{ "evaluation_id": "EVAL-20260402-181028", "question_id": "REASON-026", "question_text": "A teacher gives a test. Students who scored in the top 10% get praised. Students who scored in the bottom 10% get extra tutoring. On the next test, the top scorers decline slightly and the bottom scorers improve. The teacher concludes: 'Praise is counterproductive, but tutoring works.' (1) What's actually happening? (2) Design a study that separates regression to the mean from real effects. (3) Give three real-world examples where this fallacy leads to bad policy decisions.", "category": "reasoning", "timestamp": "2026-04-02T18:10:28.958Z", "display_date": "Apr 02, 2026", "winner": { "name": "Claude Opus 4.6", "provider": "openrouter", "score": 9.61 }, "avg_score": 9.085, "matrix_size": 90, "models_used": [ { "id": "gemini_25_flash", "name": "Gemini 2.5 Flash", "provider": "openrouter" }, { "id": "minimax_m25", "name": "MiniMax M2.5", "provider": "openrouter" }, { "id": "deepseek_v4", "name": "DeepSeek V4", "provider": "openrouter" }, { "id": "claude_opus_46", "name": "Claude Opus 4.6", "provider": "openrouter" }, { "id": "gpt_5_4", "name": "GPT-5.4", "provider": "openrouter" }, { "id": "grok_420", "name": "Grok 4.20", "provider": "openrouter" }, { "id": "claude_sonnet_46", "name": "Claude Sonnet 4.6", "provider": "openrouter" }, { "id": "mimo_v2_flash", "name": "MiMo-V2-Flash", "provider": "Xiaomi" }, { "id": "gpt_oss_120b", "name": "GPT-OSS-120B", "provider": "OpenAI" }, { "id": "gemini_31_pro", "name": "Gemini 3.1 Pro", "provider": "openrouter" } ], "rankings": { "claude_opus_46": { "display_name": "Claude Opus 4.6", "provider": "openrouter", "average_score": 9.61, "score_count": 9, "min_score": 8.65, "max_score": 10, "rank": 1 }, "gpt_5_4": { "display_name": "GPT-5.4", "provider": "openrouter", "average_score": 9.31, "score_count": 9, "min_score": 8.45, "max_score": 10, "rank": 2 }, "mimo_v2_flash": { "display_name": "MiMo-V2-Flash", "provider": "Xiaomi", "average_score": 9.19, "score_count": 9, "min_score": 8.65, "max_score": 10, "rank": 3 }, "gpt_oss_120b": { "display_name": "GPT-OSS-120B", "provider": "OpenAI", "average_score": 9.16, "score_count": 9, "min_score": 8.15, "max_score": 10, "rank": 4 }, "minimax_m25": { "display_name": "MiniMax M2.5", "provider": "openrouter", "average_score": 9.15, "score_count": 9, "min_score": 8.65, "max_score": 10, "rank": 5 }, "grok_420": { "display_name": "Grok 4.20", "provider": "openrouter", "average_score": 9.13, "score_count": 9, "min_score": 8.45, "max_score": 9.45, "rank": 6 }, "gemini_25_flash": { "display_name": "Gemini 2.5 Flash", "provider": "openrouter", "average_score": 9.11, "score_count": 9, "min_score": 8.65, "max_score": 10, "rank": 7 }, "claude_sonnet_46": { "display_name": "Claude Sonnet 4.6", "provider": "openrouter", "average_score": 9.04, "score_count": 9, "min_score": 8.05, "max_score": 10, "rank": 8 }, "deepseek_v4": { "display_name": "DeepSeek V4", "provider": "openrouter", "average_score": 8.97, "score_count": 9, "min_score": 8.25, "max_score": 10, "rank": 9 }, "gemini_31_pro": { "display_name": "Gemini 3.1 Pro", "provider": "openrouter", "average_score": 8.18, "score_count": 9, "min_score": 7.25, "max_score": 9.45, "rank": 10 } }, "judgments": [ { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.65, "brief_justification": "Accurate explanation of regression to the mean, thorough study design, clear structure, good depth with examples, and practical guidance." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 8.65, "brief_justification": "Accurately explains regression to the mean, offers a solid experimental design, and gives clear real-world examples; well‑structured and actionable, though depth could be slightly deeper." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 9.65, "brief_justification": "The response accurately identifies regression to the mean, provides a perfectly designed RCT to isolate the variables, and offers clear, well-structured real-world examples of the regression fallacy." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 10, "brief_justification": "The response perfectly identifies and explains regression to the mean, provides a flawless experimental design to isolate the effect, and offers three highly relevant real-world examples with excellent analysis of policy implications." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 10, "brief_justification": "The response perfectly identifies and explains regression to the mean, provides a robust randomized controlled trial design, and offers three highly relevant real-world examples." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9.4, "brief_justification": "The response perfectly explains regression to the mean and designs a flawless RCT. However, the first real-world policy example (hospital ratings) primarily describes selection bias/case-mix rather than regression to the mean, though the other examples are excellent." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 8.45, "brief_justification": "The response is highly accurate, deep, and well-structured, but it fails to provide the requested three examples, only providing two." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 10, "brief_justification": "The response perfectly identifies and explains regression to the mean, designs a flawless randomized controlled trial to isolate the variables, and provides three highly relevant, well-analyzed real-world examples." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.45, "brief_justification": "The response is highly accurate, well-structured with tables, and provides deep insights including advanced statistical controls like ANCOVA. It gets slightly cut off at the very end, but fully answers all prompt requirements." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 10, "brief_justification": "The response perfectly identifies regression to the mean, provides a flawless randomized controlled trial design to isolate the effect, and offers three highly relevant real-world examples with clear policy implications." }, { "judge_key": "gemini_31_pro", "judge_name": "Gemini 3.1 Pro", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 9, "brief_justification": "The response accurately explains regression to the mean and provides a well-designed study. However, the sports example fails to illustrate a 'bad policy decision' as requested, slightly reducing the depth and completeness." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 8.6, "brief_justification": "Accurate, thorough, and well-structured with practical insights." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 10, "brief_justification": "Comprehensive, accurate, and insightful analysis with clear structure and practical implications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9.45, "brief_justification": "Highly accurate, thorough, and insightful with clear practical applications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9.45, "brief_justification": "Highly accurate, thorough, and insightful with clear real-world applications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9.65, "brief_justification": "The response thoroughly explains regression to the mean, provides a robust study design to isolate real effects, and offers insightful real-world examples with clear policy implications." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.45, "brief_justification": "Highly accurate, thorough, and insightful with clear structure and practical examples." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.45, "brief_justification": "Highly accurate, thorough, and well-structured with insightful analysis and practical value." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.45, "brief_justification": "Accurate, thorough, and insightful with practical examples." }, { "judge_key": "deepseek_v4", "judge_name": "DeepSeek V4", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 9.45, "brief_justification": "Highly accurate, thorough, and insightful with practical examples." }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 8.25, "brief_justification": "The response is highly accurate in explaining regression to the mean, provides an excellent RCT design with clear logic for separating RTM from real effects, and references the Kahneman flight instructor anecdote appropriately. The explanation is exceptionally clear and well-structured. However, the response is incomplete - it cuts off mid-sentence during Example 1 of Part 3, leaving only one partially stated example instead of the three requested. This significantly impacts the completeness sco" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 9, "brief_justification": "The response accurately identifies regression to the mean, designs a proper RCT with control groups, and provides three relevant real-world examples. The explanation is exceptionally well-structured and clear. Depth is strong but could have gone slightly further—e.g., mentioning measurement error as a component of regression to the mean, discussing effect sizes, or noting more classic examples like the speed camera fallacy or the Sports Illustrated cover jinx. The study design is sound and pract" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9.45, "brief_justification": "The response is factually accurate throughout, correctly identifying regression to the mean and explaining it precisely. The study design is well-constructed with appropriate randomization within extreme groups, and includes thoughtful enhancements (multiple baselines, blinding, pre-registration). The three real-world examples are well-chosen, clearly explained, and directly relevant. The writing is exceptionally clear with good structure and formatting. Minor room for improvement: could have me" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9.2, "brief_justification": "Excellent response that correctly identifies regression to the mean, provides a well-designed RCT with proper within-group randomization, and gives three substantive real-world examples. The explanation of the statistical mechanism is precise and accessible. Minor quibbles: the hospital example is more about selection bias than pure regression to the mean (though the connection is valid), and the crime hot spots example could have been more nuanced about the evidence for hot-spots policing. The " }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9.2, "brief_justification": "Excellent response that accurately explains regression to the mean, provides multiple well-designed study alternatives, and gives compelling real-world examples. The mathematical framing (observed score = true ability + error) is correct, the study designs are methodologically sound (randomized within-group, regression discontinuity, full factorial), and the examples (aviation training via Kahneman, Scared Straight) are historically accurate and well-documented. Minor deductions: only two real-w" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9.2, "brief_justification": "Excellent response that accurately explains regression to the mean, designs a proper RCT with stratified randomization and control groups, and provides three well-chosen real-world examples. The dartboard analogy is effective, the study design is methodologically sound (though could mention blinding or multiple test administrations for robustness), and the examples are diverse and clearly articulated. Minor nitpick: could have mentioned that comparing change scores between treatment and control " }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.4, "brief_justification": "The response is exceptionally well-structured, using tables and clear formatting to walk through all three parts of the question. The explanation of regression to the mean is accurate and thorough. The study design is detailed, practical, and includes alternative approaches. The three real-world examples are relevant and well-explained, though the broken-windows policing example slightly oversimplifies the causal debate. The response also includes additional examples and a concise summary. Minor" }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.2, "brief_justification": "Excellent response that accurately explains regression to the mean, designs a well-structured controlled experiment with random assignment within extreme groups, and provides three relevant real-world examples with clear explanations of how the fallacy leads to bad policy. The explanation of the luck/ability decomposition is intuitive and correct. The study design correctly identifies random assignment within the extreme groups as the key step. Minor note: could have mentioned waitlist controls " }, { "judge_key": "claude_opus_46", "judge_name": "Claude Opus 4.6", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 9, "brief_justification": "The response is highly accurate in explaining regression to the mean, provides a well-designed experimental study with proper control groups, and gives three relevant real-world examples. The clarity and structure are excellent. Minor issues: the healthcare example is somewhat contrived and doesn't perfectly illustrate the fallacy leading to bad policy as cleanly as the others. The crime example is strong but conflates the Texas Sharpshooter Fallacy (a different concept) with regression to the m" }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 7.25, "brief_justification": "Accurately identifies regression to the mean and proposes a solid randomized controlled design, but the answer is incomplete because the third part is cut off and does not provide the requested three real-world examples." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 8.6, "brief_justification": "Accurately identifies regression to the mean, proposes an appropriate randomized control design, and gives relevant policy examples. Clear and practical, though it could go slightly deeper on study details like repeated baselines, blinding where possible, or accounting for measurement error and test comparability." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9.8, "brief_justification": "Accurately identifies regression to the mean, proposes a strong randomized-control design to isolate causal effects, and gives three relevant policy examples with practical implications. Clear, thorough, and insightful; only slightly verbose." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 8.8, "brief_justification": "Accurately identifies regression to the mean, proposes an appropriate randomized design with controls, and gives relevant policy examples. Clear and practical, though a few examples mix regression to the mean with broader selection/confounding issues." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 8.05, "brief_justification": "Accurately identifies regression to the mean and gives several sensible study designs with strong explanation. Clear and fairly deep, but incomplete because Part 3 promises three real-world examples and only provides two. Some methodological points are overstated or imprecise, especially around regression discontinuity and the claim that selecting on an independent measure removes regression pressure." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.8, "brief_justification": "Accurately identifies regression to the mean, proposes an appropriate randomized design with controls, and gives relevant real-world examples. Clear and practical; only minor limitations are that the study design could mention repeated measures/baseline adjustment and that one example slightly blurs the requested 'bad policy decisions' focus." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 8.15, "brief_justification": "Accurately identifies regression to the mean and proposes a solid randomized design with controls. Clear and thorough. Main weakness is that some real-world examples are overstated or debatable as cases where RTM was the primary driver, especially broken-windows policing and macroeconomic stimulus." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.05, "brief_justification": "Accurately identifies regression to the mean, proposes an appropriate randomized design with controls, and gives relevant policy examples. Clear and practical, though it could add nuances like test reliability, repeated baselines, or quasi-experimental alternatives." }, { "judge_key": "gpt_5_4", "judge_name": "GPT-5.4", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 8.65, "brief_justification": "Accurately identifies regression to the mean, explains the mechanism well, and proposes a solid randomized-control design. Examples are relevant, though one healthcare example is a bit muddled and the study design could be more rigorously specified for top and bottom groups separately." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 8.05, "brief_justification": "The response accurately explains regression to the mean with good examples and a solid RCT design. It is clear and insightful but incomplete, as the third real-world example is cut off mid-sentence, reducing overall completeness." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 8.8, "brief_justification": "The response accurately explains regression to the mean, provides a solid RCT design to isolate effects, and gives relevant real-world examples of the fallacy. It is clear, well-structured, and practically useful, though the examples could have slightly more nuance on policy impacts." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9, "brief_justification": "The response accurately explains regression to the mean, provides a rigorous randomized controlled design to isolate effects, and gives three relevant real-world examples with clear policy implications. It is comprehensive, logically structured, and highly insightful." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 8.8, "brief_justification": "Response accurately explains regression to the mean, provides a solid RCT design to isolate effects, and gives relevant real-world examples of the fallacy. Minor room for more statistical detail but highly complete, clear, and useful overall." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 9, "brief_justification": "Response is factually accurate, logically sound, and exceptionally thorough. It clearly explains regression to the mean with math and diagrams, provides multiple rigorous study designs that properly isolate effects, and gives relevant real-world examples with historical context. Minor deduction as one example (aviation) is well-known but still accurately applied." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.8, "brief_justification": "The response accurately explains regression to the mean, provides a solid RCT design that properly isolates effects, and gives three relevant real-world examples with clear policy implications. Minor room for more statistical nuance but highly effective overall." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 8.8, "brief_justification": "The response is factually accurate on regression to the mean, provides a rigorous randomized study design, and gives relevant real-world examples. It is comprehensive, clearly structured with tables, and offers high practical value for understanding and avoiding the fallacy." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.8, "brief_justification": "The response accurately explains regression to the mean, provides a rigorous randomized controlled study design that isolates effects, and gives three relevant real-world examples with clear policy implications. Minor room for more statistical nuance but overall excellent." }, { "judge_key": "grok_420", "judge_name": "Grok 4.20", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 8.8, "brief_justification": "The response accurately explains regression to the mean, provides a solid experimental design with proper controls, and gives relevant real-world examples. Minor inaccuracies in example 1 (hospital quality) and example 3 naming (Texas Sharpshooter is misapplied) slightly limit depth." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 8.25, "brief_justification": "Excellent explanation of regression to the mean with the Kahneman anecdote adding credibility. The RCT study design is well-structured and correctly identifies the need for control groups to isolate RTM effects. The response is cut off before completing the third real-world example, which significantly hurts completeness. The two visible sections are high quality, but the truncation is a notable flaw." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 8.25, "brief_justification": "The response correctly identifies regression to the mean and explains it clearly. The study design is sound with proper control groups. The three real-world examples are relevant though somewhat predictable. Missing some deeper nuance: could discuss how to statistically quantify regression to the mean, mention the Kahneman/Israeli Air Force example, or explore how to detect RTM mathematically. The sophomore slump example slightly conflates RTM with other phenomena. Overall solid, well-structured" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 10, "brief_justification": "Exceptional response that thoroughly addresses all three parts of the question. The explanation of regression to the mean is mechanistically precise and intuitive. The experimental design is methodologically rigorous with proper randomization within extreme groups, clear tables showing expected outcomes, and thoughtful enhancements. The three real-world examples are diverse, well-developed, and clearly articulate the policy damage. The closing synthesis elevates the response beyond mere descript" }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 9.45, "brief_justification": "The response accurately explains Regression to the Mean, provides a robust study design, and offers relevant real-world examples. The explanation is clear and well-structured." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9.6, "brief_justification": "Excellent response that accurately identifies regression to the mean, provides a rigorous experimental design with randomization within extreme groups (the key insight), and gives three compelling real-world examples. The study design is particularly strong, correctly noting that both treatment and control groups experience similar regression, isolating the true treatment effect. Minor gap: could mention using multiple baseline tests more prominently or discuss statistical power, but overall thi" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9.45, "brief_justification": "Excellent response that accurately explains regression to the mean, correctly identifies the mechanism (selection on extremes + noise), and provides a well-designed RCT solution. The three real-world examples are concrete, policy-relevant, and go beyond surface-level description. The Kahneman/Israeli Air Force reference adds credibility. Minor deduction for completeness: could have quantified expected regression magnitude or discussed effect size estimation more rigorously. Overall, a near-perfe" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 9, "brief_justification": "Excellent response that accurately identifies regression to the mean, provides a well-designed RCT with proper control groups, and gives three concrete, relevant real-world examples. The explanation is clear and well-structured with good use of formatting. Minor gap: could have discussed effect sizes, statistical power, or the need for multiple test administrations to better isolate regression effects. The dartboard analogy is helpful but slightly imprecise. Overall a thorough, accurate, and hig" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.6, "brief_justification": "Exceptionally thorough and accurate response. Correctly identifies regression to the mean, provides a rigorous randomized controlled study design with proper controls and statistical analysis, and gives three well-chosen real-world examples with clear explanations of consequences. The table format enhances clarity. Minor deduction for clarity due to the response being cut off at the end, but overall this is an outstanding answer." }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.8, "brief_justification": "Excellent response that accurately identifies regression to the mean, explains the mechanism clearly for both top and bottom scorers, and designs a solid randomized controlled study with proper control groups. The three real-world examples are relevant and well-explained with policy implications. Minor weakness: the study design could mention the need for larger sample sizes given splitting already-small extreme groups, and could discuss blinding or multiple test administrations to further contr" }, { "judge_key": "claude_sonnet_46", "judge_name": "Claude Sonnet 4.6", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 9, "brief_justification": "Excellent response that correctly identifies regression to the mean as the core phenomenon, explains it clearly with good intuition about skill vs. luck. The study design is methodologically sound with proper control groups and clear analysis logic. The three real-world examples are relevant and well-explained, though the first healthcare example is somewhat contrived and the 'Texas Sharpshooter' label is technically a different fallacy. Minor quibble: the study design could mention blinding or " }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 8.6, "brief_justification": "Accurate explanation of regression to the mean, solid RCT design, and relevant examples, though one example is incomplete." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 9, "brief_justification": "Accurate explanation of regression to the mean, thorough study design, and relevant real-world examples with clear structure." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 10, "brief_justification": "Exceptional response. It correctly identifies regression to the mean, provides a rigorous experimental design with randomization and control groups, offers three distinct and highly relevant real-world examples, and explains the deeper implications. The structure is clear and the reasoning is flawless." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9.8, "brief_justification": "Comprehensive, accurate, and well-structured response with strong practical examples and study design." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9.2, "brief_justification": "Excellent response. Correctly identifies regression to the mean, provides a robust study design (RCT with controls), and offers three distinct, high-quality real-world examples. Minor deduction in correctness for not explicitly mentioning that randomization is the key to isolating the effect, but the proposed design effectively achieves this." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 10, "brief_justification": "Exemplary response covering all three parts with mathematical precision, multiple rigorous study designs, and compelling real-world examples including the Kahneman aviation case and Scared Straight program." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 9.2, "brief_justification": "Accurate explanation of regression to the mean, thorough study design with randomization and controls, clear structure, insightful real-world examples, and highly actionable." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 9.2, "brief_justification": "Accurate explanation of regression to the mean, thorough study design, clear structure, insightful analysis, and practical examples." }, { "judge_key": "mimo_v2_flash", "judge_name": "MiMo-V2-Flash", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 9.8, "brief_justification": "Comprehensive and accurate explanation of regression to the mean, with a well-designed study and relevant real-world examples." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 7.5, "brief_justification": "Accurate explanation and solid study design, clear presentation, but response is cut off before finishing the examples, reducing completeness and overall utility." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 8.65, "brief_justification": "Accurately identifies regression to the mean, offers a solid RCT design, and gives relevant real-world examples; clear and actionable though could delve deeper into statistical nuances." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 8.65, "brief_justification": "Accurately explains regression to the mean, fully answers all parts, presents a clear experimental design, offers detailed real-world examples, and provides practical guidance." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 8.45, "brief_justification": "Accurately explains regression to the mean, offers a solid randomized study design, and gives clear real-world examples; well-structured and practically useful though could include a bit more methodological nuance." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 8.45, "brief_justification": "Accurately explains regression to the mean, offers a solid randomized design, and gives clear real-world policy examples; minor depth could be added on analysis methods." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 8.45, "brief_justification": "Accurate explanation of regression to the mean and solid study designs; clear and well-structured. Misses a third real-world example, reducing completeness." }, { "judge_key": "gpt_oss_120b", "judge_name": "GPT-OSS-120B", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.65, "brief_justification": "Accurately explains regression to the mean, offers a solid RCT design, and gives relevant real-world examples; clear and actionable though could include more statistical detail." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 10, "brief_justification": "The response is exceptionally well-structured, clear, and accurate. It thoroughly explains regression to the mean, designs a robust study, and provides excellent real-world examples. The depth of understanding is evident throughout." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 10, "brief_justification": "The response is exceptionally well-structured, accurate, and comprehensive. It clearly explains regression to the mean, provides a robust study design, and offers insightful real-world examples with policy implications. The depth of analysis is outstanding." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 9.45, "brief_justification": "The response is highly accurate, clear, and provides a comprehensive explanation of regression to the mean, a well-designed study, and relevant real-world examples. The depth is excellent, going beyond surface-level explanations." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 9.45, "brief_justification": "The response accurately identifies regression to the mean, provides a well-designed study, and offers relevant real-world examples. The explanation is clear and insightful." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 10, "brief_justification": "This response is exceptionally thorough, accurate, and well-structured. It not only correctly identifies regression to the mean but also provides detailed explanations, multiple robust study designs, and compelling real-world examples with clear policy implications. The depth of analysis, especially in the study design section and the breakdown of the teacher's errors, is outstanding. The clarity is excellent, making a complex statistical concept accessible and actionable." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 10, "brief_justification": "The response is exceptionally clear, comprehensive, and accurate. It thoroughly explains regression to the mean, provides a robust study design, and offers insightful real-world examples with detailed explanations of the fallacy's impact." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 10, "brief_justification": "The response is exceptionally thorough, accurate, and well-structured. It clearly explains regression to the mean, provides a robust study design, and offers compelling real-world examples with detailed explanations of the fallacy's impact. The use of tables enhances clarity and readability." }, { "judge_key": "gemini_25_flash", "judge_name": "Gemini 2.5 Flash", "respondent_key": "minimax_m25", "respondent_name": "MiniMax M2.5", "weighted_score": 10, "brief_justification": "The response is exceptionally well-structured, accurate, and comprehensive. It clearly explains regression to the mean, designs a robust study, and provides excellent real-world examples, demonstrating a deep understanding of the concept and its implications." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gemini_31_pro", "respondent_name": "Gemini 3.1 Pro", "weighted_score": 7.65, "brief_justification": "Accurately explains regression to the mean with a sound RCT design. However, the response is truncated mid-example, leaving the third real-world case incomplete - a significant gap in completeness." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "deepseek_v4", "respondent_name": "DeepSeek V4", "weighted_score": 8.8, "brief_justification": "Accurately identifies regression to the mean, provides a well-designed RCT with control groups, and gives three relevant real-world examples. Clear structure with good depth throughout." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "claude_opus_46", "respondent_name": "Claude Opus 4.6", "weighted_score": 9, "brief_justification": "Excellent response that correctly explains regression to the mean, provides a rigorous experimental design with clear rationale, and gives three compelling real-world examples (speed cameras, sports performance, medical treatments). Well-structured with effective use of formatting and tables. Insightfully connects the statistical concept to broader policy implications." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gpt_5_4", "respondent_name": "GPT-5.4", "weighted_score": 8.8, "brief_justification": "Accurately identifies regression to the mean, designs a sound RCT with multiple methodological improvements, and provides three relevant real-world examples with clear policy implications. Well-organized and insightful." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "grok_420", "respondent_name": "Grok 4.20", "weighted_score": 8.8, "brief_justification": "Excellent explanation of regression to the mean with clear mechanism, well-designed RCT methodology, and relevant policy examples. Thorough and accurate." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "claude_sonnet_46", "respondent_name": "Claude Sonnet 4.6", "weighted_score": 8.6, "brief_justification": "Excellent explanation of regression to the mean with strong study designs. However, only provides 2 policy examples instead of the 3 requested." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "mimo_v2_flash", "respondent_name": "MiMo-V2-Flash", "weighted_score": 8.8, "brief_justification": "Accurate explanation of regression to the mean with well-structured study design and relevant real-world examples. Clear and comprehensive coverage of all three parts of the question." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gpt_oss_120b", "respondent_name": "GPT-OSS-120B", "weighted_score": 8.4, "brief_justification": "Accurate explanation of regression to the mean with well-structured tables. Comprehensive coverage of all three parts. Clear, organized presentation. Good depth in explaining the mechanism and study design. Practical, actionable study design and relevant real-world examples." }, { "judge_key": "minimax_m25", "judge_name": "MiniMax M2.5", "respondent_key": "gemini_25_flash", "respondent_name": "Gemini 2.5 Flash", "weighted_score": 8.8, "brief_justification": "Accurate explanation of regression to the mean with clear mechanism. Well-designed controlled study with random assignment. Relevant real-world examples with policy implications. Slightly less depth than top responses but still comprehensive." } ], "meta": { "source": "The Multivac (app.themultivac.com)", "methodology": "10x10 blind peer matrix evaluation", "criteria": "correctness, completeness, clarity, depth, usefulness", "self_judgments": "excluded from rankings", "license": "Open data — cite as: The Multivac (2026)" } }