How predictions work — The Daily Coins

Every coin profile on The Daily Coins shows a 24-hour, 7-day, 30-day, 3-month, 6-month, 1-year, and multi-year price forecast. Those numbers do not come from an analyst typing into a spreadsheet. They come from a quantitative model that runs the moment you load the page. This guide is the long version of how that model works, what its inputs are, where it does well, and where it breaks. It is written for a smart non-quant — you do not need a stats background to follow along.

Why we publish predictions at all

The crypto press is full of two extremes. On one end, breathless “Bitcoin to $1 million by Christmas” takes from accounts whose careers depend on the next bull market arriving. On the other end, hedged academic commentary that refuses to commit to anything quantitative. Both are unsatisfying. Readers actually want a number — a defensible, calibrated, falsifiable number — so they can compare it to their own thinking.

That is the gap we try to fill. Our predictions are not advice; they are an output of a transparent model that anyone can replicate. The point is not that the number is right (it usually will not be exactly right). The point is that it is honest, the methodology is published, and we log every prediction we make so the track record is auditable. If the model is consistently wrong in a direction, we can see it and adjust. If it is consistently right, that should show up in the scoreboard.

Publishing predictions is also a forcing function for clear thinking. Saying “BTC looks bullish” is easy. Committing to “the model says the base case for BTC over 30 days is $84,200 with a bull case at $91,800 and a bear case at $76,500” forces you to specify what you mean. If you turn out wrong, you cannot retroactively claim you really meant the opposite.

The four inputs

The model takes four things off the shelf for every coin. Nothing fancy, nothing scraped from sentiment-mining APIs, nothing requiring proprietary data. All of these are publicly available and easy to verify.

1. Recent log returns. Over 1-day, 7-day, 30-day, and 1-year windows. We use log returns rather than simple percentages because log returns are additive across time — the 7-day log return is the sum of the daily log returns. That makes the math much cleaner when projecting multiple steps forward.

Concretely, if a coin opened at $100 and closed at $110, the log return is ln(110/100) = 0.0953. Over multiple days, daily log returns can be averaged without distortion. Over multiple coins, log returns are directly comparable. Almost every published quantitative finance paper that involves prices uses log returns; we follow the convention.

2. Realised volatility. Standard deviation of returns from the 7-day hourly price series. This is the engine of the bear/bull bands — the wider the recent swings, the wider the bands. We use hourly data rather than daily so that we have 168 data points across the window, which gives a stable σ estimate. Daily data with only 7 observations is noisy.

We annualise σ for display in our internal logs but use the raw daily figure for projection. The key property is that σ scales with the square root of time: 7-day σ is roughly √7 times the 1-day σ, assuming the daily volatility is constant. We do not assume that, but the scaling is the starting point.

3. Sentiment. The daily alternative.me Fear & Greed Index. A composite from 0 to 100 that combines momentum, volatility, dominance, volume, and Google trends. We use the index as a small adjustment factor on drift — extreme fear shifts drift slightly upward (contrarian), extreme greed shifts it slightly downward. The weight on sentiment is deliberately small (5%) because Fear & Greed has only modest predictive power on its own and we do not want a single noisy indicator to dominate.

4. Mean reversion. The 7-day moving average. Coins that have ripped well above their average get a small pull-back force; coins that have crashed well below get a small lift. This is the part of the model that prevents short-term momentum from running away with the result. Without it, a coin that just doubled in three days would be projected to keep doubling. With it, the model says “some of that move is probably going to revert”.

Why GBM and not deep learning

The biggest decision in building a price model is what shape it should take. We use geometric Brownian motion (GBM) deliberately. The alternative — neural networks, gradient-boosted trees, large language models making predictions — sounds more sophisticated and is what readers often expect in 2026. Here is why we do not use them.

Interpretability. When the GBM model says BTC’s base case is $84,200 in 30 days, we can show you exactly which inputs produced that number and how much each weighed. There are five parameters, all documented, all auditable. A neural network trained on five years of OHLC data is a black box. If it predicts something wrong, you cannot meaningfully debug it.

Calibration over accuracy. A good probabilistic model is calibrated — when it says “15% chance of a drop below this level”, that should be roughly the realised frequency. Deep learning models tend to be confidently wrong in specific regimes; they overfit to whatever distribution generated their training data. GBM with realistic volatility is honest about uncertainty. The bands are wide because crypto is volatile, not because the model is hedging.

Sample size. Bitcoin has 16 years of price history. Some altcoins have 2 to 3 years. Modern deep learning needs millions of training samples to converge. With hundreds of daily price points, you can fit a neural network — but you will be fitting noise and calling it signal. Simple parametric models work better with limited data.

Honesty about what models can do. A model is good at framing a range under stable conditions. It is not good at predicting black swan events. Pretending otherwise is the central lie of most crypto prediction services. We would rather show you a wide band that captures realised volatility than a tight point estimate that turns out to be wrong by 50%.

Drift estimation: weights and rationale

Drift is the daily expected log return — the centre of the projection cone. We compute it as a weighted blend of normalised inputs:

Short-term momentum (1 to 7 day log returns), weight 25%. Recent momentum has real predictive power on horizons of days to a couple of weeks. The weight is high enough to matter but not so high that a single bad day swamps the estimate.
Medium-term momentum (7 to 30 day log returns), weight 30%. This is the largest single weight because it is the most stable signal. Trends measured over a month tend to be more meaningful than trends measured over a week.
Long-term momentum (30-day to 1-year log returns), weight 10%. Catches the broader regime — bull market versus bear market. Lower weight because over a year, all kinds of noise gets averaged in.
Sentiment overlay, weight 5%. The Fear & Greed nudge. Deliberately small.
Mean reversion to 7-day MA, weight 30%. The damping force that prevents momentum from running away with the result. Equal in weight to medium-term momentum.

These weights total 100% and are stable across coins. They are not optimised per-coin (which would massively overfit). They are not adjusted by hand. We set them once based on backtests across the top 50 coins and have not touched them. The full weight specification is on the methodology page.

The blended drift is then clamped to a sane daily range so no single input can produce an absurd projection. A daily drift of 0.5 (+65% per day, compounded) is mechanically possible if you do not clamp; it is meaningless as an estimate. Clamping is conservative — it costs us a bit of upside when a coin is genuinely on a tear, but it prevents wild outputs in edge cases.

Volatility estimation: rolling stdev of log returns

Volatility is the rolling standard deviation of hourly log returns over the trailing 7-day window. 168 data points, one σ. We use hourly because daily data with 7 observations is too noisy, and minute-by-minute data picks up microstructure that does not generalise.

One subtle point: realised volatility itself is volatile. A single sharp move within the 7-day window can spike σ enough to widen the bands meaningfully. We accept this. The alternative — exponentially weighted volatility, GARCH-style adaptive models — is more sophisticated but harder to explain and prone to its own failure modes. The simple rolling estimate has the advantage of being completely transparent.

We do not impose a volatility floor or ceiling. If a coin’s realised σ is genuinely tiny, the bands are tight. If it is genuinely huge, the bands are wide. That is the right answer; we should not pretend a stablecoin is volatile or that a meme coin is stable.

Sentiment overlay: alternative.me F&G

The Fear & Greed index runs from 0 (extreme fear) to 100 (extreme greed). We normalise it to a value between -1 and +1 by mapping 50 to 0 and the endpoints to the bounds. We then apply that as a small multiplier on the drift estimate, with opposite sign — high greed slightly lowers drift, high fear slightly raises it.

This is a contrarian application of the index, and it is by far the smallest weight in the model. The empirical basis is straightforward: extreme greed has historically been a poor moment to buy more, and extreme fear has historically been a poor moment to sell. The effect is modest, so the weight is modest. We do not pretend Fear & Greed is more powerful than it is.

One important caveat: the index is itself a derivative measure that already includes momentum and volatility. There is a small risk of double-counting. We have tested for this and the correlation between the F&G overlay and the other inputs is low enough that it adds information rather than redundancy. If that ever changes, we will revisit.

Mean reversion: when it matters and when it does not

The mean reversion component compares current price to the 7-day moving average. If price is far above the average, the input pulls drift downward. If price is far below, the input pulls drift upward. The pull is proportional to the gap.

Mean reversion is a powerful signal on short horizons and a weak signal on long ones. Over days, prices tend to revert. Over months and years, trends tend to compound. We weight it at 30% because the prediction horizons we publish are heavily weighted toward short and medium terms. For the 1-year and 5-year horizons, the projection is dominated by drift compounded over time rather than the initial reversion impulse — which is correct.

The mean reversion input is also the safety valve that keeps the model from believing its own short-term momentum too much. A coin that pumps 40% in three days will show very high momentum on the 7-day window. Without reversion, the model would project a continued rocket ride. With reversion, the projection backs off — recognising that pumps usually have pullbacks.

Projection: geometric Brownian motion

Once we have a daily drift (call it μ) and a daily volatility (σ), projecting t days into the future is standard GBM. The three cases we publish are:

Base case = current price × exp((μ − σ²/2) × t)
Bear case = base × exp(−1.5 × σ × √t)
Bull case = base × exp(+1.5 × σ × √t)

The −σ²/2 term inside the base case is the Ito drift adjustment for log-normal processes. Without it, the median price and the mean price diverge over long horizons — the mean gets dragged upward by the asymmetry of compounding. The correction puts the base case at the median, which is what readers actually want when they see a “base case” estimate.

The √t scaling on the bands is critical. Volatility does not scale linearly with time — it scales with the square root of time. So a 30-day band is √30 ≈ 5.5 times wider than a 1-day band, not 30 times wider. This is why the bands fan out over longer horizons.

The ±1.5σ bands

We publish bear and bull cases at ±1.5 standard deviations. Under a strict normal distribution assumption, ±1.5σ bands contain about 87% of outcomes. Crypto returns are not strictly normal — they have fat tails, especially on the downside. In practice, our bands contain roughly 80% to 85% of realised outcomes when measured against major-cap coins.

We deliberately do not call the bands a 90% confidence interval or a 95% credible region. Those are language used in formal probability, and they imply guarantees that any model with non-stationary inputs cannot honestly provide. The bands are a range we expect the price to fall within most of the time, and we report the realised coverage as part of the accuracy scoreboard.

Why 1.5 and not 1.0 or 2.0? It is a compromise. Tighter bands (1.0σ) miss too many outcomes — only about 68% coverage under normal, even less with fat tails. Wider bands (2.0σ) capture more but become so wide on long horizons that they stop telling you anything useful. 1.5σ is the sweet spot we landed on after backtesting.

Horizon clamps: why the model has guard rails

Crypto can do 100x in a year, in theory. Some coins have. In practice that almost never happens for major caps over short windows, and the projection cone can grow absurdly fast when σ is high. We cap each horizon at a reasonable multiple of current price:

1.5× over 7 days
2.5× over 30 days
4× over 90 days
8× over 1 year
30× over 5 years

The clamps only kick in for very volatile micro-caps where σ is unstable. For the top 50 coins, the natural projections almost never hit the clamp. When the clamp does fire, we log it — it is a signal that the underlying volatility estimate is in noisy territory and the projection should be taken with extra salt.

What we measure

We log every prediction at the moment it is generated, with a unique ID, a timestamp, the input values, and the projected outputs. After 30 days, the actual realised price gets paired against the prediction. We track three things:

Directional accuracy. Percentage of predictions where the realised price moved in the direction implied by the base case. A coin flip would get 50%; we aim for materially above that.
Mean absolute error (MAE). Average of |predicted − realised| / realised across all predictions. Lower is better. We track this per coin and per horizon — short horizons should have lower MAE than long ones.
Band coverage. Percentage of realised outcomes that fell within the bear/bull bands. The target is around 85% — too high means the bands are too wide; too low means they are too tight.

All three are necessary. A model can have great directional accuracy and terrible MAE (always says “up”, often by way too much). Or great MAE and terrible coverage (point estimates fine, but the bands miss too many outcomes). Or good coverage with the band so wide it is useless. We monitor the trio.

The accuracy log

The methodology page publishes a live scoreboard once 30 days of paired predictions and outcomes accumulate. Until then, the section explains what is being tracked and shows the data structure being collected. We are deliberately not publishing a partial scoreboard — small samples produce misleading numbers, and we would rather wait than publish noise.

Once the scoreboard goes live, it will show directional accuracy, MAE, and band coverage per coin and per horizon. We do not promise specific numbers because we cannot — the realised performance will be whatever it is. The promise is transparency. Anyone can check whether the model is doing what we claim it does.

Where the model fails

The model is good at framing a range under stable conditions. Here is where it is not good:

Regime shifts. If we go from a low-volatility chop into a high-volatility trending market overnight, the σ estimate based on the previous week underprices the new reality. Bands will be too tight until the new volatility seeps into the rolling window. This is a known limitation we accept rather than try to fix with adaptive volatility models.

Regulatory shocks. A single SEC announcement, ETF approval, or country-level ban can move price 10 to 20% in hours. None of that is in the model’s inputs. When you see a big realised move that landed outside the bands, this is usually why.

Exchange events. The FTX collapse in November 2022 cratered markets in days. The Mt. Gox restitution announcement in 2024 was a sustained overhang. The model has no knowledge of these and will be wrong through them.

Low-liquidity coins. For coins outside the top 100, the price feed itself is noisy. A whale moving size on a thin order book produces hourly prints that are not representative. Volatility gets overstated and projections widen accordingly. We default to wider bands for these, but the model is structurally less reliable below the top 50.

Correlation breakdowns. Most of the time, altcoins follow Bitcoin. When that correlation breaks (rare but it happens — see SOL outperformance in late 2023), the model treats it as noise rather than signal. It will eventually adapt as the new returns flow into the rolling window, but there will be a lag.

How to use predictions responsibly

The model is one input among many. Here is how we use it ourselves and how we suggest readers use it:

1. Use it as a sanity check, not a target. If a coin is trading at $10 and the base case for next month is $11, that is not a buy signal. It is information about what the model considers a normal expected move. The bands tell you what a normal range looks like. If you have an independent thesis that says $25, the model’s base case is the right level to ask “why does my thesis disagree with this?”

2. Watch the bands, not the centre. The base case is one point on a distribution. The bull and bear cases give you the realistic range. Most readers obsess about the base; the experienced ones spend more time on the bands.

3. Size accordingly. If the bear case is −30% and you would not be okay losing 30%, your position is too big. Predictions are not advice but they are calibrated about typical downside, and the calibration is worth using.

4. Treat long-horizon predictions with extreme caution. A 5-year prediction has compounded uncertainty. The bands are wide for a reason. Anyone telling you they know what BTC will cost in 2031 is lying or guessing. Our 5-year band reflects how much we do not know.

5. Compare against the realised track record. Once the scoreboard is live, look at it. If the model has been systematically wrong in one direction, knowing that is more valuable than any individual prediction.

Not financial advice

Models help structure thinking; they do not replace it. Crypto markets are volatile and capable of behaviour our model would call extreme. Do your own research, size positions you can afford to lose, and treat every forecast as one input among many. Read the full disclaimer for the formal version.