SOCIAL MEDIA & ALGORITHMS

How Does Instagram's Algorithm Actually Work? The Math Behind Skill vs. Luck

KnowStatistics Jan 28, 2026 14 min read
A stylized bell curve representing Swiftie spending distribution
Figure: Feature
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The discourse surrounding Instagram growth has historically oscillated between two polarising narratives: the fatalistic view that visibility is a function of stochastic probability ("luck"), and the deterministic view that it is the result of precise engineering ("skill")[cite: 4]. [cite_start]As the platform transitions into the 2025 era, this debate requires a rigorous, data-driven re-evaluation[cite: 5]. [cite_start]By synthesising engineering documentation from Meta and large-scale data studies, we posit that while "luck" exists as a manifestation of the algorithm's ExplorationExploration Phase: The part of an algorithm's process where it tests content with a small, random sample of users to gather performance data. phase, sustainable growth is a deterministic outcome of ExploitationExploitation Phase: The phase where the algorithm distributes content to a known, receptive audience based on previously gathered data to maximise engagement. strategies[cite: 7].

The Mathematics of 'Luck': Stochasticity & Exploration

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To understand the dichotomy between skill and luck, one must first deconstruct the architecture of Instagram's ranking engines[cite: 12]. [cite_start]Users often attribute unexpected viral success to luck, yet from an engineering perspective, this "luck" is the result of specific probabilistic functions designed to solve the Multi-Armed Bandit (MAB) problem[cite: 13, 24].

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The MAB is a classic probability theory dilemma where a system must decide between two competing actions to maximise total reward[cite: 25]:

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  1. Exploitation: Showing users content the system knows they will like (based on past history) to maximise immediate engagement[cite: 26].
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  3. Exploration: Showing users new, untested content to gather data and discover new interests, despite the risk of lower engagement[cite: 27].
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For a creator, "luck" occurs strictly during the Exploration phase[cite: 28]. [cite_start]Instagram's algorithm reserves a small percentage of a user's feed (e.g., 5-10%) to randomly suggest lesser-known items[cite: 29]. [cite_start]If a creator's content is randomly selected for this slot and succeeds due to sample variance, they experience a "viral hit"[cite: 30].

[cite_start]The "Law of Large Numbers" dictates that while individual posts may succeed or fail due to variance (luck), the aggregate growth of an account over months is the result of consistent signal quality (skill)[cite: 23].
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Skill, conversely, is the mastery of the Exploitation phase[cite: 32]. [cite_start]This involves creating content that hits specific "ranking signals" the algorithm prioritises[cite: 32]. [cite_start]When a creator consistently produces high-retention content, the algorithm no longer needs to "gamble" (explore) on them; it "exploits" their content by distributing it to a known, receptive audience[cite: 33, 34].

The Frequency Calculus: Why 10+ Posts Kill Your Reach

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A common misconception in the creator economy is that "more is always better"—a brute-force approach to growth[cite: 49]. [cite_start]However, data from 2025 reveals a complex curve of diminishing returns where volume can eventually degrade account authority[cite: 50].

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A comprehensive analysis of over 2 million posts confirms that the relationship between posting frequency and growth is logarithmic, not linear[cite: 52, 53].

The Diminishing Returns of Volume

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The data indicates that the "sweet spot" for sustainable growth is 3-5 posts per week[cite: 57].

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  • 1-2 Posts/Week: Baseline growth (+0.12%)[cite: 55].
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  • 3-5 Posts/Week: Optimal growth (+0.26%)[cite: 55]. [cite_start]This offers the highest efficiency jump (+0.14% gain)[cite: 58].
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  • 10+ Posts/Week: Diminishing returns (+0.66%)[cite: 55]. [cite_start]Doubling the effort yields only a marginal 0.22% increase[cite: 59].
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Crucially, high-frequency posting carries a "Spam Score" risk[cite: 66]. [cite_start]If a creator forces 10 posts a week but 5 are low-quality "filler," the algorithm observes a drop in the average engagement rate[cite: 64]. [cite_start]Since the algorithm uses past engagement history to predict future performance, a string of low-performing posts lowers the account's overall quality score[cite: 65].

The Viral Hangover: Reversion to the Mean

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A frequent phenomenon observed by creators is the sharp decline in engagement immediately following a viral success—often described as a "viral hangover" or "shadowban"[cite: 89]. [cite_start]This is not a punitive measure, but a statistical recalibration known as Reversion to the Mean[cite: 101].

The Mechanism of Decay

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When a Reel goes viral, it breaks out of "Connected Reach" (followers) into "Unconnected Reach" (cold audiences)[cite: 92].

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  1. Audience Expansion: The algorithm notes the viral video appealed to a broad demographic (e.g., general comedy)[cite: 95].
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  3. Testing the Next Post: The algorithm attempts to "exploit" this new audience for the next post[cite: 96].
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  5. Relevance Mismatch: If the next post is niche-specific (e.g., "Advanced SEO"), the broad audience ignores it, causing a massive drop in Click-Through Rate (CTR)[cite: 98, 99].
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The "decay" is simply the system returning the account to its baseline after a failed test of the expanded audience[cite: 102]. [cite_start]The strategic solution is "Bridge Content"—posts that connect the broad topic of the viral video to the specific niche of the creator, acting as a filter to convert the new audience gradually[cite: 123, 127].

The 2025 Ranking Formula

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The "skill" component is quantified by the ranking formula used by Instagram's engineers[cite: 37]. [cite_start]While proprietary, reverse-engineering suggests the algorithm predicts value using a weighted equation similar to the following[cite: 38]:

$$ Value = (W_{like} \cdot P_{like}) + (W_{comment} \cdot P_{comment}) + (W_{save} \cdot P_{save}) + (W_{share} \cdot P_{share}) - (W_{skip} \cdot P_{skip}) $$
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In 2025, the weights ($W$) have shifted dramatically[cite: 43]:

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  • Likes ($W_{like}$): Significantly lower weight for non-followers[cite: 43]. A "Like" is passive.
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  • Sends ($W_{share}$): Highest weight[cite: 43]. A "Send" is active distribution. [cite_start]It signals content valuable enough to interrupt a friend's day[cite: 176].
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Therefore, a creator focusing on "skill" optimises their content to maximise $P_{share}$ (Probability of Share) and $P_{save}$ (Probability of Save)[cite: 44]. [cite_start]This explains the rise of "Dark Social"—traffic that happens in DMs, which doesn't show in public metrics but drives high-intent distribution[cite: 177, 178].

Infographic: Visualising the Algorithm

The following charts visualise the data driving the "Skill vs. Luck" analysis. Observe the diminishing returns of high-frequency posting and the mathematical reality of the "Viral Hangover."

The Growth Calculus

Engineering Your Way to Virality

The Diminishing Returns of Frequency

Data from over 2 million posts shows that doubling your effort from 3-5 posts/week to 10+ yields minimal returns, while significantly increasing the risk of burnout and low-quality "spam" signals.

The "Viral Hangover"

Visualising "Reversion to the Mean." After a viral spike, engagement naturally crashes as the algorithm tests the new, broader audience with niche content.

The 2025 Ranking Weights

The algorithm has shifted from passive metrics (Likes) to active distribution metrics (Shares/Sends) to define value.

Optimal Frequency

3-5

Posts Per Week

The 3-Second Rule

65%

Success Determined in First 3s

Strategy vs. Luck

99%

Attributable to Skill

Conclusion: The 99% Strategy

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The comprehensive analysis of Instagram's growth mechanics in 2025 leads to a definitive conclusion: Instagram growth is a skill-based discipline disguised as a game of luck[cite: 226]. [cite_start]While luck (stochasticity) plays a role in the initial exploration phase and random sampling, skill (strategy) controls retention, categorisation, and conversion[cite: 227, 231].

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Creators who treat Instagram as a data science problem—optimising for 3-5 high-quality posts/week, maintaining strict niche consistency, and engineering content for shares—will achieve predictable, compounding growth[cite: 245]. [cite_start]As the adage suggests, "Luck is when preparation meets opportunity"[cite: 246]. [cite_start]On Instagram, preparation is the algorithmically optimised content; opportunity is the stochastic distribution[cite: 247].

References

Instagram Algorithm DataScience GrowthHacking
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