First-Passage Probability Engine

What determines the band-fill colour?

Answer

The band fill is not assigned directly from a trend label such as “uptrend” or “downtrend”. Its direction is based on the difference between the upper-first and lower-first probabilities:

score = pUpper - pLower

The tint is smoothed, so colour changes gradually rather than reacting completely to one candle. Trend influences the model indirectly through drift or recent momentum, but the result also depends on volatility, barrier distance, candle-and-volume pressure, and the selected horizon.

A larger downtrend can therefore contain a blue band when the engine sees a higher chance of a short-term rebound reaching the upper barrier first. The fill answers a short-horizon first-touch question; it does not declare that the larger market trend has turned bullish.

A practical starting preset for IBM Daily

IBM is an individual stock and can be affected by earnings, guidance, corporate news, and overnight gaps. A starting preset should therefore be more conservative than one used for a smoother instrument.

Around earnings or a large gap, a continuous price-path model can become less representative because price may jump directly through a barrier. In those conditions, reduce reliance on the directional lean or wait for several candles to stabilise.

How U, L, N, View, and Conviction relate

In the example, the dashboard reports:

L 40% | N 3% | U 57%
gap +17.2pp | View: Upper lean | Conviction: +7%

U, L, and N

• U 57%: the upper barrier has an estimated 57% chance of being touched first.
• L 40%: the lower barrier has an estimated 40% chance of being touched first.
• N 3%: there is an estimated 3% chance that neither barrier is touched within the horizon.

The three numbers total approximately 100%. They describe outcome shares, not expected price return.

View and probability gap

score = U - L = 57% - 40% = +17.2 percentage points

When the score clears the Lean threshold, the dashboard reports Upper lean. A sufficiently negative score produces Lower lean. A small gap remains Balanced even if one side is marginally higher.

Why is Conviction only +7%, not +17.2%?

Conviction is not a copy of the probability gap. It discounts that gap when volatility and uncertainty are high:

uncertainty = 1 - max(U, L, N)
raw conviction = score / (sigma × 100 + 0.25 + uncertainty)

For this example:

score       = +0.172
sigma       = 4.56%
uncertainty = 1 - 0.57 = 0.43

Elevated volatility and 43% uncertainty enlarge the denominator and reduce the displayed conviction to approximately +7%. In practical language, an upper bias is present, but the environment is too volatile and unsettled to treat that bias as strong.

Volatility regime, barriers, and median touch

4.56% (EWMA) / x1.85 elevated means current volatility is 1.85 times its 120-bar median. With barriers near +6.06% / -5.80% and N at only 3%, the model expects one of the barriers to be touched relatively often. med 1.2 estimates the median touch time at about 1.2 bars among paths that touch within the horizon.

A low N does not mean U must win. It means one of the two barriers is likely to be reached.

Flags and exact math

Flags: ok means no operational warning is active for warm-up, volume availability, timeframe, or effective sample. It does not guarantee forecast quality. exact math means the probability engine uses a closed-form model instead of random simulation; it does not make the future exact.

How resolved Upper/Lower First markers are determined

The indicator stores the upper and lower barrier that existed on the original forecast candle. With a five-bar horizon, it checks the next five candles in chronological order.

The resolved marker is placed on the original forecast candle, not on the candle that eventually touched the barrier. It only becomes knowable after the forward window has elapsed, then it is positioned back on the originating bar for review.

Manual audit

1. Select the candle carrying the resolved marker.
2. Record the upper and lower barriers that belonged to that original candle.
3. Begin with the following candle; do not include the original candle.
4. Inspect the next five candles using their highs and lows, not closing prices alone.
5. Identify which original barrier was reached first.

Worked example: a resolved Lower First outcome

The indicator did not predict that price must finish at one of the two barrier levels on the fifth bar. It estimated which barrier would be touched first at any point during the five-bar window.

Original forecast:
  Upper barrier: 320.05
  Lower barrier: 284.09

Next five bars:
  If low ≤ 284.09 occurs before high ≥ 320.05,
  the resolved outcome is Lower First.

A fifth candle below 284.09 confirms that the lower barrier was reached by the end of the window. The downward triangle on the original forecast candle means lower was reached before upper, provided no earlier candle touched 320.05 first.

• If upper is touched on day one and lower on day four, the outcome remains Upper First.
• If lower is touched on day two and price later recovers, the outcome remains Lower First.
• If the first-touch candle crosses both barriers, the outcome is Ambiguous.

The live U and L labels at the far right of the chart belong to the latest chart bar. They do not represent the old 4 June forecast. Historical review should use the original bar's barrier values and Data Window readings.

Hit rates, Brier skill, and the base rate

In broad terms, yes: negative Brier skill means the historical base-rate forecast produced lower probability error across the evaluated history than the model's condition-aware U/L/N forecasts.

But the historical hit-rate row is not an accuracy percentage for this one setup. It records resolved outcome frequencies:

Historical resolved outcomes:
L 43% | N 12% | U 45%

Current model forecast:
L 40% | N 3% | U 57%

The current model adjusts away from the historical rate using the present volatility, drift, candle pressure, and volume context. In this example it raises U and sharply lowers N.

Brier skill = 1 - (Brier model / Brier baseline)

A value of -5.4% means the model's accumulated squared probability error is approximately 5.4% larger than the baseline error. This does not imply that resolved markers are wrong. It means the probability estimates made before the outcomes occurred have not been calibrated well enough to beat the simple historical benchmark.

The Brier baseline is also not simply today's final 43% / 12% / 45% row copied backward through history. At each old forecast, the baseline uses the resolved outcomes available up to that time, creating a fairer walk-forward comparison.

What “historical” actually refers to

Yes. Historical refers to old outcomes whose forward windows have finished: resolved Upper First, resolved Lower First, and resolved No Touch. Ambiguous cases are excluded because their intrabar order cannot be established from the chart timeframe.

The important distinction is that a historical resolved outcome is no longer a prediction. It is the observed answer to an earlier prediction:

1. At candle T
   The model issues U/L/N probabilities.

2. After the next five candles
   The actual price path resolves to U, L, or N.

3. Once the outcome is known
   The old model probabilities are compared with the actual outcome.
   The historical base-rate probabilities are compared with the same outcome.

For illustration:

Approximate base rate: L 43%, N 12%, U 45%
Model forecast:        L 40%, N  3%, U 57%

If the actual result is Lower First, the model may have allocated too much probability to U and too little to N, giving it a larger Brier error than the baseline. If the result is Upper First, the model may do better. The final Brier skill aggregates these probability errors across all eligible resolved forecasts.

Historical resolved outcomes are the observed answers to earlier forecasts. The base rate is built from those observed answers. Negative Brier skill means the model's conditional probability adjustments have not improved on that historical benchmark overall.

How to use the readout more safely

• Use U/L/N to understand the three barrier outcomes for the current horizon.
• Use View and Conviction as relative direction and quality context, not an automatic trade command.
• Read N together with Volatility/Regime to distinguish likely movement from no-touch or range risk.
• Use resolved markers to audit old forecasts, not as signals that were available on the original candle.
• Treat negative Brier skill seriously by reducing confidence or re-testing the setup walk-forward.
• Avoid tuning settings to one dramatic event; look for stability across nearby settings and out-of-sample periods.