Darkmoon Card: Wrath
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 Darkmoon Card: Wrath
 Item Level 100
 Binds when equipped
 Unique
 Trinket
 Requires Level 70
 Equip: Each time one of your direct damage attacks does not critically strike, you gain 17 critical strike rating for the next 10 sec. This effect is consumed when you deal a critical strike.
 Sell Price: 10
This is one of the four available Darkmoon Cards trinkets added with the Burning Crusade expansion.
Contents
[show]Obtaining the Trinket Edit
Darkmoon Card: Wrath is obtained by gathering all eight of the Storms cards, creating the Storms Deck by rightclicking on any of the cards, and turning in the deck to the Darkmoon Faire. All the individual cards and the deck itself are BoE items. Cards 2 through 4 are world drops, 5 through 8 are world drops from elite mobs, and the Ace drops from end bosses in instances.
Effects on Critical Strike Chance (general) Edit
Using the following java program we're able to simulate what happens to our crit rating when we use this trinket:
public static void main(String[] args) { double crit=0; double x=0; double sum=0; int i=0; Random generator = new Random(); for (crit=10;crit<40;crit++){ sum=0; for (i=1;i<1000000;i++){ if (generator.nextInt(100)+1>crit+x) x+=0.72; else x=0; if (x>0.72*20) x=0.72*20; sum+=x; } System.out.println("<tr><th>"+crit+"<td align=\"center\">"+(crit+sum/i)+"</td><td align=\"center\">"+((double)sum/i)*23.6+"</td>"); } }
This simulates the behavior of the trinket after 1.000.000 strikes. The output is the following:
Base Crit %  Average Crit % with trinket  Average Crit rating given by the trinket 

10.0  13.75669935999994  88.65810489599859 
11.0  14.579983279999517  84.4876054079886 
12.0  15.400025759999032  80.24060793597717 
13.0  16.23302031999849  76.29927955196442 
14.0  17.066904799997513  72.37895327994127 
15.0  17.91872735999656  68.88196569591881 
16.0  18.78558639999541  65.7398390398917 
17.0  19.649998159993984  62.53995657585808 
18.0  20.53643903999262  59.859961343825795 
19.0  21.41053695999086  56.88867225578434 
20.0  22.305600559989124  54.412173215743366 
21.0  23.205454319986963  52.0487219516923 
22.0  24.10476519998469  49.6724587196387 
23.0  25.021187599984636  47.700027359637424 
24.0  25.927840319984885  45.49703155164326 
25.0  26.855198079985033  43.78267468764679 
26.0  27.772040239985333  41.820149663653865 
27.0  28.69780175998559  40.06812153565995 
28.0  29.631598479985943  38.50572412766823 
29.0  30.564353359986253  36.91873929567558 
30.0  31.50758135998664  35.57892009568475 
31.0  32.450161359987035  34.22380809569411 
32.0  33.3870418399876  32.734187423707354 
33.0  34.33595207998803  31.528469087717557 
34.0  35.28205215998843  30.25643097572705 
35.0  36.23152759998903  29.06405135974111 
36.0  37.180114559989676  27.850703615756263 
37.0  38.132822799990215  26.734618079769085 
38.0  39.09364543999077  25.810032383782215 
39.0  40.05120071999136  24.80833699179606 
With those results you should able to determine, considering your base chance to crit, if this trinket is a good choice for your character.
Effects on Critical Strike Chance for Casters Edit
The crit benefits of this trinket are affected by the chance of the player to have a streak of noncrit hits. These streaks are less likely for players who already have a high crit chance. Also, the trinket itself, by increasing crit chance, progressively makes long noncrit streaks less likely.
Streaks of NonCrits Edit
In this example, resists will not be counted. A player with a 25% crit rate will be assumed to have a 75% noncrit hit rate. The probability that a series of noncrits of a certain length (called a streak on this page) occurring can be calculated by multiplying the noncrit hit rate to the power of its streak length. To clarify; the streak is quantified by presuming event X+1 is a critical. In other words:
 chance of streak = x^{y} (where x = noncrit chance and y = length of streak)
# of Casts  Crit Chance  NonCrit Chance  Chance of NonCrit Streak 

1  0.2500  0.7500  0.7500 
2  0.2500  0.7500  0.5625 
3  0.2500  0.7500  0.4219 
4  0.2500  0.7500  0.3164 
5  0.2500  0.7500  0.2373 
6  0.2500  0.7500  0.1780 
7  0.2500  0.7500  0.1335 
8  0.2500  0.7500  0.1001 
9  0.2500  0.7500  0.0751 
10  0.2500  0.7500  0.0563 
So with a 25% crit rate, the probability of having a streak of 10 noncrits is 5.63%. Although each cast has a 75% of being noncrit, the percentages have a cumulative effect when looking specifically for a block (or streak) of 10 noncrits in a row.
However, with the trinket, x in the above formula changes with each new noncrit in the streak, because the buff increases the crit rate cummulatively as the streak continues. The modified version this:
# of Casts  Crit Chance  NonCrit Chance  Chance of NonCrit Streak 

1  0.2500  0.7500  0.7500 
2  0.2577  0.7423  0.5567 
3  0.2654  0.7346  0.4090 
4  0.2731  0.7269  0.2973 
5  0.2808  0.7192  0.2138 
6  0.2885  0.7115  0.1521 
7  0.2962  0.7038  0.1071 
8  0.3038  0.6962  0.0745 
9  0.3115  0.6885  0.0513 
10  0.3192  0.6808  0.0349 
The new Chance of NonCrit Streak is equal to new NonCrit Chance times the previous Chance of NonCrit Streak. The blue * yellow = green numbers demonstrate this formula.
 0.7269 * 0.4090 = 0.2973
 0.6808 * 0.0513 = 0.0349
As you can see, players with a 25% crit rate will have a crit rate of 32% if they have had 10 noncrits in a row, but the chance of having 10 noncrits in a row is only 3.5%. To get an idea of how effective the trinket is, the number of extra crits contributed by the trinket for each scenario must be calculated and then added together.
In the table above, we listed the chance of having a streak of at least X noncrits in a row. The table below breaks down the contribution of the trinket for each streak scenario. This contribution is calculated by multiplying the bonus critical of the trinket by the incidence of the streak. The incidence can be calculated from the above table by deducting the nonstreak chance of X from the chance of X1. For example, there is a 0.75 incidence of a noncritical, and the incidence of a second noncritical is 0.5567 (these values are fractions of the total number of casts done.) The fraction of streaks that end at 1 (i.e. the second cast is a crit) is 0.1933, since the remainder (0.5567) had a second noncrit event. The final column is the product of this number and the increase in crit caused by the trinket, which tells us the fraction of streaks that ended because of the trinket.
X = Streak Length  Additional Crit from Trinket  Streak Incidence  Incidence of crits due to trinket 

0  0.0000  0.2500  0.0000 
1  0.0077  0.1933  0.0015 
2  0.0154  0.1477  0.0023 
3  0.0231  0.1117  0.0026 
4  0.0308  0.0835  0.0026 
5  0.0385  0.0617  0.0024 
6  0.0462  0.0451  0.0021 
7  0.0538  0.0325  0.0017 
8  0.0615  0.0232  0.0014 
9  0.0692  0.0164  0.0011 
10  0.0769  0.0114  0.0009 
TOTALS:    0.9765  0.0185 
For example, a streak of 5 noncrits followed by one crit has a fraction of 0.0617 of all streaks, and the increase in crit from the Wrath trinket is 3.85%. In other words, Wrath provided a 3.85% increased chance to crit for 6.17% of crit events. The table above shows the first 11 (and most likely) occurrences: that you have a streak of noncrits of length zero, a streak of length 1, a streak of length 2, etc. Adding their fractions together, these 11 possibilities summarises 97.65% of all cases (the remaining cases are streaks longer than 10). If we then add up the fractions of crits caused by the trinket, the wrath trinket increases the incidence of crits by 1.85% of all casts. The real figure is higher than this, but this is pretty close since streaks above 10 are unlikely, and its contribution soon becomes insignificant (if you go to 20, you cover 99.977% of the streaks and an increase of 2.0857%; at 29 it is 99.9998% of cases and an increase of 2.0892%).
The table above was calculated for someone who had a base crit rate of 25% (i.e. excluding contributions by the trinket.) If we convert the summed incidence of crits caused by the trinket and convert it to an equivalent critical strike rating, we get the approximate values below (to 20 iterations).
Base Crit Rate  Equivalent Crit Rating 

45%  20 
40%  24 
35%  30 
30%  37 
25%  46 
20%  59 
15%  77 
10%  104 
5%  146 
As your base crit rate increases, the value of this trinket decreases, but it is a very valuable trinket at lower rates. For those who are comparing various trinkets, this trinket has a critical rating of exactly 40 (the equivalent of [Battlemaster's Depravity], without the very useful temporary health bonus, or [Sextant of Unstable Currents] without the potential increase in spell damage) at a base critical rate of 28.13%. It also has a critical rating of exactly 32 (like the spell critical bonus of [Xi'ri's Gift], for example) at a base critical rate of 33.32%.
The sections below will be of interest to players concerned about long streaks of noncrits (perhaps warlocks trying to keep up Improved Shadowbolt procs).
Rating the effect of the trinket Edit
The significant effect of the trinket is in how it decreases the Chance of NonCrit Streak. You can think of Chance of NonCrit Streak as the opposite of crit chance over a given number of casts. For example, in the above chart, there is a 10.71% chance for a streak of 7 noncrits. That also means that there is a 89.29% chance that the streak will fail, that any one cast out of a block of 7 will crit. However, without the effect of the trinket, the streak chance is 13.35% for 7 casts. Without the trinket, there is an 86.65% chance the streak will fail.
So the trinket has increased the chance of at least one crit in any seven casts by 2.64%. Even though the 7 charges would add 5.38% crit chance to the next cast, the unlikelihood of getting 7 noncrits in a row balances that out. This includes the cumulative effect of the base crit rate and the trinket's increasing charges.
In other words, the effect of the trinket can be expressed in terms of the difference between the likelihood of noncrit streaks with and without the trinket. The following graph shows net crit chance increase caused by the trinket over a number of casts for players with different amounts of base crit.
So, as an example from the graph, a player with a base crit rate of 15% will be about 6% less likely to have a string of 14 noncrits due to the trinket. That is to say, he will be 6% more likely to have any one cast crit out of a block of 14. As you can see, the more base crit you have, the less benefit you get from the trinket, because the likelihood of long strings of noncrits is so low. Also, as you consider longer and longer streaks, the net benefit of the trinket actually begins to decrease. This is because the chance of one crit in say 18 or 20 casts is so high that any amount of crit increase is insignificant.
Summary Edit
Since Darkmoon Card: Wrath increases a player's crit rate only while the player is not critting, it is reducing its chance to build charges while building charges. So even though at 7 charges the trinket increases crit rate by 5.38%, we have to balance that with the increasing unlikelihood that the player will have 7 noncrits in a row, an unlikelihood affected by base crit plus added crit from the trinket.
Instead of looking flatly at crit increase, we can look at the difference in likelihood of noncrit streaks between streaks affected by the trinket and streaks with only base crit. The difference in these is the increased chance that any one cast across the streak will crit. Interestingly, we found that the benefit of the trinket maxes out at a certain point, and that longer streaks of noncrits are so unlikely that the trinket adds little to the cumulative effect of the base crit rate. Using this difference as a yardstick for the trinket's effect, here are some results for various base crit rates:
Base Crit  Average Effect  Maximum Effect 

10%  4.9% crit increase 54% of the time  12.7% crit increase 10.2% of the time 
15%  2.8% crit increase 49% of the time  6.7% crit increase 10% of the time 
20%  1.5% crit increase 50% of the time  4% crit increase 9.4% of the time 
25%  0.6% crit increase 56% of the time  2.6% crit increase 10.7% of the time 
30%  0.5% crit increase 49% of the time  1.8% crit increase 10% of the time 
 Average Effect is the crit rate increase for streaks that have a ~50% chance of occurrence
 Maximum Effect is the largest difference in likelihood of noncrit streaks caused by the trinket
Raw Data Edit
Chance of NonCrit Streak (10% base)  Crit Chance Increase  Chance of NonCrit Streak (15% base)  Crit Chance Increase  Chance of NonCrit Streak (20% base)  Crit Chance Increase  

# of casts  w/o trinket  with trinket  w/o trinket  with trinket  w/o trinket  with trinket  
1  0.9000  0.9000  0.0000  0.8500  0.8500  0.0000  0.8000  0.8000  0.0000  
2  0.8100  0.8031  0.0069  0.7225  0.7160  0.0065  0.6400  0.6338  0.0062  
3  0.7290  0.7104  0.0186  0.6141  0.5976  0.0166  0.5120  0.4973  0.0147  
4  0.6561  0.6230  0.0331  0.5220  0.4941  0.0279  0.4096  0.3864  0.0232  
5  0.5905  0.5415  0.0490  0.4437  0.4048  0.0389  0.3277  0.2972  0.0305  
6  0.5314  0.4665  0.0649  0.3771  0.3285  0.0486  0.2621  0.2263  0.0358  
7  0.4783  0.3983  0.0799  0.3206  0.2641  0.0565  0.2097  0.1706  0.0391  
8  0.4305  0.3371  0.0934  0.2725  0.2102  0.0622  0.1678  0.1273  0.0405  
9  0.3874  0.2826  0.1048  0.2316  0.1658  0.0658  0.1342  0.0940  0.0402  
10  0.3487  0.2348  0.1139  0.1969  0.1294  0.0674  0.1074  0.0687  0.0387  
11  0.3138  0.1932  0.1206  0.1673  0.1001  0.0673  0.0859  0.0497  0.0362  
12  0.2824  0.1576  0.1249  0.1422  0.0766  0.0657  0.0687  0.0355  0.0332  
13  0.2542  0.1273  0.1269  0.1209  0.0580  0.0629  0.0550  0.0252  0.0298  
14  0.2288  0.1018  0.1270  0.1028  0.0435  0.0592  0.0440  0.0176  0.0264  
15  0.2059  0.0807  0.1252  0.0874  0.0323  0.0550  0.0352  0.0122  0.0230  
16  0.1853  0.0633  0.1220  0.0743  0.0237  0.0505  0.0281  0.0083  0.0198  
17  0.1668  0.0492  0.1176  0.0631  0.0173  0.0459  0.0225  0.0056  0.0169  
18  0.1501  0.0378  0.1123  0.0536  0.0124  0.0412  0.0180  0.0038  0.0142  
19  0.1351  0.0288  0.1063  0.0456  0.0088  0.0368  0.0144  0.0025  0.0119  
20  0.1216  0.0217  0.0999  0.0388  0.0062  0.0325  0.0115  0.0016  0.0099 
Chance of NonCrit Streak (25% base)  Crit Chance Increase  Chance of NonCrit Streak (30% base)  Crit Chance Increase  

# of casts  w/o trinket  ;with trinket  w/o trinket  with trinket  
1  0.7500  0.7500  0.0000  0.7000  0.7000  0.0000  
2  0.5625  0.5567  0.0058  0.4900  0.4846  0.0054  
3  0.4219  0.4090  0.0129  0.3430  0.3318  0.0112  
4  0.3164  0.2973  0.0191  0.2401  0.2246  0.0155  
5  0.2373  0.2138  0.0235  0.1681  0.1503  0.0178  
6  0.1780  0.1521  0.0258  0.1176  0.0994  0.0182  
7  0.1335  0.1071  0.0264  0.0824  0.0650  0.0173  
8  0.1001  0.0745  0.0256  0.0576  0.0420  0.0156  
9  0.0751  0.0513  0.0238  0.0404  0.0268  0.0135  
10  0.0563  0.0349  0.0214  0.0282  0.0169  0.0113  
11  0.0422  0.0235  0.0187  0.0198  0.0105  0.0092  
12  0.0317  0.0156  0.0160  0.0138  0.0065  0.0074  
13  0.0238  0.0103  0.0135  0.0097  0.0039  0.0057  
14  0.0178  0.0067  0.0111  0.0068  0.0024  0.0044  
15  0.0134  0.0043  0.0091  0.0047  0.0014  0.0033  
16  0.0100  0.0027  0.0073  0.0033  0.0008  0.0025  
17  0.0075  0.0017  0.0058  0.0023  0.0005  0.0019  
18  0.0056  0.0011  0.0046  0.0016  0.0003  0.0014  
19  0.0042  0.0006  0.0036  0.0011  0.0002  0.0010  
20  0.0032  0.0004  0.0028  0.0008  0.0001  0.0007 
Simulation Edit
A simple script that runs simulations of stacking Wrath buffs for casters, and computes the effective crit increase, can be found here.
External linksEdit
