studentbench

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 It does not include control, human-tutor, pilot, superseded, or failure-archive records.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.