← Back to article

Equation 18 · Why Cost and Latency Belong in the Evaluation Score, Not a Footnote

What does this equation mean?

Uλ(A)=sA−λc cA−λl lA.U_{\lambda}(A) = s_A - \lambda_c\, c_A - \lambda_l\, l_A .

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationss_A - lambda_c c_A - lambda_l l_A
Result or conditionU_λ(A)
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

UλU_{\lambda}

Symbol U_λ

U_λ is part of the quantity the equation computes from the expression on the right.

Understand this part →

AA

Symbol A

the agent.

Understand this part →

sAs_A

Symbol s_A

sAs_A is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

λc\lambda_c

Symbol lambda_c

lambdaca_c is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

cAc_A

Symbol c_A

cAc_A is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

λl\lambda_l

Symbol lambda_l

lambdala_l is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

lAl_A

Symbol l_A

lAl_A is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

=

=

The expressions on both sides represent the same quantity under the stated assumptions.

Understand this part →

See an illustrated explanation →
subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Understand this part →

subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Understand this part →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

Make that judgment explicit and it becomes a scalarized score. Choose exchange rates λc\lambda_c (accuracy points per dollar) and λl\lambda_l (accuracy points per second of latency), and define Uλ(A)=sA−λc cA−λl lAU_{\lambda}(A) = s_A - \lambda_c\, c_A - \lambda_l\, l_A . This is a legitimate way to rank agents, and it is what most procurement decisions ultimately have to do. But writing it out this explicitly makes the hidden step visible: the ranking that comes out depends entirely on λc\lambda_c and λl\lambda_l , numbers that are not properties of the agents at all. A call center with razor-thin per-ticket margins and a research lab doing one-off due-diligence work on a handful of contracts will set λc\lambda_c at wildly different values, and the two will…
Read the full surrounding passage
Make that judgment explicit and it becomes a scalarized score. Choose exchange rates λc\lambda_c (accuracy points per dollar) and λl\lambda_l (accuracy points per second of latency), and define Uλ(A)=sA−λc cA−λl lAU_{\lambda}(A) = s_A - \lambda_c\, c_A - \lambda_l\, l_A . This is a legitimate way to rank agents, and it is what most procurement decisions ultimately have to do. But writing it out this explicitly makes the hidden step visible: the ranking that comes out depends entirely on λc\lambda_c and λl\lambda_l , numbers that are not properties of the agents at all. A call center with razor-thin per-ticket margins and a research lab doing one-off due-diligence work on a handful of contracts will set λc\lambda_c at wildly different values, and the two will reasonably reach opposite conclusions about which agent to deploy, from identical measured data. A leaderboard that publishes a single blended score has made this choice for every reader, usually without saying so, and usually without saying what the choice was.

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to Why Cost and Latency Belong in the Evaluation Score, Not a Footnote

See this formula across 1 published context →

Browse the mathematical compendium →