This is the post I saved from the Druid Forum where other methodical testing was done. Testing by Chibi.
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Kenco on the warrior forum posted some nice numbers for warrior threat. So naturally this causes me to wonder how druids compare. I tried sifting through tons of posts of mostly anecdotal evidence, but I was unsatisfied and decided to do the testing myself. So here the data I gathered on Maul. Swipe will be incoming, but this was boring so it might be a while. :)
The tests were preformed with me (Chibi, a warrior) using Recap, a Warlock (Impudence), and a Druid with "defiance" (Alys).
The druid initialized combat with a single maul in bear form. Enrage was not used, since I felt it could cause threat. Then the warlock would punch the mob (four damage per swing generally) until he pulled aggro. This resulted in the following data.

NORMAL MAUL
# MAUL PULLED DIDN'T THREAT THREAT BASE Â* BASE Â* MAX Â* MIN Â* MAX % Â*MIN %
Â*Â* Â* Â* DMG Â* Â*PULL Â* MAX Â* Â*MIN Â* Â*THREAT THREAT DIFF. DIFF. OF DMG OF DMG
Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* MAX Â* Â*MIN
1 Â*285 796 Â* Â*792 Â* Â*723.6 Â*720.0 Â*499.0 Â*496.6 Â*214 Â* 211.6 75.1 Â* 74.2
2 Â*292 818 Â* Â*814 Â* Â*743.6 Â*740.0 Â*512.8 Â*510.3 Â*220.8 218.3 75.6 Â* 74.8
3 Â*263 735 Â* Â*731 Â* Â*668.2 Â*664.5 Â*460.8 Â*458.3 Â*197.8 195.3 75.2 Â* 74.3
4 Â*270 755 Â* Â*751 Â* Â*686.4 Â*682.7 Â*473.4 Â*470.8 Â*203.4 200.8 75.3 Â* 74.4
5 Â*288 806 Â* Â*802 Â* Â*732.7 Â*729.1 Â*505.3 Â*502.8 Â*217.3 214.8 75.5 Â* 74.4
6 Â*286 801 Â* Â*797 Â* Â*728.2 Â*724.5 Â*502.2 Â*499.7 Â*216.2 213.7 75.6 Â* 74.7
7 Â*277 774 Â* Â*770 Â* Â*703.6 Â*700.0 Â*485.2 Â*482.8 Â*208.2 205.8 75.2 Â* 74.3
8 Â*268 749 Â* Â*745 Â* Â*680.9 Â*677.3 Â*469.6 Â*467.1 Â*201.6 199.1 75.2 Â* 74.3
9 Â*266 744 Â* Â*740 Â* Â*676.4 Â*672.7 Â*466.5 Â*463.9 Â*200.5 197.9 75.4 Â* 74.4
10 260 726 Â* Â*722 Â* Â*660.0 Â*656.4 Â*455.2 Â*452.7 Â*195.2 192.7 75.1 Â* 74.1
Threat min and max are determined by dividing damage by 1.1. 10% is the melee range stickiness, that is, the amount needed beyond the current aggro holder's threat in order to pull aggro. This was determined by various sources (including myself) in other tests.
Base threat is determined by dividing threat totals by 1.45. The 1.45 threat modifier in bear form was crudely tested beforehand, but mostly this number comes from faith in thottbot.com and the assumption that bear form works just like defensive stance for warriors.
DIFF. means difference which is determined by subtraction (duh!).
Smallest max difference: 195.2
Largest min difference: 218.3
From this impossible range we can conclude maul does not have a fixed modifier as heroic strike (similar warrior skill), but notice the beautiful final columns.
Smallest max % of damage: 75.1%
Largest min % of damage: 74.8%
I feel fairly confident saying maul provides a 1.75 threat modifier to its damage from this data.
To verify these findings and investigate the possibility of strange crit behaviour we tested a few crits using the same methods.
CRIT MAUL
# MAUL PULLED DIDN'T THREAT THREAT BASE Â* BASE Â* MAX Â* MIN Â* MAX % Â*MIN %
Â*Â* Â* Â* DMG Â* Â*PULL Â* MAX Â* Â*MIN Â* Â*THREAT THREAT DIFF. DIFF. OF DMG OF DMG
Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* Â* MAX Â* Â*MIN
1 594 Â*1659 Â*1651 Â* Â*1508.2 1500.9 1040.1 1035.1 446.1 441.1 75.1 Â* 74.3
2 575 Â*1610 Â*1602 Â* Â*1463.6 1456.4 1009.4 1004.4 434.4 429.4 75.5 Â* 74.7
3 596 Â*1665 Â*1661 Â* Â*1513.6 1510.0 1043.9 1041.4 447.9 445.4 75.2 Â* 74.7
4 587 Â*1640 Â*1636 Â* Â*1490.9 1487.3 1028.2 1025.7 441.2 438.7 75.2 Â* 74.7
Crits apparently function the same.
So threat from maul is:
Maul_Damage * 1.75 * 1.3 (or 1.45 with talent)
And
We went back and tested swipe.
The data is broken into two tables so that it won't be too wide.

# Â*TOTAL WHITE SWIPE PULLED DIDN'T
Â* Â*DMG Â* DMG Â* DMG Â* Â* Â* Â* Â*PULL
1 Â*220 Â* 153 Â* 67 Â* Â*432 Â* Â*428
2 Â*369 Â* 302 Â* 67 Â* Â*670 Â* Â*662
3 Â*214 Â* 146 Â* 68 Â* Â*424 Â* Â*421
4 Â*222 Â* 154 Â* 68 Â* Â*436 Â* Â*433
5 Â*219 Â* 146 Â* 73 Â* Â*439 Â* Â*435
6 Â*218 Â* 151 Â* 67 Â* Â*430 Â* Â*426
7 Â*205 Â* 137 Â* 68 Â* Â*412 Â* Â*405
8 Â*218 Â* 151 Â* 67 Â* Â*432 Â* Â*424
9 Â*238 Â* 164 Â* 74 Â* Â*470 Â* Â*466
10 211 Â* 144 Â* 67 Â* Â*418 Â* Â*414
11 252 Â* 180 Â* 72 Â* Â*491 Â* Â*487
12 Â*67 Â* Â* 0 Â* 67 Â* Â*188 Â* Â*184
13 Â*67 Â* Â* 0 Â* 67 Â* Â*191 Â* Â*187
14 284 Â* 145 Â*139 Â* Â*627 Â* Â*623
15 302 Â* 158 Â*144 Â* Â*654 Â* Â*650
16 293 Â* 147 Â*146 Â* Â*643 Â* Â*639
17 275 Â* 140 Â*135 Â* Â*604 Â* Â*600
# THREAT THREAT WHITE SWIPE SWIPE BASE BASE MAX MIN MAX % MIN %
MAX MIN THREAT THREAT THREAT SWIPE SWIPE DIFF. DIFF. OF DMG OF DMG
MAX MIN THREAT THREAT
MAX MIN
1 392.7 389.1 221.9 170.8 167.2 117.8 115.3 50.8 48.3 75.8 72.1
2 609.1 601.8 437.9 171.2 163.9 118.1 113.0 51.1 46.0 76.3 68.7
3 385.5 382.7 211.7 173.8 171.0 119.9 117.9 51.9 49.9 76.3 73.4
4 396.4 393.6 223.3 173.1 170.3 119.4 117.4 51.4 49.4 75.6 72.6
5 399.1 395.5 211.7 187.4 183.8 129.2 126.8 56.2 53.8 77.0 73.7
6 390.9 387.3 219.0 171.9 168.3 118.6 116.1 51.6 49.1 77.0 73.3
7 374.5 368.2 198.7 175.8 169.5 121.2 116.9 53.2 48.9 78.2 71.9
8 392.7 385.5 219.0 173.7 166.5 119.8 114.8 52.8 47.8 78.8 71.3
9 427.3 423.6 237.8 189.5 185.8 130.7 128.1 56.7 54.1 76.6 73.1
10 380.0 376.4 208.8 171.2 167.6 118.1 115.6 51.1 48.6 76.3 72.5
11 446.4 442.7 261.0 185.4 181.7 127.9 125.3 55.9 53.3 77.6 74.0
12 170.9 167.3 0 170.9 167.3 117.9 115.4 50.9 48.4 76.0 72.2
13 173.6 170.0 0 173.6 170.0 119.7 117.2 52.7 50.2 78.7 74.9
14 570.0 556.4 211.7 358.3 344.7 247.1 237.7 108.1 98.7 77.8 71.0
15 594.5 590.9 229.1 365.4 361.8 252.0 249.5 108.0 105.5 75.0 73.3
16 584.5 580.9 213.2 371.3 367.7 256.1 253.6 110.1 107.6 75.4 73.7
17 549.1 545.1 203.0 346.1 342.1 238.7 235.9 103.7 100.9 76.8 74.7
Once again the smallest maximum difference is 50.8 and the largest minimum difference is 107.6, which creates an impossible range. So swipe appears to be affected by a threat multiplier like maul.
The range for the swipe multiplier is 1.75 to 1.749. 1.75 might be a good guess :) This is the exact same modifier that maul has, and since swipe and maul are your only damage causing abilities (as far as I know), we could generally say bear damage causing abilities cause damage * 1.75 threat.
So swipe's threat, like maul is calculated thus:
Swipe_Damage * 1.75 * 1.3 (or 1.45 with talent)
We also did some quick fairy fire and demo shout tests. The warlock was wimping out cause he wanted to go to sleep, so there isn't much data. Sorry. Here are the results.
Demo shout was used once. The warlock pulled with 67 damage. 63 damage did not pull.
67 / 1.1 / 1.45 = 42.0
63 / 1.1 / 1.45 = 39.5
Faery fire at one application (pulled_number / 1.1 / 1.45):
1) 180 pulled aggro. 172 did not. 112.9 max base threat. 107.8 min base threat.
2) 174 pulled aggro. 170 did not. 109.1 max base threat. 106.6 min base threat.
Faery fire at two applications (pulled_number / 1.1 / 1.45 / 2):
3) 345 pulled aggro. 341 did not. 108.2 max base threat. 106.9 min base threat.
Faery fire at four applications (pulled_number / 1.1 / 1.45 / 4):
4) 693 pulled aggro. 689 did not. 108.6 max base threat. 108.0 min base threat.
Thus, before bearform modifier:
Fairy Fire: 108.0-108.2
Demo shout: 39.5-42