نمودار رنگین‌کمان بیت‌کوین در مقابل مدل ذخیره به جریان: انحرافات S2F و قانون توان توضیح داده شد

به‌روزرسانی شده در آوریل ۲۰۲۶

نمودار استوک-تو-فلو، نمودار رنگین‌کمان و قانون توان بیت‌کوین: چرا مدل‌های قیمت‌گذاری مرتباً ناکام می‌مانند

مدل‌های قیمت‌گذاری بیت‌کوین برای بیش از یک دهه معامله‌گران و سرمایه‌گذاران را مجذوب خود کرده‌اند. این چارچوب‌های ریاضی قول می‌دهند که حرکات نوسانی قیمت بیت‌کوین را رمزگشایی کرده و قیمت‌های آینده را پیش‌بینی کنند. اما بارها و بارها، این مدل‌ها در مواجهه با واقعیت غیرقابل پیش‌بینی بیت‌کوین شکست می‌خورند.

عبارت «تمام مدل‌های شما نابود شده‌اند» به یک شعار در جامعه بیت‌کوین تبدیل شده است. مایکل سیلر این عبارت را رایج کرد در حالی که توضیح می‌داد چگونه رویدادهای غیرمنتظره می‌توانند حتی پیچیده‌ترین مدل‌های قیمت‌گذاری را از هم بپاشند. وقتی میلیاردرها ناگهان تصمیم می‌گیرند بیت‌کوین بخرند یا صرافی‌های بزرگی یک شبه فرو می‌ریزند، مدل‌های سنتی بی‌فایده می‌شوند. این الگوی شکست مدل‌ها آنقدر تکرار شده که بخشی از هویت بیت‌کوین شده است.

جستجو برای یک مدل قیمت‌گذاری قابل اعتماد بیت‌کوین بازتاب‌دهنده نیاز عمیق انسان به قطعیت در بازارهای نامطمئن است. سرمایه‌گذاران به دنبال چارچوب‌هایی هستند که به آنها بگویند چه زمانی خرید کنند، چه زمانی بفروشند، و قیمت‌ها به کجا می‌روند. اما تاریخچه بیت‌کوین نشان می‌دهد این مدل‌ها تا زمانی کار می‌کنند که کار نکنند. و وقتی شکست می‌خورند، اغلب به صورت چشمگیری شکست می‌خورند.

Bitcoin Stock-to-Flow Model: Deviations, Criticism and Controversy

The Stock-to-Flow model was the dominant Bitcoin pricing framework of the early 2020s. PlanB, an anonymous analyst, built it by borrowing from commodity valuation, comparing Bitcoin's existing supply to the new supply entering circulation through mining. The concept was clean. Bitcoin's supply grows more slowly after each halving, so scarcity increases, so price should follow.

The predictions were anything but modest. The basic S2F model called for $100,000 multiple times between 2021 and 2023. The Cross-Asset version pushed that to $288,000 by 2024. These weren't ballpark figures either. They came with charts, formulas, and historical data that looked, at least on the surface, convincing.

For a while, it seemed to work. Prices rose after halvings, roughly in line with what the model suggested, and PlanB's follower count grew accordingly. The four-year halving cycle formed the backbone of the whole theory. Cut the new supply in half, double the stock-to-flow ratio, prices go up. Simple enough that almost anyone could understand it.

Then came the deviations. The $100,000 floor that was supposed to hold by end of 2021 never appeared. Bitcoin traded around $47,000 instead. Then it crashed to $15,500 in 2022, more than 80% below what S2F projected for that period. PlanB acknowledged the gaps but attributed them to external factors rather than model failure, which struck many critics as convenient.

By 2025 and into 2026, the numbers had become almost surreal. The S2F average price projection for this period had risen to around $500,000. Bitcoin peaked at $126,000 in October 2025 and then corrected to the $65,000 to $75,000 range in early 2026. A model predicting $500,000 while the asset trades at $70,000 is no longer really a model. It's a wishlist.

The deeper criticism was always statistical. The model is auto-correlative, meaning the prediction line is shaped by the same historical prices it claims to be predicting. Both variables trend upward together over time, which creates the appearance of correlation without proving causation. Most serious analysts have quietly moved on and now treat S2F as a historical artifact rather than a live forecasting tool.

Bitcoin Rainbow Chart: How It Survived and Where It Stands Currently

The Rainbow Chart shouldn't have survived. It started as a meme, got broken by market conditions in 2022, and had to be rebuilt from scratch. Yet here it is today, still being used and still broadly relevant. That says something.

The origin story helps explain why. In 2014, a BitcoinTalk user called "Trolololo" posted a logarithmic regression model during one of Bitcoin's early bear markets. A Reddit user named "azop" took that framework and threw rainbow colors on it with joke labels. "Fire Sale" at the bottom. "Maximum Bubble Territory" at the top. It was designed to be funny as much as useful, and that self-awareness turned out to be its greatest strength.

Rohmeo at BlockchainCenter.net brought it into the modern era in 2019, turning it into a proper interactive tool. Eric Wall helped send it viral in 2020. By that point it had moved from forum curiosity to something people actually referenced when making investment decisions, which probably wasn't the original intention.

The crisis came in late 2022. Bitcoin fell below the lowest band for the first time in nearly a decade, which technically broke the model. But rather than defending a broken framework, Rohmeo simply updated it. Version 2 launched in November 2022 with recalibrated formulas, followed by another adjustment in 2023 to reflect a maturing market with lower volatility than earlier cycles.

That willingness to adapt is precisely what the S2F model lacked. Where PlanB defended his projections in the face of mounting evidence, the Rainbow Chart just changed. You can debate whether that makes it more honest or less rigorous. Probably both.

At the time of writing, the chart is in the green "BUY" to "Accumulate" bands following the correction from Bitcoin's October 2025 all-time high of $126,000. For context, that ATH touched the upper orange bands without ever breaching dark red "Maximum Bubble Territory," which V2's recalibration made harder to reach than the original model. The April 2026 band levels sit roughly as follows: Fire Sale around $56,000, BUY around $75,000, Accumulate around $97,000, Still Cheap around $126,000. Current price puts Bitcoin in early accumulation territory by the chart's logic.

How to Read and Use the Bitcoin Rainbow Chart

Understanding the Rainbow Chart requires grasping both its technical structure and practical limitations. The chart displays Bitcoin's price on a logarithmic scale, which means each vertical increment represents a multiplication rather than addition. This logarithmic view makes long-term trends clearer by preventing recent price movements from overwhelming historical data.

The rainbow bands themselves follow a mathematical formula based on regression analysis of historical prices. Each color band represents a different deviation from the logarithmic growth trend. The bands get their names from market sentiment rather than mathematical properties. Dark blue sits at the bottom, followed by light blue, green, yellow, orange, light red, and dark red at the top.

For a detailed breakdown of how the log bands work, see the Bitcoin Rainbow Chart guide.

Bitcoin Price Rainbow Chart (Image From Blockchaincenter)

Understanding Each Rainbow Band

Practical Application Strategies

The chart works best as a macro lens, not a trading signal. Most experienced users combine it with on-chain data like MVRV or SOPR rather than acting on band position alone. When multiple indicators align with the Rainbow Chart's reading, conviction is higher. When they diverge, it usually pays to be cautious.

Time horizon is everything here. The bands can look wildly different month to month. Someone using this for short-term trades will find it frustrating. For investors thinking in years, it offers a useful sanity check on whether they're buying near historical extremes.

Dollar-cost averaging pairs naturally with the Rainbow Chart. Increasing purchases in blue bands, pulling back in orange and red, is a systematic approach that takes emotion out of the equation. It doesn't require you to time anything perfectly.

The chart helps manage psychological biases. During euphoric bull markets, the red bands remind investors that extremes don't last. During depressing bear markets, blue bands suggest the worst may be near. This psychological anchoring proves valuable even if specific predictions fail.

Common Mistakes to Avoid

Treating the chart as a schedule is probably the most common mistake. Bitcoin can sit in one band for months or jump several bands in weeks. The colors indicate tendencies, not timelines.

Rigidity is the other one. Investors who refuse to buy above dark blue or sell below dark red end up missing most of the market. The chart is context, not a rulebook.

And always check which version you're looking at. The November 2022 recalibration shifted all the bands significantly. Old screenshots floating around online will give you completely wrong readings.

Bitcoin (BTC) Long Term Power Law Chart (Created by: @BitboBTC, Inspired by: @Glovann35084111)

Bitcoin Halving and the Rainbow Chart: How Each Cycle Shifts the Bands

Across the 2012, 2016, and 2020 halvings, the pattern was consistent. Bitcoin sat in the lower blue and green bands around the halving date, then climbed into yellow and orange over the following 12 to 18 months. It wasn't perfect every cycle but it was close enough that people built strategies around it.

The 2024 halving was different. Bitcoin entered the event already above $60,000, sitting in yellow territory rather than the classic accumulation zone. The market had priced in the halving well in advance, which reflects how much more institutional and anticipatory the participant base has become. You don't get the same slow build from the bottom when hedge funds and ETF buyers are already positioned.

Post-halving, Bitcoin still reached a new all-time high of $126,000 in October 2025, touching upper orange bands without breaching dark red. The 2026 correction pulled it back into green accumulation territory, which mirrors the mid-cycle dip pattern seen in previous cycles, though it's worth being careful about reading too much into a sample size of four halvings.

The April 2028 halving will drop the block reward to 1.5625 BTC. The Rainbow Chart's band levels for that period will sit meaningfully higher given the model's logarithmic growth assumption, though whether Bitcoin will actually trade anywhere near those levels depends on factors no chart can predict.

Bitcoin Power Law and Rainbow Chart: Is the Model Still Valid Now?

Giovanni Santostasi's Power Law model took a different approach to everything that came before it. Rather than tying price to supply metrics like S2F, he plotted the logarithm of Bitcoin's price against the logarithm of time. The resulting line was surprisingly straight, suggesting Bitcoin's growth follows a consistent mathematical pattern across its entire history.

The physics background helped with credibility. Power laws show up throughout nature, in earthquake magnitudes, city sizes, metabolic rates. Applying that framework to Bitcoin gave the model a scientific legitimacy that S2F's commodity comparisons lacked. And unlike S2F, the Power Law offered a range rather than specific price targets, which made it harder to definitively disprove.

Santostasi's original projection placed Bitcoin at approximately $210,000 by January 2026. The actual price was somewhere between $90,000 and $96,000, well below the model's projected fair value of $136,000 to $142,000. That's a significant miss. Critics pointed to everything the time-based model ignores: Fed rate decisions, the surprisingly flat 2025 that defied supercycle expectations, the $8 billion in ETF outflows that hammered price in early 2026.

Yet the Power Law hasn't technically broken. Its support floor sits near $45,000 to $48,000 and Bitcoin has stayed above it. Some analysts describe it as the last long-term model still standing, though they tend to use it for risk management floors now rather than price targets. The controversy deepened when Santostasi applied similar power law analysis to smaller altcoins, which alienated much of his Bitcoin-focused audience. If the same pattern fits random altcoins, what does it actually tell you about Bitcoin specifically?

Where the model goes from here depends largely on whether Bitcoin can close the gap with its projected fair value over the next 12 to 18 months. If it does, the Power Law gets rehabilitated. If it doesn't, it joins S2F in the graveyard of models that looked unbreakable until they weren't.

شخصیت‌های کلیدی پشت مدل‌های بیت‌کوین

چندین شخصیت شکل‌دهنده‌ی اوج و نزول مدل‌های قیمت‌گذاری بیت‌کوین بودند. داستان‌های آن‌ها نشان می‌دهد چگونه امید، غرور و شوخ‌طبعی در بازارهای ارزهای دیجیتال تلاقی می‌کنند.

مایکل سیلور کمتر سازنده مدل است و بیشتر نقاد مدل‌هاست. عبارت او «تمام مدل‌های شما نابود شدند» بهتر از اکثر مدل‌هایی که به آن‌ها اشاره داشت، جا افتاده است. نکته او همیشه این بوده که بیت‌کوین یک پدیده انسانی است و تصمیمات انسانی، آن‌هایی که غیرقابل پیش‌بینی‌اند، همیشه چارچوب‌های ریاضی را نقض خواهند کرد.

پلن بی محبوب‌ترین مدل بیت‌کوین دوران خود را ساخت و شاهد فروپاشی تدریجی آن بود. پیش‌بینی‌های S2F که میلیون‌ها دنبال‌کننده جذب کرد، اکنون منبعی از تحقیر مداوم است، زیرا مدل قیمت‌هایی پیش‌بینی می‌کرد که هیچ شباهتی به جایگاه واقعی بیت‌کوین در بازار ندارد. ناشناسی او دست‌کم او را از تمام هزینه‌های شخصی آن حفظ کرده است.

جیوانی سانتوستاسی دقت علمی واقعی را به این حوزه آورد. قانون توان او با دقت بیشتری نسبت به بسیاری ساخته شده بود. اما هدف 210,000 دلار در ژانویه 2026 که بیش از نصف کمتر شد و تصمیم به اعمال همان منطق به آلت‌کوین‌ها، اعتبار قابل توجهی را که نزد مخاطبانش به دست آورده بود، از دست داد.

رومئو به طور قابل بحث‌ترین شخصیت عملی در این داستان است. او چیزی ساخت، دید که شکست خورد، آن را تعمیر کرد و بدون بزرگ‌نمایی بیش از حد، به کار خود ادامه داد. نمودار رنگین‌کمان هنوز زنده است تا حد زیادی به خاطر این رویکرد است.

مت کراسبی از بیت‌کوین مگازین پرو نمایانگر جایی است که تحلیل جدی به آنجا منتقل شده است. داده‌های زنجیره‌ای به صورت زنده، چارچوب‌های چندمدلی، و شک منطقی نسبت به هر چیزی که وعده یقین بیش از حد می‌دهد.

نمودار S2F و نمودار رنگین‌کمان نمایانگر شرط‌های کاملاً متضادی درباره عواملی هستند که قیمت بیت‌کوین را تعیین می‌کنند.

S2F می‌گوید عرضه است. کمیابی متغیری است که اهمیت دارد، نصف‌شدن‌ها محرک هستند، و اگر آن‌ها را درست مدل‌سازی کنید می‌توانید قیمت را پیش‌بینی کنید. این یک نظریه پاک است که برای چند چرخه به اندازه کافی خوب کار کرد تا معتبر به نظر برسد. مشکل این است که تقاضا، تنظیمات قانونی، شرایط کلان اقتصادی و رفتار انسانی در هیچ جای این فرمول ظاهر نمی‌شود.

نمودار رنگین‌کمان ادعا نمی‌کند که چرا بیت‌کوین حرکت می‌کند را توضیح می‌دهد. فقط جایگاه قیمت را نسبت به مسیر تاریخی‌اش نقشه‌برداری می‌کند و برچسب‌های احساسی می‌چسباند تا به مردم کمک کند فکر کنند آیا بر اساس ترس یا شعف خرید می‌کنند. این کمتر یک مدل و بیشتر یک آینه است. به همین دلیل است که از همه چیز دیگر ماندگارتر بوده است، واقعاً نمی‌توان یک آینه را رد کرد.

مدل S2F روی زیبایی ریاضی شرط بست و وقتی واقعیت متفاوت بود، هزینه آن را پرداخت کرد. نمودار رنگین‌کمان روی فروتنی و سازگاری شرط بست و این استراتژی پایدارتر از آن درآمد.

رویکردهای مدرن به تحلیل بیت‌کوین