Bluetracker

Tracks Blizzard employees across various accounts.

Expedition Rewards and expected value

Preamble

I'll continue to update this post once I get some data from the rewards, meanwhile I can only talk about what we know as facts right now. If you'd like to contribute, I need data on two things: what you recieve on each run (type of chest and shard amount), and the content of the chest that you opened.

Did I make a mistake? Was my math wrong? I only checked by putting all the tables and checking that everything amounts to 100% so I may have made a mistake that fitted completely right and wouldn't realize it. If you catch anything wrong with it, be sure to let me know so I can fix it.

General Notes

• Expeditions cost 400 coins, 4000 shards or 1 token.
• Once you start an expedition, you're allowed two draft runs, called Trials ingame. The rewards will only be from the highest run of the two.
• You can only do rewards run three times each week. Once finished, you can do as many drafts as you want, but they will be phantom drafts (no rewards).
• If you don't have enough shards, tokens or coins to finish all 3 expeditions, you won't be able to continue playing by doing phantom drafts. You're forced to either cough up for coins or farm a little constructed for the shards you're missing. This has been acknowledged as a potential issue by Riot and may change by the time the game is released.
• To "lose" an expedition, you must either lose 2 games in a row (0-5 wins) or lose once if you already have 6 wins.

Distribution of Trials by Wins

This is assuming draws are considered as neither a win or a loss, with your record intact.

• 0 wins run: 0-2, since you have a 50/50 of winning/losing and you need two losses in a row, you get 50%^2, which is a 25%.
• 1 win run: Since you need to pass the first win, of whom 75% of the field will do, then you require the 0-2, which will be 18.75% of the runs.
• 2 wins run: 56.25% of the field will go 2 wins, and of these people, only 25% will be stuck here, or 14.06% of all attempts.
• 3 wins run: Only 42.18% will pass here, and 10.54% of all runs will not get through.
• 4 wins run: With only 31.64% people still here, 7.91% are going straight to Thresh's Lantern.
• 5 wins run: 23.73% will make it this far, but 5.93% won't take a single extra step.
• 6 wins run: The final Showdown. 17.79% of the runs end here, and with a single elimination, this means that half of them, or 8.89% will only have a second place medal, or first loser.
• 7 wins run: A winner is you, only 8.89% of players will go for broke.

Now, with the 2 losses and you're out rule and recovery from a single loss at each step, the distribution for the game (25%, 18.8%, 14.1%, 10.5%, 7.9%, 5.9%, 8.9%, 8.9%) isn't that different than, for example, Magic Arena's (12.5%, 18.8%, 18.8%, 15.6%, 11.7%, 8.2%, 5.5%, 9.0%). It's still tilted towards greater rewards. But this is only for a single trial.

Adjusting for two trials, one reward

Since we now know the variables of wins for each trial, we can also determine how many times you will get each reward, taking into account that you must do two different trials.

The formula for this is: P1T*Sum(P2T<=) + P2T*Sum(P1T<). Yes I know I could use better notation but it's plain text.

• 0 wins: 6.25%
• 1 win: 12.89%
• 2 wins: 14.28%
• 3 wins: 13.31%
• 4 wins: 11.44%
• 5 wins: 9.40%
• 6 wins: 15.42%
• 7 wins: 17.01%

As you can see, the top side of the rewards is heavily increased, with the brunt of the percentage taken out of 0 wins.

Now, if you want a side by side comparison between single trials and double trials.

Single	Doubles
25%	6.25%
18.75%	12.89%
14.06%	14.28%
10.54%	13.31%
7.91%	11.44%
5.93%	9.4%
8.89%	15.42%
8.89%	17.01%

Rewards

• 0 wins reward: One champion card.
• 1 win reward:
• 2 wins reward:
• 3 wins reward:
• 4 wins reward:
• 5 wins reward: One Gold Chest, One Champion card, 800 shards.
• 6 wins reward:
• 7 wins reward: Champion Capsule, 4000 shards.

Now, for the contents of the chests:

• Bronze Chest: 2 Cards and ~100 Shards.
• Silver Chest: 3 commons, 2 rares and ~500 shards.
• Gold Chest:
• Champion Capsule: Champion Card, an epic card and 3 rare cards.

With the chest rewards being upgradable to become X rarity wildcard instead of X rarity card.

Technically, you never "lose" by going expedition, as one Champion card costs 4000 shards, the same as an expedition, but you also get a random card instead of something you'd actually want for constructed.

I also have no idea on duplicate protection, but I expect champion cards to be able to appear as duplicates for 25% of their cost, for expedition only players they'll always want to end up with a fourth copy, as that's an extra reward to recoup costs.

Expected Rewards by wins

This section is somewhat blank right now, as I first need to know the rewards data.

0 wins: With a champion that you'd actually want, it's free. If it's a champion that's only a fourth duplicate, then you lost 3000k (I'm unsure if le champion gives you 1000 shards).

---

---

---

5 wins: With a gold chest (worth being ~) and 800 shards, you're getting ~1800 shards in price. If it's a champion you want, it's worth 5800, while if it isn't, you're getting only 2800 back.

7 wins: Since it straight up gives you 4000 shards, you can only win. With a champion for free, an epic and 3 rares as an extra. Total reward: 225+(4th copy epic)+4000=4225+ to almost 9000 depending on the cards being rewarded.

Adjusting for your winrate

Now, you're thinking: Well, he's only refering to players that are on a 50% winrate, but I'm really good and why isn't this taking into account that I win 60% of my matches.

Well, you're in luck. Here's a table with the wins in your runs taking into account 25-75% winrate, with 5% steps.

Single Trials:

Wins	25%WR	30%	35%	40%	45%	50%	55%	60%	65%	70%	75%
0	56,25%	49,00%	42,25%	36,00%	30,25%	25,00%	20,25%	16,00%	12,25%	9,00%	6,25%
1	24,61%	24,99%	24,40%	23,04%	21,10%	18,75%	16,15%	13,44%	10,75%	8,19%	5,86%
2	10,77%	12,74%	14,09%	14,75%	14,72%	14,06%	12,88%	11,29%	9,43%	7,45%	5,49%
3	4,71%	6,50%	8,14%	9,44%	10,26%	10,55%	10,27%	9,48%	8,28%	6,78%	5,15%
4	2,06%	3,31%	4,70%	6,04%	7,16%	7,91%	8,19%	7,97%	7,26%	6,17%	4,83%
5	0,90%	1,69%	2,71%	3,87%	4,99%	5,93%	6,53%	6,69%	6,37%	5,62%	4,53%
6	0,53%	1,23%	2,41%	4,12%	6,33%	8,90%	11,58%	14,05%	15,98%	17,04%	16,97%
7	0,18%	0,53%	1,30%	2,75%	5,18%	8,90%	14,15%	21,08%	29,68%	39,75%	50,92%

With double trials, what is the expected reward?

Compuesto	25%WR	30%	35%	40%	45%	50%	55%	60%	65%	70%	75%
0	31,64%	24,01%	17,85%	12,96%	9,15%	6,25%	4,10%	2,56%	1,50%	0,81%	0,39%
1	33,74%	30,74%	26,57%	21,90%	17,22%	12,89%	9,15%	6,11%	3,79%	2,14%	1,08%
2	18,57%	20,48%	20,77%	19,59%	17,28%	14,28%	11,03%	7,92%	5,23%	3,12%	1,63%
3	8,85%	11,70%	13,80%	14,82%	14,62%	13,31%	11,18%	8,62%	6,05%	3,80%	2,08%
4	4,01%	6,29%	8,57%	10,42%	11,44%	11,44%	10,43%	8,63%	6,44%	4,26%	2,43%
5	1,78%	3,29%	5,15%	7,05%	8,59%	9,40%	9,28%	8,23%	6,52%	4,54%	2,70%
6	1,05%	2,44%	4,70%	7,85%	11,61%	15,42%	18,54%	20,21%	19,92%	17,63%	13,78%
7	0,35%	1,05%	2,58%	5,42%	10,10%	17,01%	26,30%	37,71%	50,54%	63,70%	75,91%

Expected Value, adjusted by winrate

Just like the standard rewards, I'll only update this once I get the whole rewards data.

---

---

---

---

Tweet