<p>I'm a fan of games and activities with steep learning curves and high skill ceilings, and very precarious lines between success and failure. Such success may not be strictly linear or predictable (e.g. a significant difference in batting averages—0.300 vs 0.350—will not be immediately obvious from just a few at-bats; two chess players cannot have their ELO compared by just a couple game results), but one expects that one's &quot;skill&quot; or &quot;rate of success&quot; as a reified concept <em>is</em> <a href="https://en.wikipedia.org/wiki/Monotonic_function" rel="nofollow noreferrer">monotonically nondecreasing</a> with respect to time invested.</p>
<p>My question is about the exceptions to this intuition. <strong>What are factors that lead to such exceptions (either as a real phenomenon, or as an illusory perception)? Have any such hypotheses been experimentally tested in laboratory conditions?</strong></p>
<p>I can come up with a slew of hypotheses, but don't know to what degrees they've been confirmed as significant by research:</p>
<ol>
<li>Perception: Pareidolia/losing streak/reading into unfavorable random noise; pessimist's form of confirmation bias to deal with frustration;  failures are being overcounted.</li>
<li>Perception: Expectations which grow at a faster rate than can be accommodated by skill growth; failures are not being overcounted per se but the standards of success/failure are in flux.</li>
<li>Reality: Performance anxiety (cf. 2) and losing streak mentality (cf. 1) objectively impacting measured achievement.</li>
<li>Reality: &quot;Settling down&quot; into one known way of attempting a thing eliminates pathways for success present while in an earlier, more freeform stage of learning.</li>
<li>Reality: Changes in the body in response to learning (e.g. developing motor neural pathways) throw off the learner's performance temporarily as they adjust to their (hopefully better) bodily circuitry.</li>
<li>Reality: Other means of &quot;learning the wrong things&quot; whether that be muscle memory, fallacious strategy, etc.</li>
</ol>

CC BY-SA 4.0
2021-07-02T22:45:32.967Z
Reaction times decrease monotonically with age, which is likely to impact many skills that involve reaction times (I know this is a well-known phenomenon; I don't know whether the specific pathophysiology is known, but it does not seem like something that is avoidable but is rather part of normal aging). More generally "forgetting" is in well-studied and is missing from your list. One might expect people to plateau once their rate of forgetting equals their rate of learning, and decline if it exceeds the rate of learning.
Bryan Krause
CC BY-SA 4.0
2021-07-02T23:04:09.297Z
Indeed in this question I'm not interested in explanations otherwise attributable to an ailing body/mind. "Forgetting" is a good inclusion even for those in their prime, though I'm mostly interested in cases where rate of time investment is held constant (in which case I would expect a tapering off of a graph of "ability vs time invested" at the "learning = forgetting" asymptote).
Feryll
CC BY-SA 4.0
2021-07-02T23:35:47.643Z
The reaction time decreases are apparent even among younger vs older adolescents, so I wouldn't limit that aspect to "ailing" body/mind. Or at least I'd prefer to think I started ailing more recently than that :-D
Bryan Krause
CC BY-SA 4.0
2021-07-03T07:41:46.623Z
I would say changing your approach puts you back a couple of steps since it takes a while to reconcile it with your previous progress (at least when you use the new method). Perhaps there is a name for this in reinforcement learning somewhere but I don't know it.
Emil
CC BY-SA 4.0
2021-07-06T18:00:49.727Z
This reminds me of "[mount stupid](https://psychology.stackexchange.com/q/17825/7001)", and [similar](https://miro.medium.com/max/750/1*my25_TGuJsZEyzL5NBK-NA.png) learning curve memes, but I don't know of any supportive evidence for those.  However, this phenomenon is replicated in machine learning - see [saddle points](https://ai.stackexchange.com/q/18410) - in multi-dimensional learning curves.
Arnon Weinberg
<learning><measurement><bias>
Where and why would "skill" not increase monotonically with time invested?
Feryll
# Where and why would "skill" not increase monotonically with time invested?

(Asked by: username_0 on 2021-07-02)

I'm a fan of games and activities with steep learning curves and high skill ceilings, and very precarious lines between success and failure. Such success may not be strictly linear or predictable (e.g. a significant difference in batting averages—0.300 vs 0.350—will not be immediately obvious from just a few at-bats; two chess players cannot have their ELO compared by just a couple game results), but one expects that one's "skill" or "rate of success" as a reified concept *is* [monotonically nondecreasing](https://en.wikipedia.org/wiki/Monotonic_function) with respect to time invested.

My question is about the exceptions to this intuition. **What are factors that lead to such exceptions (either as a real phenomenon, or as an illusory perception)? Have any such hypotheses been experimentally tested in laboratory conditions?**

I can come up with a slew of hypotheses, but don't know to what degrees they've been confirmed as significant by research:

1. Perception: Pareidolia/losing streak/reading into unfavorable random noise; pessimist's form of confirmation bias to deal with frustration; failures are being overcounted.
2. Perception: Expectations which grow at a faster rate than can be accommodated by skill growth; failures are not being overcounted per se but the standards of success/failure are in flux.
3. Reality: Performance anxiety (cf. 2) and losing streak mentality (cf. 1) objectively impacting measured achievement.
4. Reality: "Settling down" into one known way of attempting a thing eliminates pathways for success present while in an earlier, more freeform stage of learning.
5. Reality: Changes in the body in response to learning (e.g. developing motor neural pathways) throw off the learner's performance temporarily as they adjust to their (hopefully better) bodily circuitry.
6. Reality: Other means of "learning the wrong things" whether that be muscle memory, fallacious strategy, etc.

**Tags:** learning, measurement, bias

> **Comments:**
> **username_1**: Reaction times decrease monotonically with age, which is likely to impact many skills that involve reaction times (I know this is a well-known phenomenon; I don't know whether the specific pathophysiology is known, but it does not seem like something that is avoidable but is rather part of normal aging). More generally "forgetting" is in well-studied and is missing from your list. One might expect people to plateau once their rate of forgetting equals their rate of learning, and decline if it exceeds the rate of learning.  
> **username_0**: Indeed in this question I'm not interested in explanations otherwise attributable to an ailing body/mind. "Forgetting" is a good inclusion even for those in their prime, though I'm mostly interested in cases where rate of time investment is held constant (in which case I would expect a tapering off of a graph of "ability vs time invested" at the "learning = forgetting" asymptote).  
> **username_1**: The reaction time decreases are apparent even among younger vs older adolescents, so I wouldn't limit that aspect to "ailing" body/mind. Or at least I'd prefer to think I started ailing more recently than that :-D  
> **username_2**: I would say changing your approach puts you back a couple of steps since it takes a while to reconcile it with your previous progress (at least when you use the new method). Perhaps there is a name for this in reinforcement learning somewhere but I don't know it.  
> **username_3**: This reminds me of "[mount stupid](https://psychology.stackexchange.com/q/17825/7001)", and [similar](https://miro.medium.com/max/750/1*my25_TGuJsZEyzL5NBK-NA.png) learning curve memes, but I don't know of any supportive evidence for those.  However, this phenomenon is replicated in machine learning - see [saddle points](https://ai.stackexchange.com/q/18410) - in multi-dimensional learning curves.  

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## 0 answers

