New, Updated System
On July 27, 2017, the developers changed how the loot boxes in Overwatch work. They did two things:
- Drastically reduced the number of duplicates that players were getting
- Increased the frequency of credit drops to compensate for not getting any credits from duplicates
In the old system, the more items you had, the more credits you would get in each loot box. This is because your chances of getting a duplicate increase as you collect more items. This point is made clearer in a graph made by Alp_PS2 where they calculated the average credits dropped vs the number of loot boxes opened, which can be found here.
If players get no duplicates from loot boxes, the amount of credits in each loot box is easy to calculate. It would just be the rate at which credit drops are given times the value of the credit drop in each loot box. The new drop rates can be estimated by guessing how many credits Blizzard wants players to get out of every loot box. It should be somewhere between the minimum number of credits (when players get no duplicates) and the maximum (when players get only duplicates. The number of credits with no duplicates is the weighted average of the credit drops times four. The number of credits with all duplicates is the weighted average of the credit drops plus the weighted average of the item duplicate value. These are calculated in the table below:
| Drop Type | Old Frequency | Value | Duplicate Value | Weighted Value (no duplicates) | Weighted Value (all duplicates) |
| Common Item | 58.81% | 25 | 5 | 14.70 | 2.94 |
| Rare Item | 27.08% | 75 | 15 | 20.31 | 4.06 |
| Epic Item | 4.76% | 250 | 50 | 11.90 | 2.38 |
| Legendary Item | 1.97% | 1000 | 200 | 19.70 | 3.94 |
| Rare Credits | 4.29% | 50 | - | 2.15 | 2.15 |
| Epic Credits | 2.59% | 150 | - | 3.89 | 3.89 |
| Legendary Credits | 0.50% | 500 | - | 2.50 | 2.50 |
| Total | 100% | - | - | 75.14 | 21.65 |
| Total times 4 | - | - | - | 300.56 | 86.61 |
The data point at zero loot boxes opened from Alp's post is slightly higher than my estimate. This is because they used a slightly different drop distribution. The credits at 2000 loot boxes opened are lower than my estimate of 87. This is because more than 5% of the simulations do not have a complete set of items yet. I believe Blizzard has edited the drop rates to put the average credits given per loot box somewhere between these two extremes (34 and 87).
I will assume that Blizzard shifted the drop rates to give players 87 credits per loot box. This is the most extreme scenario. They most likely adjusted the drop rates to give players something between 34 and 87 credits.
When you got a single drop in the old system, the chances of it being a credit drop is just the sum of the credit drop frequencies which is 7.38%. This gives you 34 credits per loot box. In order to get 87 credits per loot box, the credit drop frequency must increase by a factor of 87/34 which is 2.56. Therefore, the fraction of drop frequencies should be 18.88%. Item drop rates would change from 92.62% to 81.12%. If the relative frequencies of the items and credit drops stay the same, the new drop probabilities can be calculated. The item drop rates would change by a factor of 81.12/92.62 (0.88). The assumed new rates are in the table below.
| Drop Type | Old Frequency | New Frequency | Value | New Weighted Value |
| Common Item | 58.81% | 51.51% | 25 | 12.88 |
| Rare Item | 27.08% | 23.72% | 75 | 17.79 |
| Epic Item | 4.76% | 4.17% | 250 | 10.425 |
| Legendary Item | 1.97% | 1.72% | 1000 | 17.2 |
| Rare Credits | 4.29% | 10.97% | 50 | 5.49 |
| Epic Credits | 2.59% | 6.63% | 150 | 9.95 |
| Legendary Credits | 0.50% | 1.28% | 500 | 6.4 |
| Total | 100% | 100% | - | 80.14 |
| Total times 4 | - | - | - | 320.56 |
The total value of the items and credits in the new loot boxes would be 320.56 credits. This is higher than the old value of 300.56 credits. If I assume not duplicates, then it is easy to calculate how many loot boxes it takes to get a complete set of items. It would just be the total cost of the items divided by the average credit value of one loot box.
As of March 29, 2018, a full set of items has a value of 484,550 credits. After subtracting away the event items, a full set of normal items costs 235,625 credits. This is higher than the credit cost in the tool (190,675) because there are four more heroes since the last update of the simulation tool as well as many new items added for existing heroes. Getting all of the normal items would take between \[235625/320.56 = 735\] and \[235625/300.56 = 783\] loot boxes.
Reducing the number of duplicates is very much in line with Blizzard's philosophy around Overwatch which was that any "un-fun" mechanic shouldn't be in the game. Things such as running out of ammo and doing damage to teammates were not included because they are considered not fun. High level players were complaining about loot boxes because they would get only duplicate items which was no fun! This change to reduce duplicates makes the loot boxes fun to open for the higher level players again. The more casual players can still use credits to buy specific items that they want.
Collecting icons no longer falls under the "coupon collector" category. Since you are unlikely to get any duplicates, the probability of getting an icon you are missing increases drastically.