Pack of the Week Probabilities

I will be trying to make this a weekly thing. This took much longer than last week, so I will miss out some of the boring calculations.

TL;DR at the end

This post assumes that you are attempting to complete the objective by opening the free packs, as they are the best to open for this pack of the week.

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The Pack of the Week requires 2 English Premier League players, 1 German Bundesliga Card and 1 Italian Serie A card.

Let's look at German Bundesliga cards.

There are: 2 walkouts, 1 87, 2 86s, 1 85, 5 84s, 2 83s, 6 82s, 2 81s, 8 80s, 6 79s, 13 78s, 12 77s, 10 76s, 19 75s, 12 74s, 16 73s and 8 64s. There are also UCL cards, but as they have a drop rate of around 0.04 (You need to open 25 packs to get one) I have added them as small decimal numbers.

If you are wondering at this point how do you know the drop rate of UCLs, it is because I opened >250 packs and recorded the results (so I have calculated the drop rates of 85s, 84s, 83s all the way down to 64s, as well as specials, walkouts and UCLs.

Now, the way I am going to work out the probability of packing each and every card and add it together, to find the probability of packing a German Bundesliga Card.

Probability of packing 2 German Bundesliga walkouts= 1/Drop rate divided by (Cards we want/Total cards of that rating)

Therefore the probablity of packing 2 German Bundesliga 88s: 1/0.014 ÷ (2/17). You need to open 607 packs to get one of them. I am excluding high rated (86+ special cards) as their drop rate is below 0.001.

Therefore the probability of packing 1 German Bundesliga 87s 1/0.019 ÷ (1.04/17) Please Note: The 0.04 is added on to take into account UCL card drop rates. You need to open 860 packs to get one.

The probability of packing 2 German Bundesliga 86s 1/0.027 ÷ (2.1/18) You need to open 317 packs to get one.

The probability of packing 1 German Bundesliga 85s 1/0.048 ÷ (1.05/36) You need to open 714 packs.

The probability of packing 5 German Bundesliga 84s 1/0.0694 ÷ (5.25/49) You need to open 134 packs.

This continues for all ratings 83-73 and 64. I then did 1/607 + 1/860 + 1/317... and added up all the probabilities of getting a German Bundesliga player at each rating to get the total probability. This comes to 0.39, meaning you would have to open 2.56 packs to get a German Bundesliga player.

Now the method is relatively simple (but takes ages). Do the same for the other leagues and nations and multiply the decimal probabilities. However before the multiplication, note that the English probability needs to be halved as 2 English Pl players are needed.

Probability of packing an English PL player= 0.48

Probability of packing 2 English PL players = 0.24. However as 1 player in the pack must have already been a Bundesliga player, we multiply 0.24 by 8 ninths to get:

Probability of packing 2 English PL players=0.21

Probability of packing 1 Italian Serie A player= 0.36. However as 3 players in the pack are already German BuLi and English EPL, we do 6 ninths times 0.36 to get the true probability of 0.24.

Now to get to the final calculation.

To work out the probability of these all occuring together, we simply multiply them to get 0.39 x 0.21 x 0.24 to get 0.019

Therefore, the probability of getting the pack of the week is 0.019, which means you would have to open 51 free packs to get this weeks pack of the week.

This means that this is one of the easiest packs of the week yet. Compared to last week's POTW, this POTW is 7 times easier.

Interesting things I found while doing this: The amount of 75s and 74s in the game is exactly the same, at 499.

The drop rate of 80s is 0.09. The drop rate of 79s, however, is more than 10times this, at 1.03.

**TL;DR You would have to open 51 FREE packs to get the Pack of the Week on average.

German BuLi every 2.56 packs

2 English PL every 4.1 packs

1 Italy Serie A every 2.85 packs**

PS: I will try and make this a weekly thing.