Where does leverage collide?

The multiplication of force a rigid bar gives when it turns about a fulcrum: a small force applied far from the pivot balances a large force close to it, in inverse proportion to the distances. Archimedes fixed the law in On the Equilibrium of Planes (magnitudes balance at distances reciprocally proportional to their weights) and derived it from symmetry, a derivation Mach in 1883 argued already assumed what it proved. The gain in force is paid for in distance: the long arm moves further than the short one, and work is conserved. Every borrowed meaning keeps the first half of this, a small input producing a large output, and forgets the second, that the input has to travel further.[1][2]

Unit

A rigid body about a pivot, at equilibrium or in motion

Recovery means

Not applicable, the criterion is balance: whether the moments about the fulcrum sum to zero

Measured by

Ratio of load to effort, or of effort arm to load arm; torque in newton-metres

The share of a firm's assets financed by borrowing rather than by shareholders, and the amplification of returns to equity that follows: a fixed interest charge means a small change in operating profit becomes a large change in what is left for the owners. Modigliani and Miller proved in 1958 that in a frictionless market this amplification is neutral, the firm's value does not depend on how it is financed, because leverage raises the expected return on equity exactly as much as it raises its risk. Lev showed in 1974 that the same arithmetic applies to fixed operating costs: a firm with high fixed costs has operating leverage, and its equity beta rises with it. Leverage here is a ratio in the accounts, and its whole content is the fixed charge.[3][4]

Unit

A firm, at a balance-sheet date

Recovery means

Deleveraging, paying down debt or issuing equity until the ratio returns to target

Measured by

Debt to equity or debt to assets at book or market value; degree of operating leverage as the elasticity of profit to sales

The practice of making a firm's resources go further than a rival's by concentrating them, accumulating them faster, blending them into competences, conserving them and recovering them quickly. Hamel and Prahalad fixed the term in 1993 against the reigning idea of fit: a firm should choose ambitions that stretch beyond its resources and then leverage those resources to close the gap. Their 1990 article had already made the core competence the thing to be leveraged, a collective learning that can be carried across products and markets. Leverage here is a verb and a managerial programme; the input is a capability and the output is a market position. Nothing is borrowed and nothing balances.[15][5][6]

Unit

A firm, across its portfolio, over a strategic horizon

Recovery means

Not applicable, the criterion is aspiration: whether the firm closes the gap between ambition and resources

Measured by

Not measured directly; inferred from case comparisons of resource use and competitive outcome

The capacity of one party to a bargain to impose costs on the other, or to walk away at low cost, and so to move the settlement toward its own terms. Schelling fixed the strategic version in 1960: bargaining power comes from commitment, and a party that can credibly bind itself gains at the table. Fisher and Ury made it practical in 1981 with the best alternative to a negotiated agreement, leverage is having a better fallback than the other side. Levitsky and Way carried the word into comparative politics in 2006, defining Western leverage over a regime as its vulnerability to external pressure, and separating it from linkage, the density of ties that makes pressure bite. Leverage here is a relation between two actors, and it exists only in comparison.[7][8][9]

Unit

One party relative to another, in a specific bargaining situation

Recovery means

Not applicable, the criterion is the settlement: how far the outcome moves toward one side's terms

Measured by

Value of each side's outside option; asymmetry of dependence; concession patterns and outcomes

The influence an observation's position in predictor space gives it over the regression fit, read off the diagonal of the hat matrix, which maps observed responses onto fitted ones. Hoaglin and Welsch fixed the term in 1978: the element hᵢᵢ says how much the fitted value at point i depends on the response at point i, and a point far from the centre of the predictors has high leverage whether or not its response is unusual. Cook had shown in 1977 that leverage combined with the residual gives the point's influence on the estimated coefficients. Leverage here is a property of the design alone, computed before any response is looked at, and it is bounded between zero and one.[10][11]

Unit

One observation in a fitted linear model

Recovery means

Not applicable, the criterion is influence: whether removing the point changes the fit

Measured by

Diagonal of the hat matrix, with 2p/n as a conventional cut-off; Cook's distance for influence

A point in a complex system where a small change in one thing produces a large change in the system's behaviour. Meadows fixed the list in 1999, ordered from weakest to strongest: parameters and numbers at the bottom, then buffers, structures, delays, feedback loops, information flows, rules, self-organisation, goals, and, at the top, the paradigm the system arises from and the power to transcend paradigms. Her 2008 book kept the ranking and the warning that people push hardest on the low-leverage points because they are visible. Abson and colleagues in 2017 grouped the twelve into four realms and argued that sustainability research clusters at the shallow end. Leverage here is a property of a place in a structure, not of an actor, and the strongest points are the least tangible.[12][13][14]

Unit

A point of intervention in a system, ranked against other points

Recovery means

Not applicable, the criterion is depth: whether the intervention reaches a goal or paradigm rather than a parameter

Measured by

Not measured; assigned by position on Meadows's ordered list, or by simulated system response