# Reinforcement Threshold Reference Reinforcement uses defined **word-level and concept-level recall thresholds** to determine when previously developed knowledge requires additional retrieval support and when that support has been sufficient for the concept to return to Practice or Learning. These thresholds work alongside **Mastery, Confidence and Evidence Strength**. Half-life influences how quickly concept Recall Probability changes over time, but it is not itself a Reinforcement entry or exit threshold. ## Purpose This reference brings together the thresholds used across the Reinforcement state. The thresholds allow Bedrock to distinguish between: - **stable retrieval**, where the concept can remain in Practice; - **weakening retrieval**, where Reinforcement is required; - **recovered retrieval**, where the concept can leave Reinforcement; - **a broader learning need**, where the concept should return to Learning; and - **insufficiently reliable evidence**, where the concept should enter Diagnostic. The thresholds should be interpreted as **decision boundaries within the adaptive model**, rather than as definitive statements that a student has remembered or forgotten something. ## Reinforcement entry from Practice A concept moves from **Practice to Reinforcement** when either the word-level or concept-level recall condition is met. ### Word-level recall trigger A concept enters Reinforcement when: **any relevant word has Recall Probability < 70** A word with Recall Probability exactly equal to 70 does not trigger Reinforcement. This allows Bedrock to respond when an individual part of the concept's vocabulary becomes less readily retrievable, even where the wider concept model remains strong. ### Concept-level recall trigger A concept also enters Reinforcement when: **Concept Recall Probability < 70% of Mastery** and all of the following are true: - **Mastery ≥ 80** - **Evidence Strength ≥ 70** - **Confidence ≥ 50** The complete rule is therefore: `Recall Probability < (0.70 × Mastery)` with: `Mastery ≥ 80` `Evidence Strength ≥ 70` `Confidence ≥ 50` The recall comparison is strict. A Recall Probability exactly equal to 70% of Mastery does not trigger Reinforcement. The additional thresholds ensure that concept-level forgetting is acted upon only when the engine has sufficiently strong evidence that the concept had previously been established. ## Reinforcement entry reference | Measure | Threshold | Role | |---|---:|---| | **Word Recall Probability** | < 70 for any relevant word | Triggers Reinforcement | | **Concept Recall Probability** | < 70% of Mastery | Triggers Reinforcement when the concept evidence conditions also pass | | **Mastery** | ≥ 80 | Required for the concept-level recall trigger | | **Evidence Strength** | ≥ 70 | Required for the concept-level recall trigger | | **Confidence** | ≥ 50 | Required for the concept-level recall trigger | The word-level route does not require the concept-level Mastery, Evidence Strength or Confidence thresholds. ## Reinforcement exit A concept remains in Reinforcement until **all relevant words have recovered to Recall Probability ≥ 70**. Once the word-level recovery gate has passed, Mastery and Confidence determine whether the concept returns to Practice or Learning. | Word-level recovery | Mastery | Confidence | Result | |---|---:|---:|---| | Every relevant word ≥ 70 | ≥ 70 | ≥ 70 | **Practice** | | Every relevant word ≥ 70 | < 70 | Any value | **Learning** | | Every relevant word ≥ 70 | Any value | < 70 | **Learning** | | One or more relevant words < 70 | Any value | Any value | **Remain in Reinforcement** | The exit thresholds are inclusive. A value exactly equal to 70 satisfies the corresponding condition. ## Returning to Practice The complete Reinforcement-to-Practice gate is: - **Recall Probability ≥ 70 for every relevant word** - **Mastery ≥ 70** - **Confidence ≥ 70** This indicates that the vocabulary requiring Reinforcement is sufficiently retrievable again and that the broader concept evidence remains strong enough for the student to resume Practice. Returning to Practice does not mean that the concept is permanently complete. Recall continues to be monitored and the concept can return to Reinforcement if retrieval later weakens. ## Returning to Learning A concept returns from Reinforcement to **Learning** when: - every relevant word has **Recall Probability ≥ 70**; but - **Mastery < 70** or **Confidence < 70**. This distinction is important. The word-level Reinforcement need has been resolved, but the wider concept model indicates that the student requires further development of their understanding rather than continued retrieval Practice. ## Re-Diagnostic thresholds Following an assessment, the engine also evaluates whether the evidence remains sufficiently reliable to support the normal adaptive-state decision. A concept enters **Diagnostic** when one or more of the following conditions are met: | Measure | Diagnostic trigger | |---|---:| | **Evidence Strength** | < 30 | | **Confidence** | < 40 | | **Precision** | < 50 | | **Consistency** | < 60 | These comparisons are strict. A value exactly equal to the threshold does not trigger Diagnostic. More than one condition can be present at the same time, and each applicable reason is recorded. Diagnostic takes precedence where the evidence indicates that the engine needs to establish a more reliable view of the student's current understanding before continuing with Reinforcement, Practice or Learning. ## Half-life Half-life determines **how quickly Recall Probability changes over time**. It does not act as a direct Reinforcement threshold. ### Concept half-life A new concept begins with a half-life of: **5 days** Concept half-life is updated following assessment evidence and has a minimum value of: **0.1 days** Concept Recall Probability is calculated using: `λ = ln(2) / half-life` and: `Recall Probability = Mastery × e^(-λ × elapsed days)` A longer half-life therefore produces slower modelled decay, while a shorter half-life produces faster decay. There is no separate rule such as "enter Reinforcement when half-life falls below X days". Instead, half-life influences the Recall Probability that is evaluated against the Reinforcement threshold. ### Word half-life A new word begins with a half-life of: **2.5 days** Successful, fluent retrieval can increase word half-life, up to: **30 days** Word half-life also contributes to the calculation of Word Recall. The half-life component of Word Recall reaches its maximum contribution at: **14 days** These values influence the word model but are not themselves Reinforcement entry or exit thresholds. ## Recall Probability and time Concept and word Recall Probability are time-sensitive measures. At concept level, Recall Probability begins from the latest Mastery estimate and decreases according to the concept's half-life: `Recall(t) = Mastery × 2^(-t / half-life)` At word level, Recall Probability is derived from Word Recall using the word decay model: `Word Recall Probability = Word Recall × e^(-0.10 × elapsed days)` This means that a student can retain strong accumulated evidence while their estimated **current retrievability** becomes weaker over time. Reinforcement responds to this change in retrievability rather than automatically reducing the student's underlying Mastery or Word Recall. ## Confidence and Precision Confidence and Precision are updated from assessment evidence rather than simply decreasing because time has passed. They therefore serve a different purpose from Recall Probability: - **Recall Probability** represents changing retrievability over time. - **Confidence** represents how certain the model is in its concept estimate. - **Precision** represents how precise that estimate is. Confidence contributes directly to Reinforcement routing. Precision does not directly trigger Reinforcement, but sufficiently low Precision can trigger **Diagnostic** because the engine no longer has a sufficiently precise estimate to support the normal adaptive journey. ## Threshold summary | State decision | Threshold | |---|---| | **Practice → Reinforcement: word route** | Any relevant word Recall Probability < 70 | | **Practice → Reinforcement: concept route** | Concept Recall Probability < 70% of Mastery | | **Concept-route Mastery requirement** | ≥ 80 | | **Concept-route Evidence Strength requirement** | ≥ 70 | | **Concept-route Confidence requirement** | ≥ 50 | | **Reinforcement word recovery** | Every relevant word Recall Probability ≥ 70 | | **Reinforcement → Practice Mastery** | ≥ 70 | | **Reinforcement → Practice Confidence** | ≥ 70 | | **Reinforcement → Learning** | Word recovery complete, but Mastery < 70 or Confidence < 70 | | **Diagnostic: Evidence Strength** | < 30 | | **Diagnostic: Confidence** | < 40 | | **Diagnostic: Precision** | < 50 | | **Diagnostic: Consistency** | < 60 | | **Initial concept half-life** | 5 days | | **Minimum concept half-life** | 0.1 days | | **Initial word half-life** | 2.5 days | | **Maximum word half-life** | 30 days | | **Word Recall half-life scaling point** | 14 days | ## Boundary behaviour Threshold boundaries are deliberately explicit. ### Reinforcement entry - Word Recall Probability of **69.9** triggers Reinforcement. - Word Recall Probability of **70** does not. - Concept Recall Probability below **70% of Mastery** can trigger Reinforcement. - Concept Recall Probability exactly equal to **70% of Mastery** does not. ### Reinforcement recovery - Word Recall Probability of **70** satisfies the recovery threshold. - Mastery of **70** satisfies the Practice threshold. - Confidence of **70** satisfies the Practice threshold. ### Diagnostic entry - Evidence Strength of **29.9** triggers Diagnostic; **30** does not. - Confidence of **39.9** triggers Diagnostic; **40** does not. - Precision of **49.9** triggers Diagnostic; **50** does not. - Consistency of **59.9** triggers Diagnostic; **60** does not. ## Key rules - Reinforcement can be triggered by **word-level or concept-level recall**. - A relevant word below **70 Recall Probability** is sufficient to trigger Reinforcement from Practice. - Concept-level Reinforcement requires Recall Probability below **70% of Mastery**, together with sufficient Mastery, Evidence Strength and Confidence. - Half-life affects **how quickly Recall Probability changes**, rather than acting as a direct state threshold. - Every relevant word must recover to **Recall Probability ≥ 70** before the normal Reinforcement exit gate can pass. - **Mastery ≥ 70** and **Confidence ≥ 70** are then required to return to Practice. - If word recall has recovered but Mastery or Confidence is below 70, the concept returns to Learning. - Evidence Strength, Confidence, Precision and Consistency can independently indicate that the concept requires Re-Diagnostics. - Confidence and Precision change through assessment evidence rather than through time-based decay. - Recall thresholds are adaptive-model decision boundaries, not definitive measures of whether a student knows or has forgotten something. ## What Product, Data and Support need to know When investigating an unexpected Reinforcement transition, the relevant values must be considered **together and at the point the decision was made**. Review: - the previous concept state; - concept Mastery; - concept Recall Probability; - concept half-life; - Confidence; - Evidence Strength; - Precision; - Consistency; - the relevant vocabulary set; - Word Recall for each relevant word; - Recall Probability for each relevant word; - word half-life; - assessment evidence and timestamps; - the Reinforcement transition history; - any Diagnostic-entry reasons; and - the resulting adaptive state. Particular care should be taken around threshold boundaries and the distinction between **accumulated learning evidence and current retrievability**. The central principle is that **Reinforcement is triggered and resolved through evidence of retrieval, while Mastery, Confidence and evidence-quality measures ensure that the resulting adaptive decision remains appropriate for the student's wider concept model**. ## Related articles - [Reinforcement State Entry Triggers](State%204%20-%20Reinforcement_Reinforcement%20State%20Entry%20Triggers.md) - [Reinforcement Session Exit Criteria](State%204%20-%20Reinforcement_Reinforcement%20Session%20Exit%20Criteria.md) - [Half-Life Update Logic](State%204%20-%20Reinforcement_Half-Life%20Update%20Logic.md)

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