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A year ago, someone crunched pull income across the big gachas and called it "f2p friendliness." But that post had issues: free characters counted as limited, incomplete region data, and the assumption that more pulls equals a friendlier game.

And for obvious reasons, it's not. So instead of measuring "friendliness," I'd like to try measuring something more concrete.

Something I actually care about:

As a f2p, how many limited waifus can I actually walk away with at the end of a region?

*Disclaimer: All data is sourced from a single comparable region for each game, all spanning across 9 patches: Natlan (Genshin), Rinascita (WuWa), and Amphoreus (HSR). Data will be normalized to account for period differences.

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X.0: Calculating the Base Pulls

Total f2p pulls in a single region (9 patches)

Game	Total Pulls	Source
Genshin (Natlan)	722.03	u/sectoidfodder
WuWa (Rinascita)	1001.9	u/Aizen_Myo
HSR (Amphoreus)	969.4	u/arkkus

Average f2p pulls per patch:

Game	Total/9 (patches)
Genshin	80.2
WuWa	111.3
HSR	107.7

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X.1: Adjusting Character Pulls

WuWa is the only game among the three to give free pulls on weapon banners.

...but personally, I can't goon to weapons.

And the banner is separate. Over 2.x, f2p received 83 weapon pulls in total. That's 9.2 per patch.

Adjusted Character Pulls (WuWa Only)

Base Pulls	Weapon Pulls	Total Chara Pulls	Avg Chara Pulls/patch
1001.9	83	918.9	102.1

Adjusted Character Pulls

Game	Total Pulls	Avg Pulls/Patch
Genshin	722.03	80.2
WuWa	918.9	102.1
HSR	969.4	107.7

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X.2: Normalize to 365 Days

The involved regions all have different lengths. To make it fair, all totals are adjusted to a standard 365-day year.

Game	Chara Pulls	Days	Normalized*
Genshin	722.03	378	697.1
WuWa	918.9	357	939.5
HSR	969.4	394	898.0

*Normalized Pulls = Total Character Pulls × (365 ÷ Actual Days)

WuWa gets a slight boost (the shortest region). HSR takes a small hit (longest region). Genshin barely moves.

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X.3: Counting New Baddies

5-Stars released within the period.

Game	Released	Free/Non-Limited	Limited	Female
Genshin	11	1*	10	9
WuWa	15	-	15	13
HSR	17	2**	15	12

*Mizuki (free & non-limited)

**DHPT & Actually Satan (free)

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X.4: Main Calculations

To cut out probability and bias, I'm using hard pity only. Every 5-star is assumed to cost the maximum: 90 pulls for Genshin and HSR, 80 for WuWa. In the worst case, losing every 50/50 doubles that.
Think of it as measuring the floor, not the ceiling.

Best Case: Win Every 50/50

- All new limited characters:

Game	Max Pity	Guarantees*	Roster	% Coverage**
Genshin	90	7.75	10	77.5%
WuWa	80	11.74	15	78.3%
HSR	90	9.98	15	66.5%

*Guarantees = How many characters you can afford with your total income (Normalized Total Pulls ÷ Max Pity)
**% Coverage = Percentage of guarantees (Guarantees ÷ Roster) × 100

- Female characters only:

Game	Pity	Guarantees	Roster	% Coverage
Genshin	90	7.75	9	86.1%
WuWa	80	11.74	13	90.3%
HSR	90	9.98	12	83.2%

Worst Case: Lose Every 50/50 (No Safety Nets)

- All new limited characters:

Game	Pity	Guarantees	Roster	% Coverage
Genshin	180	3.87	10	38.7%
WuWa	160	5.87	15	39.1%
HSR	180	4.99 (lmao)	15	33.3%

- Female characters only:

Game	Pity	Guarantees	Roster	% Coverage
Genshin	180	3.87	9	43.0%
WuWa	160	5.87	13	45.2%
HSR	180	4.99	12	41.6%

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X.5: Enter Capturing Radiance

Now here's the catch. Genshin prevents you from losing more than three 50/50s in a row. Seeing that we are calculating 50/50 losses in the worst-case scenario, I'll assume CR triggers exactly on the third consecutive loss.*

Cycle: Lose (90) → Guarantee (90) → Lose (90) → Guarantee (90) → Lose → CR triggers (90)

That's 3 limited characters for 450 pulls. Meaning that in the worst-case scenario, it's 150 pulls per character. Down from 180.

*note that Capturing Radiance (CR) increases the probability of winning the 50/50 after each consecutive loss. It can trigger as early as the second loss. Consider this a slight handicap against Genshin.

Worst Case With Capturing Radiance (Genshin Only)

- All new limited characters:

Game	Cost/Char	Guarantees	Roster	% Coverage
Genshin (CR)	150	4.65	10	46.5%
WuWa	160	5.87	15	39.1%
HSR	180	4.99	15	33.3%

- Female characters only:

Game	Cost/Char	Guarantees	Roster	% Coverage
Genshin (CR)	150	4.65	9	51.6%
WuWa	160	5.87	13	45.2%
HSR	180	4.99	12	41.6%

This part answers my initial question: As a f2p, how many limited waifus can I actually walk away with at the end of a region? Shown by the number of guarantees.

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X.6: Adding Up and Rounding Down

Well, the waifu math is done. Now I want to look at the bigger picture.

These three games aren't strictly limited to new 5-star characters. Some things don't touch your pull income but still pad your roster. Like free event 4-star and 5-star selectors.

The problem is, ignoring them undercounts what a f2p account actually walks away with.

Again, this is about the bigger picture. This part isn't trying to crown the most "f2p friendly" game (as that old post did).

Anyway. Since luck is off the table, you "technically" can't pull 0.99 of a character. Everything rounds down.*

*note that rounding up is just as valid. If you started HSR at 3.0, beginner rewards push you past 4.99 anyway. I just like the sound of "up and down" better. It's either +1 or -1.

Best Case: Win Every 50/50

Game	Guarantees	Free Limited Chara	Free Non-Limited Chara	Total Chara
Genshin	7	-	+4**	11
WuWa	11	-	-	11
HSR	9	+2*	+2***	13

Worst Case: Lose Every 50/50

Game	Guarantees	Free Limited Chara	Free Non-Limited Chara	Total Chara
Genshin	4	-	+4**	8
WuWa	5	-	-	5
HSR	4	+2*	+2***	8

* DHPT & Actually Satan
** Free Anniversary 5*, Kachina (5.0), Lan Yan (5.3), Ororon (5.5)
*** 2 Golden Companion Spirit

4-stars that weren't released within the region will be excluded from the count (e.g., Candace, Sethos).

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X.7: Summary

-All pullable characters:

Game	Limited	Worst-case	Best-case	Median*	# of Free Character
Genshin	10	46.5%	77.5%	62.0%	4
WuWa	15	39.1%	78.3%	58.7%	0
HSR	15	33.3%	66.5%	49.9%	4

- Female characters only:

Game	Released	Worst-case	Best-case	Median*	# of Free Character
Genshin	9	51.6%	86.1%	68.85%	4
WuWa	13	45.2%	90.3%	67.75%	0
HSR	12	41.6%	83.2%	62.4%	4

*The median is an interesting piece of data to have. Though I'm not quite sure if it's a good representation of the middle ground in Gachas.
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X.8: Insights

I'm genuinely surprised how neutral this turned out to be. Three games, three different models. Each has a clear strength. Each has a clear weakness (depending on what you value). It is actually the exact opposite of the aforementioned post from last year.

- Genshin is somehow the safest pick. 

If your luck is garbage, Genshin is the only game that keeps you above water. 46.5% coverage for all characters, 51.6% for waifu only. Both the highest worst-case numbers among the three. Most surprisingly, it is also on par with WuWa in the best case scenario. With 77.5%/78.3% coverage, and 11/11 total character)

Really surprising, given all the doomposting around it.

- WuWa is the best pick for waifu collectors. 

Despite having the shortest region, WuWa gave the most amount of pulls. Best pull efficiency per day of the three, and it has the largest female roster (13), with 90.3% coverage in the best-case scenario (holy sheet). It is also the only game that gives away weapon pulls, which, in the worst-case scenario, can guarantee you a free signature weapon.

But it is also the only game without free characters. Not even a free 4-star.

- HSR is the 5-star machine. 

13 total characters in best case, 8 in worst. Two free limited 5-star, two standard selectors. No other game puts more gold borders in your account. The catch? It also releases the most characters, so percentage-wise, you're always behind. But in raw numbers, HSR simply gives you more 5-stars than anyone else.

Fun fact: over its lifetime, HSR has given out more free 5-stars than Genshin and WuWa combined. Even if you count the free constellations Genshin handed out.

Closing

Speaking of free constellations, there are plenty of things I couldn't account for here. Soft pity, signature weapon reliance, cashback system, and a few other variables I found too tricky to include without introducing bias. If someone finds a way to factor them in fairly, let me know. I hope this post was informative regardless.

Though, there's one thing I noticed while making this: every model has a "catch."

Recently, we've been seeing new games experiment with different gacha models. Such as Endfield with its permanent units, and NTE with a 100% pull rate.
So I'd like to take the chance to ask YOU, gacha veterans, some questions:

- What do you think will be the catch for the new gachas?
- Which model do you think is healthiest in the long run?
- Does a gacha really need four stars?
- Can you goon to weapons?

And finally, how good was Honkai Impact 3rd?

Because in the process of making this, I came across the Da Capo animation, and it brought me to fkn tears. Like, what? I only know half these girls from HSR. Why am I crying? Where does this emotion come from?

It doesn't make sense.
Cover art by Adven Samson. Thank you for letting me use your work.