After completing full PADP protocol, my probability estimate is 50% (80% CI: [30%, 70%]) that Google retains the #1 AI model on LMSYS Arena by Dec 31. Market prices this at 89%, creating 38.5% edge on NO contracts. Core thesis: Historical base rates show 60% of leaders overtaken within 30 days, and Gemini 3 Pro's 10-point lead sits within a ±17-point confidence interval. Kelly/5 sizing (8.7% of bankroll) yields $76 position with $255 expected value.
The Question
Will Google retain the #1 position on LMSYS Chatbot Arena Leaderboard on December 31, 2025, 12:00 PM ET?
Current situation (Nov 29, 2025):
- Gemini 3 Pro: #1 at 1492 Elo (±17 CI)
- Grok 4.1-thinking: #2 at 1482 (10-point gap)
- Released Nov 18 (11 days old)
- Top-5 within 31-point spread
Resolution Criteria
This market resolves YES if any Google-owned model holds the highest Arena Score on the LMSYS Chatbot Arena Leaderboard (https://lmarena.ai/leaderboard/text) when sorted by "Arena Score" on December 31, 2025, 12:00 PM ET.
Multiple Google models can exist; only one needs to be #1. Score is based on Bradley-Terry Elo from blind user voting.
The Core Thesis
Betting NO because historical base rates show 60% of leaderboard leaders are overtaken within 30 days, and Google's current 10-point lead falls within the ±17-point confidence interval, creating statistical overlap with #2 (Grok 4.1-thinking at 1482).
The Base Rates
After analyzing N=52 historical cases across 6 reference classes:
- Leadership Persistence: 60% overtaken within 30 days → 40% retention base rate
- Score Gap Significance: 80% of ≤10-point leads fail within 30 days
- Google-Specific: Median leadership duration 7-14 days (Gemini 3 Pro at 11 days)
- Late December Releases: 0% major releases Dec 24-31 (0/2 years)
- Google Release Success: 100% of Google releases reach #1 (8/8)
Competitive Landscape Assessment
Grok 5 (xAI):
- Officially delayed to Q1 2026 (Nov 14 announcement)
- Elon Musk 0% track record on EOY promises (0/2 cases)
- Would need Dec 15-20 release to accumulate sufficient votes
- P(Grok 5 by Dec 31): ~2%
GPT-5.5 (OpenAI):
- GPT-5.1 just released Nov 12 (17 days ago)
- No announcements of follow-up
- 33-day window insufficient for major version historically
- Sam Altman Nov 20 memo shows concern but no action signals
- P(GPT-5.5 by Dec 31): ~6%
Claude 5.0 (Anthropic):
- Opus 4.5 released Nov 24 (5 days ago)
- 33% Arena success rate (vs Google 100%)
- Style bias: concise responses penalized on Arena
- P(Claude 5.0 by Dec 31): ~3%
Unknown Entrants:
- DeepSeek V4 delayed due to chip restrictions
- Meta Llama far from competitive (100+ rank positions behind)
- Alibaba Qwen frequent releases but never #1
- P(Other): ~1%
Why This Creates a Coin Flip
- Confidence interval overlap: Gemini 3 Pro (1492 ±17) overlaps with Grok 4.1 (1482), suggesting statistical tie
- Score instability: Only 11 days old, within LMSYS "minimum two weeks" evaluation period
- Quality issues documented: Temporal recognition bugs, code failures, 25% negative feedback
- Tight clustering: Top-5 within 31 points = high volatility environment
- Holiday timing: Dec 24-31 reduces platform activity, but also reduces late-release probability
However:
- No confirmed competitive releases announced
- Google demonstrated rapid counter-release capability (2-week response to GPT-4o)
- Late December window historically sees 0% releases
Net assessment: 50% probability, not 89%.
Probability Estimate
| Stage | Estimate |
|---|---|
| Base rate (leadership retention) | 30-40% |
| P_initial (adjusted for specifics) | 65% |
| P_revised (post stress testing) | 50% |
| P_final | 50% |
| Confidence interval (80%) | [30%, 70%] |
Translation: Coin-flip probability Google retains #1.
The Trade
| Parameter | Value |
|---|---|
| Side | NO (Google does NOT retain) |
| Entry Price | 11¢ |
| Shares | 690.9 |
| Position Size | $76 |
| Edge | +38.5% |
| Kelly/5 sizing | 8.7% of bankroll |
| Expected Value | +$255 (+29% of bankroll) |
Payoff structure:
- If NO wins: 690.9 shares × $1 = $690.90 (profit $614.90)
- If NO loses: -$76.00
Key Risks
- Model uncertainty: 40pp confidence interval reflects high uncertainty (70% inference/speculation vs 30% hard data)
- Fog of war: Companies may have stealth development; absence of announcements ≠ absence of models
- Google counter-release: 100% historical success rate; could release Gemini 3.1/Ultra if threatened
- Confidence interval naivety: ±17 points genuinely wide; true score could be higher than point estimate
Stress Testing
Pre-mortem (what makes me wrong):
- Grok 5 surprise release despite Q1 2026 announcement (Musk misdirection)
- Gemini 3 Pro score collapses below 1482 with additional votes
- OpenAI stealth GPT-5.5 release mid-December
- Google self-cannibalizes with Gemini 3.1 (still resolves YES for Google)
Red team (best argument against):
- Anchoring on "no announcements" ignores modern release patterns (1-3 day notice)
- Underweighting Google's 100% success rate (8/8) and rapid iteration capability
- Market has $1.1M liquidity suggesting informed traders; my 50% vs 89% = potential arrogance
- Confidence interval overlap exists but point estimates still favor Google
Why I'm Comfortable
Despite significant model uncertainty, the bet represents sound Bayesian reasoning:
- Base rates (60% overtaken) > current market price (11% NO)
- Edge (38.5%) exceeds confidence interval width, suggesting genuine mispricing
- Kelly/5 sizing appropriately accounts for mixed data quality
- Market likely anchors on current #1 position without weighting historical volatility
The market prices Google retention at 89% when base rates suggest 30-40%. Even accounting for Google-specific advantages (100% release success, counter-release capability), 50% represents the balanced estimate after stress testing.
Resolution Timeline
Market resolves based on LMSYS Leaderboard snapshot at December 31, 2025, 12:00 PM ET. Will track:
- Any model releases Dec 1-20 (optimal window)
- Vote accumulation rates for new models
- Gemini 3 Pro score stability (additional votes may tighten CI)
- Google counter-release signals (blog posts, API updates, NeurIPS mentions)
Thesis complete. Position opened.