Okay I've been playing with the Mandarin From Scratch blog post's ALG language acquisition equation, from a paper by Marvin Brown about ALG.
y = C(1-e^(-kx/L))
Below the cut, a bunch of me messing with the ALG equation and comparing it with Dreaming Spanish estimates to try and figure out WHAT is an accurate estimate of time it will take to learn a language with comprehensible input.
Y is understanding/fluency, which their goal is to get to 88%. I wanted to look at how many hours it would take me to reach 88%, then something over 90%, then something approaching my estimated "ceiling". Average ceilings were 95% - after which point students struggled to improve further. So I set mine as 0.95.
(Note: they say their goal for students is to reach 88% fluency/understanding, but I am not sure if that's B2, or lower, or higher. My goal is around upper intermediate/B2 so that's kind of fucking important for me to know... I want to be able to read, listen to audio, watch shows, and eventually have conversations about anything on my mind in at least a basic way - which would be B2 conversationally and possibly higher comprehension for passive skills)
C is the ceiling.
y is how much language they know (1 = native). If you have a ceiling, then y would never surpass the ceiling.
x is how many hours they have understood.
k is the acquisition constant: .0018
e is the natural logarithm base: 2.718
I plugged in a few potential amounts of hours I could study:
It looks like if I aim for 1500 hours, I'll hit 88% fluency. This seems a bit low for my goals, considering thats only 600 more hours from where I am. But it sure would be nice if that's all it took.
When I solved for x instead I got ~1448 hours.
If I aim for over 90% comprehension, then it looks like I'll hit that around 2000 hours.
If I solve for x, setting understanding y =0.90, then it would take ~1636 hours
And if I wanted to get as fluent as I possibly could? Which would be around 95%, assuming I have some ceiling like ab average learner, then 2600 hours will get me close to as much as I could hope to be fluent.
If I solve for x and set goal fluency y to 0.94, then it would take ~2530 hours.
This is significantly LESS TIME than FSI estimates - which would be 3520 hours of some form of Chinese study. I do have 1500 hours of prior study if we don't count comprehensible input. So 1500 hours prior study, plus the comprehemsible hours I currently have 913, would total to 2413 hours so far... so with FSI Estimate, I have to get ~1107 more hours of Chinese study (in some form) to reach B2/upper intermediate.
The ALG estimate assumes NO explicit study, and the Ceiling value in fact decreases with significant explicit study. So who fucking knows, maybe my true ceiling would be 88%. Or something.
I do find it interesting that ALG estimates it's going to take me 1448 hours to 2530 hours for "fluency" of 88% to 94%. I suppose wherever I stopped seeing progress, would indicate when I hit my true "ceiling."
These are both lower estimates than Dreaming Spanish gives. Dreaming Spanish predicts for English spealers they'll need 3000 hours of comprehensible input in Chinese to reach B2. Dreaming Spanish, like ALG, assumes the learner is only learning with comprehensible input and no explicit study. So I am curious why Dreaming Spanish's estimate is ~500 hours longer than ALG's.
And if 95% fluency is ONLY B2 that doesn't seem to make sense... Marvin Brown estimated his own fluency at 95% and guessed most people who explicitly study can never improve past 90% - so many C1 learners would be 90% at best, according to Brown. Brown taught Thai, so he had exceptionally good Thai, and he considered himself 95% fluent. So 95% being only B2 would seem... low.
B2 fluency I would consider like... 80-90% maximum. But 1500 hours for an English speaker learning Spanish is only going to get them to B2, based on all the results people have shared (C1 for English speakers learning Spanish through comprehensible input seems to take 2500 hours). And I imagine ALG's equation estimate would say less than 1500 hours for Spanish... hold on I'm going to plug in some more numbers.
Okay ALG estimates the L number, language similarity, to be 0.4 for European languages like English to Spanish. So plugging in the numbers for an English speaker with a average ceiling of 0.95 to achieve as high a fluency as they can (arouns 94%) would take: ~1011 hours
But we know, from all the progress updates people post on reddit.com/r/dreamingspanish, that at around 1000 hours most people are only a B1 level. Maybe B2 in comprehension, but not able to speak at a B2 level for another 500-800 hours (500 more hours of input, and 300 hours of some combination of reading and or speaking practice).
A blog post from ALG World may have answers for us. A Thai learner shared that he studied about 1150 hours at AUA Thai School, and his comprehension was good but he could barely speak, his grade for comprehension was 70% (this is for Thai not Spanish, and so 70% for 1000 hours is pretty average... Thai is expectee to take 1800 hours of comprehensible input to reach 88% comprehension of the language). He said after another 1.5 years living in Thailand, he finally felt he could speak about whatever he wanted, "My speaking ability followed along the same curve of development as my listening had, at a gap of about 800 or 900 hours." So lets give him a total of 1150+900=2050 hours to express himself however, with some writing practice with a tutor as part of those later 900 hours.
So perhaps it took him 2050 hours to reach B2 overall, including speaking skills, which is closer to what I might expect from Dreaming Spanish's results. However, this guy never mentions if his comprehension improved from 70% to something better/higher... and I have to guess 70% isn't B2 in passive comprehension yet. Since he had around 1000 hours as an English speaker learning Thai, and 1000 hours for English Speakers learning Spanish only gets them to B1....
Unless we make the guess that 1000 hours in Dreaming Spanish actually makes listening skills B2, and 1500 makes their listening skills higher than B2. So that assumption would mean 1000 hours of an English speaker learning Spanish through comprehensible input results in passive B2 skills, active A2-B1 skills.
But then... does Thai even take much longer? 1000 hours perhaps got that guy to B1 skills in listening, and A2 skills in speaking, and then his 900 hours later got him to B2 listening skills and B1+ speaking skills? Resulting in more hours needed for Thai, which is what we expect.
Perhaps, making a guess, if he had done 1800 hours as recommended by ALG to achieve 88% fluency, then 900 (or double so 1800 hours) continuing to engage with Thai in his life, so 2700-3600, he would achieve C1 listening skills and B2 speaking skills. Which is closer to what Dreaming Spanish predicts for English speakers learning a language like Thai or Chinese. And perhaps its where Pablo got the estimate of 3000 hours, double the roadmap. He learned Thai through ALG, and that influenced his estimates I'm sure.
I think the real answer is... the ALG formula probably underestimates, or it's percent fluency value needs more work. I think the formula needs to more clearly define what percent fluency values match up to A2, B1, B2, C1. But I know they're not going to care what I think lol ToT
For fun:
Lets calculate using the ALG formula, and Dreaming Spanish values, and figure out what percent fluency actually matches B1 and B2 and C1. Which in Dreaming Spanish is 1000 hours, 1500 hours, and 2500 hours, from users mentioning in progress updates the tests they could pass at different hours of comprensible input.
I'm going to set L to 1 just because it may help me get the percent fluency levels to something more realistic for B1, B2 and C1.
I feel like I'm reverse engineering whatever Pablo did to give his roadmap estimated hours.
Okay so for 1000 hours for Dreaming Spanish, we get a fluency percent of 79%. This seems like a value that might be realistic for B1. B1 is what a DS learner can pass after 1000 hours (although for some people their passive understanding is B2 and their speaking is A2)
For 1500 hours Dreaming Spanish, we get a fluency percent of 89%, which is somewhere in the 80s range, we know 1500-1800 hours for many Dreaming Spanish learners (if they read and speak a bit) is enough to pass a B2 test. (With some people's passive comprehension higher and closer to C1, and some people's speaking closer to B1)
For 2500 hours of Dreaming Spanish, we get a fluency percent of 94%. People pass C1 level around 2500-3000 hours into Spanish comprehensible input.
So for Spanish:
B1 is 1000 hours, is lets say 75-79% fluency
B2 is 1500 hours, is lets say 85-89% fluency
C1 is 2500 hours, is lets say 91-94% fluency
What would it be for a language unlike one you know already? Well fuck. I would need to start messing with the L number. I tried 3 instead of 1, and the hour estimates are way too high.
My guess is that if Pablo used this formula, he used L=2 for languages very unlike ones you know. Because L has to be 2 when I plug in the hour estimates on the roadmap doubled. (Which makes sense lol - double the time, double the L number)