| # Main-AI token, cache, and cost data |
|
|
| This folder contains de-identified LLM accounting data for every AI-tutor student in the |
| final main leaderboard: 1,139 Quant students and 1,000 Verbal students. It does not include |
| control, human-tutor, pilot, superseded, or failure-archive records. |
|
|
| ## Files |
|
|
| Each instrument contains: |
|
|
| - `llm_cost_records.csv`: one row per known lesson-plan generation, AI tutor output, or live |
| practice-problem generation attempt. Request IDs are task-local anonymous sequence keys. |
| No database IDs, raw participant IDs, prompts, responses, or other content are included. |
| - `student_cost_summary.csv`: one row per final AI student, with request counts, explicit |
| unmetered-call counts, token totals, recorded cache/cost coverage, a replay-estimated total, |
| and the best available total. |
|
|
| These files are the only authoritative location for AI cost in this dataset. The main |
| `student_data/student.json` profiles intentionally do not duplicate cost or token totals; |
| the older `cost_usd`, `in_tok`, `out_tok`, and `reas_tok` profile fields used a retired |
| calculation that omitted live practice-problem generation. |
|
|
| Exact record counts are: |
|
|
| | Instrument | Students | Plan calls | Tutor calls | Live-practice generation calls | Total records | |
| |---|---:|---:|---:|---:|---:| |
| | Quant | 1,139 | 1,217 | 69,802 | 16,983 | 88,002 | |
| | Verbal | 1,000 | 1,024 | 54,616 | 20,595 | 76,235 | |
|
|
| Failed or unused lesson-plan attempts are retained because they incurred tokens and possibly |
| cost even when they did not become the released primary plan. `lesson_plan_usage` distinguishes |
| the primary plan, another plan demonstrably used during tutoring, and an unused or failed attempt. |
| Live practice generation uses one source carrier row per successfully persisted generation call; |
| it is not counted once per generated problem. Provider attempts with no persisted carrier remain |
| as separate timestamped rows with null usage and cost. |
|
|
| ## Recorded versus estimated cost |
|
|
| Request-level cost and cache accounting were available for only part of the study. Missing values are not zero: |
|
|
| - Quant has 20,264 request rows with a recorded production cost and 9,853 with recorded cache |
| accounting. The later Gemini 3.6 Flash and Opus 5 Quant collections have production cost for |
| every surviving usage-bearing row, but any explicitly listed unmetered call remains outside |
| that sum. |
| - The earlier Quant AI students have token counts but incomplete request-level cost/cache |
| fields. Their best available total is a session-level replay estimate. |
| - The pre-Gemini-3.7 Verbal collections preceded request-level accounting and retain replay |
| estimates. The retained Verbal table has 7,944 rows with recorded production cost and 186 |
| rows with request-level cache accounting. Known unmetered calls remain explicit. Best |
| available Gemini 3.7 totals are the complete recorded |
| production sums rather than replay estimates. |
|
|
| The release also contains calls for which the application preserved the fact and timestamp of |
| the provider call but no token or charge fields. Quant contains 3 such tutor calls and 691 live- |
| practice generation attempts; Verbal contains 2,916 tutor calls and 1,740 live-practice |
| generation attempts. These rows have `token_usage_recorded = false`; their token, cache, and cost |
| fields are null—not zero—and no missing value was estimated at request level. Request type |
| distinguishes saved tutor calls from live-practice attempts without a persisted usage carrier. |
| Therefore affected student, session, and arm totals are lower bounds on true spend; tutor-call |
| coverage by recorded token evidence is 69,799/69,802 (99.996%) for Quant and 51,700/54,616 |
| (94.66%) for Verbal. |
|
|
| Request-level accounting availability is encoded directly in the accounting fields, without a |
| second evidence-label column: |
|
|
| - A nonblank `recorded_cost_usd` means production recorded the request's cost. A blank means that |
| exact request-level cost was not recorded; it never means zero. |
| - Nonblank `prompt_tokens` or `completion_tokens` means ordinary token usage was recorded. |
| `reasoning_tokens` may still be blank because some providers do not report it separately. |
| - Nonblank `cache_read_tokens` or `cache_write_tokens` means cache accounting was recorded. A |
| recorded zero is written as `0`; two blanks mean cache accounting was not recorded. |
| - `token_usage_recorded` is `true` when at least one token-count field was preserved and `false` |
| when none was preserved. It reports token evidence, not whether the provider call occurred. |
|
|
| ## Request and validation status fields |
|
|
| The request table separates concepts that were formerly mixed in one `source_status` column: |
|
|
| - `request_completion_status` is the normalized request outcome: `completed`, |
| `max_output_tokens`, `error`, or `unknown`. Lesson-plan calls that returned an output for |
| validation are `completed`, even if that output was later rejected by validation. |
| - `provider_finish_reason_raw` retains the exact provider term when one was stored. `STOP` |
| (Gemini), `stop` (OpenAI/OpenRouter), `end_turn` (Anthropic), and `completed` (OpenAI Responses) |
| all normalize to `request_completion_status = completed`. `MAX_TOKENS` and `length` normalize |
| to `max_output_tokens`; `error` and `MALFORMED_RESPONSE` normalize to `error`. Capitalization |
| therefore has no effect on cost or research interpretation. |
| - `lesson_plan_validation_status` is populated only for lesson-plan generation and is one of |
| `valid`, `repaired`, `invalid`, or `leak_blocked`. This is the production parser/schema/leak |
| validation result; `valid` does not certify mathematical or pedagogical correctness. It is |
| blank for tutor and live-practice calls. |
| - `token_usage_recorded` is independent of completion and validation. For example, an error can |
| still have recorded tokens, while a known saved call can have an unknown finish reason and no |
| recorded tokens. |
|
|
| `replay_estimated_total_cost_usd` applies the arm-specific input-cost multiplier measured by |
| byte-faithful API replay. The released pricing inputs fix the cost basis used in the paper. Output-token cost is not |
| discounted. When an arm has no eligible replay multiplier, the conservative full-input-price |
| basis is used. Gemma uses its independently measured production-equivalent rate; it is not |
| treated as free. `cache_multiplier_state` and `cache_input_cost_multiplier` are stored once |
| per AI model in the root `collection_metadata.json`, under the matching cost-summary table |
| path. Join them to a student summary using `ai_model_preset_id`. |
|
|
| ### Evidence behind each input-cost multiplier |
|
|
| The multiplier applies to input-token cost only; it is not the ratio between cached and |
| uncached total session cost because output-token cost is unaffected. The evidence gate was at |
| least 50 calls from at least two sessions. The final replay expanded the six initially thin |
| auto-caching samples to four sessions each; notably, Kimi is based on 136 calls from four |
| sessions, not the earlier 22-call/one-session result. |
|
|
| | AI arm | Multiplier | Evidence | |
| |---|---:|---| |
| | `gemini-3.1-pro-high` | 0.456208 | 390 calls / 4 sessions; 2,113,278 of 3,490,812 input tokens cached | |
| | `gemini-3.5-flash-low` | 0.478723 | 364 calls / 4 sessions; 1,950,690 of 3,353,845 input tokens cached | |
| | `gemini-3.6-flash-low` | 0.504675 | 385 calls / 4 sessions; 1,807,251 of 3,283,752 input tokens cached | |
| | `gemini-3.7-flash-medium` | not used | complete request-level production cost is recorded for the frozen Quant and Verbal cohorts | |
| | `gpt-5.4-mini-none` | 0.289747 | 422 calls / 4 sessions; 2,565,888 of 3,251,374 input tokens cached | |
| | `gpt-5.5-high` | 0.314441 | 240 calls / 4 sessions; 1,545,728 of 2,029,229 input tokens cached | |
| | `gpt-5.5-pro-med` | 1.000000 | 54 calls / 2 sessions; vendor returned zero cached tokens | |
| | `kimi-k2.6` | 0.599054 | 136 calls / 4 sessions; 641,499 of 1,175,219 input tokens cached | |
| | `opus-4.8-off` | 0.409288 | 591 calls / 11 sessions; 5,361,629 of 7,129,404 input tokens cached | |
| | `opus-4.8-xhigh` | 0.368793 | 693 calls / 11 sessions; 6,335,875 of 8,246,394 input tokens cached | |
| | `opus-5-high` | 0.396712 | 535 calls / 10 sessions; 5,634,626 of 7,509,917 input tokens cached | |
| | `sonnet-4.6-low` | 0.275159 | 942 calls / 10 sessions; 7,411,416 of 8,736,036 input tokens cached | |
| | `sonnet-5-low` | 0.405505 | 997 calls / 10 sessions; 8,708,996 of 11,792,337 input tokens cached | |
| | `gemma-4-31b-high` | 1.000000 | no cache replay multiplier; its production-equivalent route was fit from 24 real charges and priced cached and uncached input equally | |
|
|
| The replay source was a byte-faithful replay of the exact recorded requests against the live |
| vendor APIs, preserving the recorded request intervals under each vendor's cache lifetime. Gemma's |
| 1.0 and GPT-5.5-pro's 1.0 have different meanings, captured by `cache_multiplier_state`: |
| `NO_DISCOUNT_ON_RATE` versus `MEASURED_NO_CACHING`. |
|
|
| Never fill a blank per-request `recorded_cost_usd`, `cache_read_tokens`, or |
| `cache_write_tokens` with zero. The task-level estimate is the honest recoverable quantity for |
| the earlier collections; exact historical request-level charges and cache splits cannot be |
| reconstructed from fields that were never recorded. |
|
|
| ## Timestamp and token semantics |
|
|
| Lesson-plan and tutor calls retain their event time in seconds from the shared study-session origin. Successful live-practice rows use |
| the production `practice_problem` carrier, which did not record a generation timestamp, so their |
| `occurred_elapsed_seconds` is blank rather than inferred from when a problem was later shown or answered. |
| Unmetered live-practice attempts retain the event time from the provider-call log on the same relative clock. |
|
|
| For Anthropic records, `prompt_tokens` excludes cache-read/write tokens when those cache fields |
| are present. For OpenAI and Gemini records, prompt tokens are gross and already include cache |
| reads. `reasoning_tokens` is provider-specific: it can be a subset of completion tokens or a |
| separate output count. Anthropic does not report thinking tokens separately; they are already |
| inside `completion_tokens`, so Anthropic request rows and their student-summary |
| `reasoning_tokens` cells are blank rather than zero. A blank summary also occurs whenever none |
| of that student's request records reported a separate reasoning count. A numeric zero means a |
| provider reported a separate count of zero. The Opus 4.8 off arm did run with reasoning disabled, |
| but that configuration fact should not be inferred from the reporting field. Use the supplied |
| summary cost rather than applying one universal token formula across providers. |
|
|
