# Merge 05 — batch r4-extend — group s3-midsize (blocks a, b, c) One frozen candidate against one frozen comparator, three blocks of 500 seeds each, paired by seed. This file merges the three item results; it runs no simulations and copies the items' statistics. The pooled figures below are computed only from each block's `n`, `sum_d` and `sum_d2`. **These are screening seeds, not finalist seeds.** All seeds here (430500–431999) are below 900000. Under the goal's rules a promotion needs a paired gain above twice its standard error on the finalist seeds 900000–903999, which no item in this group ran. Nothing here promotes anything. ## Candidate and comparator | | name | SHA-256 of UTF-8 code bytes | |---|---|---| | candidate | `d-s3-mid-size-up` — "larger desired size at the rival level at middle probabilities, spread 3" (idea text from items a, b, c) | `1317a49c96f2085e904ffdf7e19ba0d968e30f3f0019a404586c42316602248e` | | comparator | `N` (the name items b and c give it; item a names it only by hash) | `bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae` | All three items report verifying both hashes by script before running (each item's `notes`). The item results do not carry the comparator's artifact URL, so none is cited here; the hash is its identifier. Simulator, as stated in each item's `notes`: https://github.com/danrobinson/prediction-market-challenge at commit `b244530ee2a6247b5f930830eeca9dd950da0e7e`, unmodified, default configuration, single process, Python 3.12.3. Items b and c state that the comparator's check values were reproduced; item a reports the same four values (to more decimals) and mentions "four check runs" without saying so explicitly. Each item reports that the first rival quote gap equalled 2·s−1 on every seed. ### Sources (the three item results, read as data) | item | path | SHA-256 (from the task brief) | |---|---|---| | item-s3-midsize-a | `.imd/reads/artifacts/item-s3-midsize-a` (same bytes as `artifacts/goal/batches/r4-extend/items/s3-midsize-a/result.json`) | `d97e1598df95bc7c37ed1705755ad0790710f3070f93e5c5fde14a7e461cb899` | | item-s3-midsize-b | `.imd/reads/artifacts/item-s3-midsize-b` (same bytes as `artifacts/goal/batches/r4-extend/items/s3-midsize-b/result.json`) | `f757ce53555f42bba7744c8441aa9bd127d12fac72db4e60bb6b7a9cf53c0803` | | item-s3-midsize-c | `.imd/reads/artifacts/item-s3-midsize-c` (same bytes as `artifacts/goal/batches/r4-extend/items/s3-midsize-c/result.json`) | `52663e5ef221e90a63d0028f6395269969c5bf88b2156fe85ed5e1b98df48f19` | ## Blocks Values are copied as reported in each item's `overall`. `failures` is the length of the item's `failures` list. `flag` is set only for the brief's criteria: incomplete, failures, a hash unlike the others, or check values off. | key | seeds | n | complete | failures | mean_diff | se | retail_diff | arb_diff | python_version | flag | |---|---|---|---|---|---|---|---|---|---|---| | s3-midsize-a | 430500–430999 | 500 | true | 0 | 0.15432111472559992 | 0.09472163607858995 | 0.12172825225659986 | 0.03259286246600001 | 3.12.3 | none | | s3-midsize-b | 431000–431499 | 500 | true | 0 | 0.04422054903759989 | 0.019520057940022296 | 0.10119866377779374 | -0.0569781147419981 | 3.12.3 | none | | s3-midsize-c | 431500–431999 | 500 | true | 0 | 0.050273 | 0.040632 | 0.119504 | -0.069231 | 3.12.3 | none | Per-block inputs to the pooling (copied): | key | n | sum_d | sum_d2 | comparator_mean | candidate_mean | check_values | s/sim | |---|---|---|---|---|---|---|---| | s3-midsize-a | 500 | 77.16055736279996 | 2250.468494405582 | 109.4414535838618 | 109.59577469858739 | [17.1160017503, 20.0171113118, 2.3903113616, 241.4847522404] | 1.4178374240775593 | | s3-midsize-b | 500 | 22.110275 | 96.045378 | 90.7981984582868 | 90.8424190073244 | [17.116002, 20.017111, 2.390311, 241.484752] | 0.559 | | s3-midsize-c | 500 | 25.136268 | 413.174572 | 103.651689 | 103.701962 | [17.116002, 20.017111, 2.390311, 241.484752] | 0.4213 | Flag review: no block is incomplete, none lists a failure or missing seed, all three carry the same candidate and comparator hashes, and the check values agree (item a reports them to 10 decimals, items b and c to 6; they match to rounding). Within every block the reported `mean_diff` equals `sum_d/n`, the reported `se` equals the formula below, `retail_diff + arb_diff` equals `mean_diff`, the four `by_spread.n` sum to 500, and the `per_seed` rows sum to `sum_d` within their 6-decimal rounding. Per-simulation time differs between machines (1.42 s, 0.56 s, 0.42 s); that is not a result difference and is not flagged. ### Per block by spread (copied) | key | spread | n | sum_d | sum_d2 | mean_diff | se | retail_diff | arb_diff | |---|---|---|---|---|---|---|---|---| | s3-midsize-a | 1 | 122 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | s3-midsize-a | 2 | 118 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | s3-midsize-a | 3 | 131 | 77.16055736279996 | 2250.468494405582 | 0.5890118882656485 | 0.3598313045745623 | 0.4646116498343506 | 0.12440023841984735 | | s3-midsize-a | 4 | 129 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | s3-midsize-b | 1 | 120 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | s3-midsize-b | 2 | 144 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | s3-midsize-b | 3 | 114 | 22.110275 | 96.045378 | 0.1939497764807013 | 0.08439722748777892 | 0.44385378849912627 | -0.24990401202631674 | | s3-midsize-b | 4 | 122 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | s3-midsize-c | 1 | 118 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | s3-midsize-c | 2 | 120 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | | s3-midsize-c | 3 | 139 | 25.136268 | 413.174572 | 0.180836 | 0.145955 | 0.42987 | -0.249034 | | s3-midsize-c | 4 | 123 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | ## Pooled statistics Pooled from the blocks' `n`, `sum_d` (S) and `sum_d2` (Q) only: mean = S/n, se = sqrt((Q − S²/n)/(n−1)/n); `retail_diff` and `arb_diff` are n-weighted means of the blocks' values. Figures are shown to 6 decimals; S and Q are given in full so the figures can be recomputed. | scope | n | S = Σ sum_d | Q = Σ sum_d2 | mean_diff | se | mean/se | retail_diff | arb_diff | |---|---|---|---|---|---|---|---|---| | overall | 1500 | 124.40710036279997 | 2759.6884444055822 | 0.082938 | 0.034968 | 2.37 | 0.114144 | -0.031205 | | spread 1 | 360 | 0.0 | 0.0 | 0.000000 | 0.000000 | — | 0.000000 | 0.000000 | | spread 2 | 382 | 0.0 | 0.0 | 0.000000 | 0.000000 | — | 0.000000 | 0.000000 | | spread 3 | 384 | 124.40710036279997 | 2759.6884444055822 | 0.323977 | 0.135978 | 2.38 | 0.445873 | -0.121897 | | spread 4 | 374 | 0.0 | 0.0 | 0.000000 | 0.000000 | — | 0.000000 | 0.000000 | ## Reading of the results - **The whole effect sits on spread 3.** In all three blocks every seed with competitor spread 1, 2 or 4 has d = 0 (1116 seeds), so the candidate and comparator behave identically there, as the idea ("spread 3") intends. On the 384 spread-3 seeds the pooled paired difference is 0.323977 (se 0.135978), from retail 0.445873 and arbitrage -0.121897. - **Pooled overall: 0.082938 (se 0.034968), about 2.4 se**, over 1500 screening seeds. This is a small gain, and these are screening seeds: it is evidence for sending the candidate to a finalist-seed measure, not a promotion. - **Block a is dominated by one seed.** Its `per_seed` row for seed 430678 (spread 3) reports d = 45.85497; that single seed is 93.4% of block a's `sum_d2` and 59% of its `sum_d`. Recomputing block a from its reported rows without that seed gives mean 0.062737 (se 0.024224) on 499 seeds — in line with blocks b and c rather than above them. This is derived from the item's own `per_seed` data; the item itself reports no problem with the seed, and a large paired difference on one seed is not a flag criterion. The next largest |d| in the group are seed 431589 (d = −13.290849) and seed 431698 (d = −8.204464), both in block c and both against the candidate. - **The blocks disagree on the sign of the arbitrage term.** Block a reports `arb_diff` +0.0326 overall (+0.1244 on spread 3), blocks b and c report −0.0570 and −0.0692 overall (−0.2499 and −0.2490 on spread 3). The n-weighted pooled arbitrage term is -0.031205; the retail term is positive in all three blocks (0.12172825225659986, 0.10119866377779374, 0.119504). Items report per-seed totals only, not a per-seed retail/arbitrage split, so this file cannot say whether block a's positive arbitrage term comes from seed 430678. - Block b's standard error (0.0195) is much smaller than a's (0.0947) and c's (0.0406); the per-seed rows show block b simply drew no large |d| (its largest is 5.863632 at seed 431451). Nothing in the three items suggests a procedural difference. - Not done here: no simulations were run, no finalist seeds were used, no code was changed, and the comparator's artifact URL is not cited because the items do not carry it. ## Merged data (JSON) `blocks[*].overall` and `blocks[*].by_spread` are copied as reported. `pooled` is computed as described above. `per_seed` concatenates all three blocks' rows, ordered by seed, each row `[seed, competitor_spread, d]` where d is candidate minus comparator edge as the items report it. ```json { "candidate_sha256": "1317a49c96f2085e904ffdf7e19ba0d968e30f3f0019a404586c42316602248e", "comparator_sha256": "bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae", "candidate_name": "d-s3-mid-size-up", "comparator_name": "N", "seeds_are_finalist": false, "blocks": [ { "key": "s3-midsize-a", "seeds": { "start": 430500, "end": 430999 }, "n": 500, "complete": true, "failures_count": 0, "missing_seeds_count": 0, "check_values": [ 17.1160017503, 20.0171113118, 2.3903113616, 241.4847522404 ], "python_version": "3.12.3", "seconds_per_simulation": 1.4178374240775593, "flag": "none", "overall": { "n": 500, "sum_d": 77.16055736279996, "sum_d2": 2250.468494405582, "mean_diff": 0.15432111472559992, "se": 0.09472163607858995, "comparator_mean": 109.4414535838618, "candidate_mean": 109.59577469858739, "retail_diff": 0.12172825225659986, "arb_diff": 0.03259286246600001 }, "by_spread": { "1": { "n": 122, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "comparator_mean": 45.75923746144918, "candidate_mean": 45.75923746144918, "retail_diff": 0.0, "arb_diff": 0.0 }, "2": { "n": 118, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "comparator_mean": 95.62232832857796, "candidate_mean": 95.62232832857796, "retail_diff": 0.0, "arb_diff": 0.0 }, "3": { "n": 131, "sum_d": 77.16055736279996, "sum_d2": 2250.468494405582, "mean_diff": 0.5890118882656485, "se": 0.3598313045745623, "comparator_mean": 114.67834917048931, "candidate_mean": 115.26736105875497, "retail_diff": 0.4646116498343506, "arb_diff": 0.12440023841984735 }, "4": { "n": 129, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "comparator_mean": 176.99070804285114, "candidate_mean": 176.99070804285114, "retail_diff": 0.0, "arb_diff": 0.0 } } }, { "key": "s3-midsize-b", "seeds": { "start": 431000, "end": 431499 }, "n": 500, "complete": true, "failures_count": 0, "missing_seeds_count": 0, "check_values": [ 17.116002, 20.017111, 2.390311, 241.484752 ], "python_version": "3.12.3", "seconds_per_simulation": 0.559, "flag": "none", "overall": { "n": 500, "sum_d": 22.110275, "sum_d2": 96.045378, "mean_diff": 0.04422054903759989, "se": 0.019520057940022296, "comparator_mean": 90.7981984582868, "candidate_mean": 90.8424190073244, "retail_diff": 0.10119866377779374, "arb_diff": -0.0569781147419981 }, "by_spread": { "1": { "n": 120, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "comparator_mean": 47.845470400452506, "candidate_mean": 47.845470400452506, "retail_diff": 0.0, "arb_diff": 0.0 }, "2": { "n": 144, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "comparator_mean": 51.38938116759722, "candidate_mean": 51.38938116759722, "retail_diff": 0.0, "arb_diff": 0.0 }, "3": { "n": 114, "sum_d": 22.110275, "sum_d2": 96.045378, "mean_diff": 0.1939497764807013, "se": 0.08439722748777892, "comparator_mean": 118.18809850139738, "candidate_mean": 118.38204827787807, "retail_diff": 0.44385378849912627, "arb_diff": -0.24990401202631674 }, "4": { "n": 122, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "comparator_mean": 153.96826773603115, "candidate_mean": 153.96826773603115, "retail_diff": 0.0, "arb_diff": 0.0 } } }, { "key": "s3-midsize-c", "seeds": { "start": 431500, "end": 431999 }, "n": 500, "complete": true, "failures_count": 0, "missing_seeds_count": 0, "check_values": [ 17.116002, 20.017111, 2.390311, 241.484752 ], "python_version": "3.12.3", "seconds_per_simulation": 0.4213, "flag": "none", "overall": { "n": 500, "sum_d": 25.136268, "sum_d2": 413.174572, "mean_diff": 0.050273, "se": 0.040632, "comparator_mean": 103.651689, "candidate_mean": 103.701962, "retail_diff": 0.119504, "arb_diff": -0.069231 }, "by_spread": { "1": { "n": 118, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "comparator_mean": 35.552525, "candidate_mean": 35.552525, "retail_diff": 0.0, "arb_diff": 0.0 }, "2": { "n": 120, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "comparator_mean": 83.933689, "candidate_mean": 83.933689, "retail_diff": 0.0, "arb_diff": 0.0 }, "3": { "n": 139, "sum_d": 25.136268, "sum_d2": 413.174572, "mean_diff": 0.180836, "se": 0.145955, "comparator_mean": 119.272677, "candidate_mean": 119.453514, "retail_diff": 0.42987, "arb_diff": -0.249034 }, "4": { "n": 123, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "comparator_mean": 170.566681, "candidate_mean": 170.566681, "retail_diff": 0.0, "arb_diff": 0.0 } } } ], "pooled": { "overall": { "n": 1500, "sum_d": 124.40710036279997, "sum_d2": 2759.6884444055822, "mean_diff": 0.08293806690853331, "se": 0.034967950382045414, "retail_diff": 0.1141436386781312, "arb_diff": -0.031205417425332692 }, "by_spread": { "1": { "n": 360, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "retail_diff": 0.0, "arb_diff": 0.0 }, "2": { "n": 382, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "retail_diff": 0.0, "arb_diff": 0.0 }, "3": { "n": 384, "sum_d": 124.40710036279997, "sum_d2": 2759.6884444055822, "mean_diff": 0.32397682386145826, "se": 0.13597849310543245, "retail_diff": 0.4458734062947925, "arb_diff": -0.12189675035937526 }, "4": { "n": 374, "sum_d": 0.0, "sum_d2": 0.0, "mean_diff": 0.0, "se": 0.0, "retail_diff": 0.0, "arb_diff": 0.0 } } }, "per_seed": [ [430500,4,0.0],[430501,1,0.0],[430502,1,0.0],[430503,3,0.958946],[430504,4,0.0],[430505,2,0.0],[430506,4,0.0],[430507,3,1.225479],[430508,4,0.0],[430509,4,0.0], [430510,2,0.0],[430511,4,0.0],[430512,4,0.0],[430513,4,0.0],[430514,4,0.0],[430515,3,-0.210824],[430516,1,0.0],[430517,4,0.0],[430518,1,0.0],[430519,1,0.0], [430520,1,0.0],[430521,4,0.0],[430522,1,0.0],[430523,4,0.0],[430524,4,0.0],[430525,3,0.084671],[430526,4,0.0],[430527,4,0.0],[430528,4,0.0],[430529,3,0.410969], [430530,3,-0.036455],[430531,3,0.198232],[430532,2,0.0],[430533,4,0.0],[430534,3,0.222769],[430535,1,0.0],[430536,3,0.925723],[430537,1,0.0],[430538,1,0.0],[430539,4,0.0], [430540,4,0.0],[430541,4,0.0],[430542,2,0.0],[430543,2,0.0],[430544,2,0.0],[430545,1,0.0],[430546,1,0.0],[430547,1,0.0],[430548,1,0.0],[430549,3,0.57798], [430550,3,0.796697],[430551,1,0.0],[430552,3,-0.565712],[430553,4,0.0],[430554,3,0.4026],[430555,2,0.0],[430556,2,0.0],[430557,2,0.0],[430558,2,0.0],[430559,4,0.0], [430560,3,1.103427],[430561,3,0.229534],[430562,1,0.0],[430563,3,0.663654],[430564,3,0.150509],[430565,1,0.0],[430566,1,0.0],[430567,1,0.0],[430568,2,0.0],[430569,4,0.0], 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