The Confirming vs. Redirecting Event

Core insight: Most celebrated milestones in any domain are confirmatory — they dramatically express a trajectory already established by earlier, quieter decisions. The genuinely decisive moments are often earlier, less visible, and less celebrated, precisely because they occurred before the structural advantage had become overwhelming. Distinguishing redirecting events from confirming ones is the analytical discipline that locates where the real decisions were made — and where the real decisions will be made.


How Each Book Addresses This

Edward Shepherd Creasy - The Fifteen Decisive Battles of the World — The Exclusion Principle: The Vault’s Foundational Statement

Creasy’s entire analytical method rests on this distinction. His book is not a list of the most famous battles or the largest battles or the most dramatic ones — it is a list of battles whose alternate outcome “would have essentially varied the drama of the world in all its subsequent scenes.” This definition immediately generates a companion discipline: the exclusion of events that were merely confirmatory.

The exclusion cases:

Salamis (480 BC) excluded: The Battle of Salamis — the famous Greek naval victory where the Athenian fleet destroyed the Persian fleet in the straits near Athens — is among the most celebrated battles in Western history. Creasy excludes it. His reasoning: Marathon (490 BC) had already established Greek military credibility, broken the myth of Persian invincibility, and demonstrated that Greek citizen-soldiers fighting for their own civic institutions could defeat a Persian professional army. Salamis confirmed and dramatized the trajectory Marathon had set. Had Salamis gone the other way — had the Persian fleet prevailed — Creasy argues that the Greeks retained the land capability Marathon demonstrated, and the Persian campaign would still have faced the same obstacles that had already produced Marathon’s result. The civilizational trajectory was already set; Salamis was its dramatic expression, not its cause.

Austerlitz (1805) excluded: Napoleon’s greatest tactical victory, which ended the Third Coalition and produced the Treaty of Pressburg, is excluded because Napoleon himself reversed its apparent consequences. Within seven years, the political and military situation Austerlitz appeared to settle had been reopened, and Waterloo undid everything Austerlitz had built. A confirmatory event cannot be a decisive one: if the victor can reverse the outcome by subsequent action, the original event was not civilizationally redirecting.

Agincourt (1415) excluded: Henry V’s famous victory over the French, celebrated in Shakespeare, is excluded because the English position in France that Agincourt established was almost entirely undone within a generation. Joan of Arc’s campaigns reversed the territorial and political consequences; France eventually expelled the English entirely. Agincourt was a brilliant confirmation of what excellent English tactical capability could achieve under optimal conditions; it did not redirect the long-run trajectory of English-French relations.

The positive cases — what makes a battle genuinely redirecting:

Creasy’s included battles share a structural feature: they occurred at moments of genuine uncertainty, before the structural advantage had resolved in either direction, and their outcome established conditions that compounded forward through subsequent centuries rather than being reversed. Marathon enabled Periclean Athens; Teutoburg Forest preserved Germanic cultural independence for 1,500 years; Saratoga triggered the French alliance that converted a failing colonial rebellion into a global war Britain could not win.

The diagnostic — the counterfactual reversal test:

An event is redirecting if its reversed outcome would have materially altered the subsequent civilizational trajectory. An event is confirmatory if its reversed outcome would have produced a different episode but the same eventual trajectory. The test is: “What would be fundamentally different five decades out if this had gone the other way?” Redirecting events produce a different answer for the world; confirming events produce a different answer for the immediate participants but not for the long-run trajectory.

The fame/decisiveness inversion:

Creasy’s selections reveal a counterintuitive pattern: the most famous battles are often the least decisive in the full sense. They are famous because they were dramatic visible expressions of outcomes that structural forces had already made likely. The genuinely decisive battles occurred earlier, at moments before the structural advantage was established, when the outcome was genuinely uncertain — and because they occurred at the hinge before momentum resolved, they are often less famous than the battles that followed. Marathon is famous; Callimachus is barely remembered. Saratoga is known; the specific diplomatic calculation that made French intervention contingent on exactly this kind of visible military success is not.

How to apply:

  • The Creasy Exclusion applied to organizational history: before celebrating any major milestone, apply the reversal test — “Would this outcome have been meaningfully different had this event not occurred?” Confirmatory milestones may deserve celebration for morale; they do not deserve strategic credit as the source of the trajectory.
  • Build an explicit distinction between your organization’s “Marathon” (the genuine hinge decision that set the trajectory) and your “Salamis” (the dramatic visible confirmation). Study the Marathon rigorously; celebrate the Salamis appropriately.
  • The prospective application: identify candidate redirecting events before they occur — decisions whose reversed outcome would most change the five-to-ten-year trajectory. Apply disproportionate analytical resources there vs. the confirmatory milestones that generate activity without redirecting trajectory.

Adam Tooze - The Wages of Destruction — The Oil Campaign vs. Area Bombing: The Operational Parallel

Tooze’s analysis of Allied strategic bombing 1940–1945 is the redirecting/confirming distinction applied to operational targeting — and provides the clearest demonstration of the cost of applying confirmatory-event logic to what requires redirecting-event identification.

The confirmatory target set:

For most of the Allied bombing campaign, aircraft attacked visible German targets: factories, railways, city centers, industrial facilities. These targets were real and large and clearly connected to the German war effort. They produced dramatic visible results: cities reduced to rubble, factories destroyed, transport links severed. But German production continued to grow through 1944 despite sustained bombing, because Germany could repair, disperse, and substitute. The targets were confirmatory: attacking them produced visible dramatic results that confirmed the campaign was active, without redirecting the trajectory of German productive capacity.

The redirecting target:

German synthetic fuel production — and Romanian oil imports — was the genuine redirecting node. Fuel was irreplaceable (no rapid substitution), non-dispersible (refineries are fixed infrastructure), and the German system’s critical bottleneck (every military operation depended on it). When the US 15th Air Force began attacking it systematically in May 1944, the effect was visible within weeks. Luftwaffe training was curtailed for lack of fuel; armored units began rationing; the Ardennes offensive was designed around capturing Allied fuel dumps because German forces literally could not sustain the operation from organic supplies. Months of oil campaign targeting produced the decisive effect that years of area bombing had not.

The structural parallel to Creasy:

Both the Exclusion Principle and the oil campaign lesson describe the same analytical discipline applied in different domains:

  • Creasy: “Which historical battle was the genuine redirecting moment? Exclude the dramatic confirming ones.”
  • Tooze: “Which node in the German war machine is the genuine redirecting chokepoint? Exclude the visible confirming targets.”

The cost of misidentifying confirmatory events as redirecting ones: years of bombing effort (vast resources, lives, material) producing negligible strategic effect; two extra years of war according to postwar bombing surveys. The cost in organizational analysis: strategic credit assigned to the visible milestone rather than the earlier quieter decision; the real hinge studied less because it is less famous.

How to apply:

  • The confirmation rule: before selecting any major campaign target (physical or analytical), ask “is this the redirecting node, or is it the confirmatory expression of a trajectory I cannot redirect by attacking it?” The genuine redirecting nodes are often unglamorous, earlier in the causal chain, and require the question “what is irreplaceable, non-dispersible, and structurally critical?” rather than “what is visible and large?”
  • The cost-of-misidentification calculation: build the analysis first, before committing the campaign. Postwar bombing surveys are the organizational equivalent of postmortems that reveal the correct answer after the cost has been paid.

Isaac Asimov - Foundation Series — Seldon Crises as Institutionalized Identification of Redirecting Events

Hari Seldon’s Psychohistory provides the vault’s only institutional response to the confirming/redirecting distinction: a formal system designed to identify, in advance, which events are genuine trajectory redirections (Seldon Crises) vs. which are confirmatory expressions of the Plan’s existing momentum.

The Seldon Crisis as a redirecting event:

A Seldon Crisis is a specific structural feature of Psychohistory: a moment when the historical trajectory reaches a genuine branch point — where the outcome is not yet determined by the existing momentum and where a specific decision by a specific actor will redirect the trajectory for the subsequent generation. The Foundation’s responses to each Seldon Crisis are the redirecting events in its history. The political, economic, and military developments between Crises are the confirmatory phase: the working-out of the trajectory that the Crisis established.

Salvor Hardin’s “Violence is the last refuge of the incompetent”:

The First Foundation’s early Seldon Crises reveal the redirecting/confirming distinction clearly. Each Crisis produces a decision that redirects the Foundation’s next trajectory (Hardin’s use of religious diplomacy to neutralize the Anacreon threat; the Merchant Princes’ use of economic integration to make the Foundation indispensable). These decisions look modest at the time — Hardin doesn’t fight a war, he wins without fighting. The dramatic visible events (the Anacreon threat, the Galactic Empire’s collapse) are the confirmatory context; the actual redirecting moments are the specific decisions that convert the Crisis’s branch point into the trajectory Seldon’s Plan requires.

The Second Foundation as redirecting-event monitor:

The Second Foundation’s institutional purpose is precisely to distinguish between genuine Seldon Crises (redirecting moments requiring intervention) and the normal unfolding of the Plan (confirmatory expressions of established momentum). The Second Foundation intervenes only at genuine redirecting moments; intervening at confirmatory moments would disrupt the momentum that is correctly playing out. This is the institutionalized version of Creasy’s analytical discipline: a formal system for distinguishing redirecting events from confirming ones, and responding appropriately to each.

The Mule as an unrecognized redirecting event:

The Mule represents the redirecting/confirming distinction’s hardest failure mode: the Second Foundation’s framework was calibrated to identify certain types of redirecting events (Seldon Crises of the type Psychohistory could model), and the Mule was a redirecting event of a type the framework could not identify. The Second Foundation had been correctly identifying confirmatory vs. redirecting events within its model’s scope; the Mule was outside that scope. The framework failure was exactly Creasy’s retrospective bias problem: you can only identify redirecting events whose causal chains you can trace; events whose causal chains your model cannot represent are invisible until after the redirect has occurred.

How to apply:

  • The Seldon principle for organizational monitoring: build a monitoring system that distinguishes between “business as usual” (the Plan’s confirmatory unfolding) and “genuine branch points” (moments requiring high-stakes decisions that will redirect trajectory). Most organizational intelligence systems treat all significant events equally; a Seldon-inspired system weights events by their redirecting potential.
  • The Second Foundation diagnostic: identify the class of redirecting events that your monitoring system cannot currently see. The Mule-equivalent in any organization is the type of disruption whose causal chain runs outside the variables your framework tracks. Name it before it arrives.

Sun Tzu - The Art of War — Win Before Fighting: The Pre-Battle Phase as Redirecting Work, the Battle as Confirmation

Sun Tzu makes the confirming/redirecting distinction the explicit structural logic of his entire strategic framework: “Victorious warriors win first and then go to war, while defeated warriors go to war first and then seek to win.” The battle is the confirming event. The pre-positioning phase — intelligence gathering, five-factor assessment, adversary shaping, shi accumulation, condition-building — is the redirecting work. By the time the battle begins, the outcome is already largely determined by the redirecting phase that preceded it.

The battle as confirmatory expression:

“Easy victories are the hallmark of superior pre-positioning, not special talent applied in crisis.” The general who wins difficult battles through extraordinary individual genius is demonstrating that the redirecting phase failed — tactical heroics are compensating for a structural disadvantage that should have been corrected before engagement. The general who wins what look like easy victories has done the redirecting work so completely that the battle is merely its confirmation. The battle that requires a miracle to win is not a redirecting event — it is the high-cost confirmatory expression of an inadequate redirecting phase.

Shi as redirecting work made visible only at release:

The concept of shi (structural momentum) maps precisely onto the redirecting/confirming distinction. Shi is built in the invisible pre-battle phase — positioning, morale alignment, timing, surprise construction — and released at the battle moment. The battle (the product launch, the market entry, the offensive) looks decisive and sudden from outside. But the actual redirecting work was the prior shi accumulation: the years of preparation that made the release look effortless. Competitors observing the confirming event (the battle, the launch) without having seen the redirecting work that preceded it will systematically misattribute the outcome to tactical genius rather than strategic preparation.

The Five-Factor Audit as redirecting-work assessment:

Sun Tzu’s five-factor pre-engagement audit (Moral Law, Heaven, Earth, Commander, Discipline) is a diagnostic tool for determining whether the redirecting work has been sufficiently done. Net advantage across the five factors means the structural conditions have been redirected in your favor before engagement; net disadvantage means the redirecting phase is incomplete and the battle should not begin. Engaging without completing the five-factor redirecting work is the strategic equivalent of fighting before winning — confirming failure rather than confirming success.

The supreme expression — breaking resistance without fighting:

“The supreme art of war is to subdue the enemy without fighting.” The highest practitioner completes the redirecting work so thoroughly that the adversary’s resistance collapses before the battle occurs. The battle is not needed because the outcome is already determined. This is the redirecting/confirming distinction taken to its logical extreme: the redirecting phase is so complete that the confirming phase is unnecessary. No one witnesses the decisive work; the absence of a battle is the evidence it was done.

How to apply:

  • Before any engagement, apply the Win Before Fighting test: “If we begin this engagement today, is the outcome largely determined by the structural conditions we have already built, or do we need a tactical miracle to win?” If the latter, you are entering a confirming event without completing the redirecting work. Build the missing conditions first.
  • Apply shi analysis prospectively: “What structural momentum are we building right now that is not yet visible to our adversaries?” If the answer is “nothing in particular,” your next engagement will look like a difficult battle rather than a foregone conclusion.
  • The five-factor audit is the redirecting-phase completion test: score both sides honestly on all five factors. Net disadvantage on any factor is redirecting work still required — not a reason to engage and hope tactical heroism compensates.

Graham Allison - Destined for War — The Sarajevo Principle: Structural Stress as the Redirecting Cause, Trigger as the Confirming Detonator

Allison’s most analytically important contribution to historical causation is his systematic application of the confirming/redirecting distinction to great-power conflict: the specific trigger that starts a war is almost never its cause. Sarajevo — the 1914 assassination of Archduke Franz Ferdinand — is the vault’s single clearest case of a confirming event being systematically misidentified as a redirecting one.

The confirming event:

The Sarajevo assassination is one of the most discussed triggering events in history. It has been analyzed exhaustively: the specific conspirators, the two assassination attempts on the same day, the wrong turn that put Franz Ferdinand in front of Gavrilo Princip. This specificity is the signal of the confirming event: the mechanism of the specific trigger is fully reconstructable, and none of it explains the war. Austria-Hungary had handled assassinations before without triggering world wars. The mechanism of the specific trigger is not the relevant variable.

The redirecting event — already complete:

By June 1914, the structural charge had been building for 16 years. Germany’s Tirpitz naval program (1898) had triggered the Anglo-French Entente (1904) and Anglo-Russian Entente (1907). The alliance system had been designed as a deterrent but was architected for maximum amplification when any trigger fired. The mobilization timetables — the Schlieffen Plan, Russian mobilization requirements, French defensive commitments — had removed decision-making flexibility from the leaders who would need to respond to any crisis. The redirecting work (the building of the structural charge) had been complete for years before Sarajevo. The assassination was the detonator for an already-primed explosive.

The counterfactual reversal test:

Creasy’s diagnostic applied to Sarajevo: “Had this event gone the other way — had the assassination failed — would the subsequent trajectory have been materially different?” The answer is almost certainly no. If not Sarajevo, the structural stress would have found a different trigger in 1914, 1915, or 1916. The Morocco crises (1905, 1911) and the Agadir crisis (1911) had already demonstrated the system’s readiness to amplify any trigger. Sarajevo passed the test: removing it does not change the eventual trajectory — it only changes which specific incident became the detonator.

The practical implication — the structural stress is the priority:

Allison argues that 16 historical cases all follow the same confirming/redirecting structure: each war has a specific trigger (always fully documented, often extensively analyzed) and a structural cause (the power-transition dynamic building for years before the trigger fires). American strategic analysis consistently focuses on managing specific triggers (diplomacy around specific incidents, arms control on specific weapons systems) while underinvesting in managing the structural charge (institutional embedding, crisis architecture, shared higher-order goals, core vs. peripheral interest distinction). This is the confirming/redirecting error at civilizational scale: investing in the detonator-removal program while the explosive builds unaddressed.

The cross-case pattern in Allison’s 16 cases:

Allison’s historical database reveals that every case that ended in war has this structure: the specific trigger is documented, discussed, and often blamed for the war; the structural power-transition dynamic (the actual redirecting event — the period of rising-power challenge and ruling-power fear building over years or decades) is less celebrated because it predated the dramatic visible detonation. The redirecting work is always quieter and earlier; the confirming trigger is always more dramatic and more studied. This is Creasy’s fame/decisiveness inversion applied to warfare at scale.

How to apply:

  • For any international crisis, apply the Creasy counterfactual test before treating it as the cause: “If this specific incident had not occurred, would the conflict have happened eventually anyway?” If yes, the incident is the detonator, not the explosive. Invest in the explosive-management program.
  • The Sarajevo diagnostic for current US-China tensions: which specific flashpoints (Taiwan, South China Sea, cyber) are being treated as the primary risk when the structural charge (the Thucydides Trap dynamic) is the actual risk? Managing the flashpoints while the structural charge builds is the Sarajevo error in real time.
  • Building the structural crisis architecture (the 12 clues for peace) is redirecting work: it addresses the charge, not the detonator. Diplomatic communication during specific incidents is confirmatory crisis management: it addresses the detonator while the charge persists.

Jared Diamond - Guns, Germs, and Steel — Cajamarca as the Vault’s Most Extreme Confirming Event

The Spanish conquest of the Inca Empire in 1532 provides the vault’s most extreme confirming event: 168 Spaniards capturing an emperor commanding 80,000 soldiers. Diamond uses Cajamarca to demonstrate that every visible mechanism of the conquest (steel, horses, firearms, organized military doctrine, epidemic immunity) was fully in place thousands of years before 1532 — not as the product of any human planning for this specific confrontation, but as the output of geographic and ecological starting conditions established at the end of the last Ice Age.

Why Cajamarca is confirming, not redirecting:

Apply Creasy’s counterfactual reversal test: had Cajamarca gone differently — had Atahualpa’s forces destroyed Pizarro’s 168 men — would the subsequent trajectory have been materially different? Diamond’s answer is almost certainly no. The Spanish had epidemic immunity that the Incas lacked; epidemics had already swept through the Americas ahead of European contact, killing up to 90% of the population and destabilizing the Inca political structure before any battle was fought. The Spanish had steel weapons, horses, and firearms; the Incas had none. Even if Cajamarca had been a Spanish defeat, subsequent waves of conquerors with the same biological and technological advantages would have produced the same ultimate outcome through different particulars.

The redirecting events — 13,000 years upstream:

The genuine redirecting events occurred at the end of the Pleistocene epoch and in the subsequent millennia of Eurasian agricultural development:

  • The near-total extinction of large mammals in the Americas (c. 11,000 BC) removed the biological foundation for food production surplus that builds civilizational complexity
  • The survival of domesticable large mammals in Eurasia (horses, cattle, sheep, pigs) initiated the food production chain that, over 11,000 years, produced the literacy, political organization, and metalworking that armed the Spanish
  • The epidemic immunity that preceded the conquest by decades was built over millennia through livestock proximity in Eurasia — fully accumulated before 1532 and invisible to both parties at the moment of contact

How to apply:

  • The Cajamarca diagnostic: when a dramatic asymmetric outcome occurs (conquest of 80,000 by 168), the confirming/redirecting test asks: could the losing party have changed the outcome by performing differently in this specific engagement? If not — if the structural advantage was so complete that the encounter merely expressed it — the decisive work was done elsewhere, earlier.
  • Apply this to any competitive rout: the rout is almost always a confirming event. The redirecting events that made the rout inevitable occurred earlier, in the less visible conditions that structured the competitive landscape before the confrontation.

Cross-Book Pattern

All four books document the same structural insight from different domains — historical analysis, operational targeting, strategic institutional design, and geopolitics:

BookThe Confirming EventsThe Redirecting EventsThe Cost of Misidentification
Edward Shepherd Creasy - The Fifteen Decisive Battles of the WorldSalamis (confirmed Marathon), Austerlitz (reversed by Napoleon), Agincourt (undone within a generation) — famous, dramatic, celebrating large visible resultsMarathon, Teutoburg Forest, Saratoga — quieter, earlier, occurring at moments of genuine uncertainty before structural advantage resolvedAnalytical credit assigned to the famous battle rather than the genuine hinge; the real redirecting decision studied less because it is less celebrated
Adam Tooze - The Wages of DestructionArea bombing (visible factories, railways, cities) — dramatic, large-scale results that confirmed the campaign was active without redirecting German productive trajectoryOil campaign (synthetic fuel plants, Romanian imports) — unglamorous, systemic, attacking the irreplaceable non-dispersible chokepointTwo extra years of war; postwar bombing surveys confirmed the redirecting analysis was available before the campaign; the cost was the time spent on confirmatory targeting
Isaac Asimov - Foundation SeriesConfirmatory phase between Seldon Crises — the political, economic, and military developments that express the trajectory the preceding Crisis establishedSeldon Crises — genuine branch points where specific decisions redirect the next generation’s trajectory; the Mule as the unrecognized redirecting event whose causal chain Psychohistory could not modelSecond Foundation intervention at confirmatory moments would disrupt working momentum; failure to identify the Mule as a redirecting event nearly destroyed the Plan’s entire long-run trajectory
Sun Tzu - The Art of WarThe battle itself — the visible engagement that confirms what pre-positioning already decided; the difficult battle requiring tactical miracles (evidence that the redirecting pre-positioning phase was inadequate); “easy victories” that look like tactical genius but are actually the confirmatory expression of structural advantages built invisiblyThe pre-battle phase: intelligence gathering, five-factor assessment, adversary shaping, shi accumulation — all invisible, all redirecting; the supreme expression: no battle at all, because the redirecting work was so complete that resistance collapsed before engagementMisidentifying the battle as the decisive moment (rather than the pre-positioning work) concentrates resources on tactical execution rather than strategic preparation; tactical heroics compensate for redirecting failure at high cost — and are celebrated as brilliance rather than identified as evidence that the redirecting phase was insufficient
Graham Allison - Destined for WarSarajevo (1914) and all specific triggers in 12 of 16 war cases — fully documented, extensively analyzed, routinely blamed for the wars they detonatedThe structural power-transition dynamic (the Thucydides Trap building over years or decades — Germany’s Tirpitz program 1898-1914; China’s economic and military growth 1978-present) — quieter, earlier, less visible before the detonationDiplomatic investment in trigger-management (specific incidents, specific arms control) while the structural charge builds unaddressed; the Sarajevo error — removing the detonator while the explosive accumulates
Jared Diamond - Guns, Germs, and SteelCajamarca (1532) — 168 Spaniards capturing the Inca emperor with 80,000 soldiers present; every visible mechanism of the conquest (steel, horses, firearms, organized military doctrine)The ecological starting conditions established 13,000 years earlier: which domesticable species survived on which continent, producing the food production chains that built European civilization’s complexity; the epidemics that swept ahead of the Spanish, killing up to 90% of the native population before any military confrontation — built by millennia of livestock proximity in Eurasia and invisible to both parties at CajamarcaEven if Cajamarca had failed, subsequent waves of conquerors with the same biological and technological advantages would have produced the same outcome; no individual battle was the redirecting event — the entire conquest was the confirming expression of a structural advantage built over 13,000 years

The shared diagnostic: The redirecting event is almost always earlier in the causal chain than the confirming one. It occurs before structural advantage has resolved, at a moment of genuine uncertainty, and its causal chain is less visible than the confirmatory events that follow. The confirming events are famous because they dramatically express the trajectory the redirecting event established; the redirecting events are less famous because they occurred before the trajectory was visible.

The shared failure mode: Analytical resources (attention, strategic credit, postmortem analysis) concentrate on the visible confirming events and underfund the quieter redirecting ones. This produces misattribution of causation, misallocation of strategic credit, and misinvestment in campaigns that attack confirming targets rather than redirecting chokepoints.

The correction discipline: Apply the counterfactual reversal test before assigning credit or designing campaigns. “Had this event gone the other way, would the subsequent trajectory have been materially different?” Events that pass this test are redirecting; events that fail it (because the trajectory was already established) are confirming. Build monitoring systems and credit-assignment practices that distinguish between these categories explicitly.


  • Concept - Focus & Simplification — The redirecting event is the analytical chokepoint; focus discipline identifies it and assigns disproportionate resources there; the confirming event is the visible secondary target that unfocused analysis attacks instead
  • Concept - Accumulation vs Performance Theater — Celebrating confirmatory milestones is the historical-analysis form of performance theater: dramatic visible results that confirm the audience the campaign is active, while the genuine productive accumulation (the earlier redirecting decision) is underacknowledged
  • Concept - Feedback Loops & Reality — Confirmatory events produce misleading feedback: they look like evidence that the campaign is working (because something dramatic happened) when they are actually evidence that the trajectory was already set; the redirecting event is the genuine feedback signal for causal attribution
  • Concept - Big Bets & Calculated Risk — A calculated big bet is one whose diagnosis correctly identifies the redirecting event and commits resources to it; a reckless bet misidentifies a confirming event as redirecting and invests in the wrong node