: 1 13 - 27: 2 28 - 43: 3 53 - 70: 4 85 - 103: 5
27 lb: 1 - 4: 0 5 - 12: 1 13 - 26: 2 27 - 43: 3 53 - 70: 4 85 - 103: 5
28 lb: 1 - 4: 0 5 - 11: 1 12 - 25: 2 26 - 43: 3 53 - 70: 4 85 - 103: 5 148 - 148: 6
29 lb: 1 - 4: 0 5 - 11: 1 12 - 24: 2 25 - 43: 3 53 - 70: 4 85 - 103: 5 144 - 144: 6 148 - 148: 7
30 lb: 1 - 4: 0 5 - 11: 1 12 - 24: 2 25 - 43: 3 44 - 70: 4 71 - 103: 5 104 - 140: 6 144 - 144: 7
31 lb: 1 - 4: 0 5 - 8: 1 12 - 20: 2 25 - 36: 3 44 - 56: 4 71 - 84: 5 104 - 104: 6 140 - 140: 7
32 lb: 1 - 4: 0 5 - 8: 1 12 - 20: 2 25 - 36: 3 44 - 56: 4 71 - 84: 5 104 - 104: 6
33 lb: 1 - 4: 0 5 - 8: 1 12 - 20: 2 25 - 36: 3 44 - 56: 4 71 - 84: 5 104 - 104: 6
34 lb: 1 - 4: 0 5 - 8: 1 12 - 20: 2 25 - 36: 3 44 - 56: 4 71 - 84: 5 104 - 104: 6
35 lb: 1 - 4: 0 5 - 8: 1 12 - 20: 2 24 - 36: 3 40 - 56: 4 60 - 84: 5 88 - 120: 6 124 - 144: 7
36 lb: 1 - 4: 0 5 - 8: 1 12 - 16: 2 24 - 32: 3 40 - 48: 4 60 - 76: 5 88 - 104: 6 124 - 136: 7
37 lb: 1 - 4: 0 5 - 8: 1 12 - 16: 2 24 - 32: 3 40 - 48: 4 60 - 76: 5 88 - 104: 6 124 - 148: 7
38 lb: 1 - 4: 0 5 - 8: 1 12 - 16: 2 24 - 32: 3 40 - 48: 4 60 - 76: 5 88 - 104: 6 124 - 136: 7 148 - 148: 8
39 lb: 1 - 4: 0 5 - 8: 1 12 - 16: 2 24 - 32: 3 40 - 48: 4 60 - 76: 5 88 - 104: 6 124 - 140: 7
40 lb: 1 - 4: 0 5 - 8: 1 12 - 16: 2 20 - 32: 3 36 - 48: 4 52 - 76: 5 80 - 104: 6 108 - 136: 7 140 - 144: 8 847 - 847: 18 848 - 848: 19
41 lb: 1 - 4: 0 5 - 7: 1 12 - 16: 2 20 - 28: 3 36 - 45: 4 52 - 67: 5 80 - 93: 6 108 - 123: 7 140 - 144: 8
42 lb: 1 - 4: 0 5 - 7: 1 12 - 16: 2 20 - 28: 3 36 - 45: 4 52 - 67: 5 80 - 93: 6 108 - 123: 7 140 - 144: 8
43 lb: 1 - 4: 0 5 - 7: 1 12 - 16: 2 20 - 28: 3 36 - 45: 4 52 - 67: 5 80 - 93: 6 108 - 123: 7 140 - 144: 8
44 lb: 1 - 4: 0 5 - 7: 1 12 - 16: 2 20 - 28: 3 36 - 45: 4 52 - 67: 5 80 - 93: 6 108 - 123: 7 140 - 144: 8
45 lb: 1 - 4: 0 5 - 7: 1 8 - 16: 2 17 - 28: 3 29 - 45: 4 46 - 67: 5 68 - 93: 6 94 - 123: 7 124 - 158: 8 159 - 160: 9
Tiny Maracas vs. Tiny Pitchfork under the NS13 formula
If the new formula is correct, and my calculations, the pitchfork is always inferior unless your Sombrero actually has more weight than the ML you're fighting. --Missingno 18:41, 18 August 2007 (CDT)
- Correct, and the wax lips are always better. --Mercantilia 19:12, 18 August 2007 (CDT)
