Mathematics · Probability
Binary Log-Loss Contribution Calculator
Calculate log-loss contribution from outcome weight and predicted probability assigned to outcome.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=−a ln(b) with outcome weight=1 and predicted probability assigned to outcome=0.82.
- log-loss contribution=0.19845093872383832.
Understand Binary Log-Loss Contribution
One idea, three depths
Choose how deeply to explain Binary Log-Loss Contribution
Binary Log-Loss Contribution: Calculate log-loss contribution from outcome weight and predicted probability assigned to outcome.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Binary Log-Loss Contribution to answer this question: calculate log-loss contribution from outcome weight and predicted probability assigned to outcome? Enter outcome weight and predicted probability assigned to outcome; the calculator shows log-loss contribution. For example: outcome weight=1 and predicted probability assigned to outcome=0.82 produce log-loss contribution=0.19845093872383832. The answer tells you log-loss contribution.
Age 15Explain it to a 15-year-oldConnect it to the formula
A realized outcome contributes minus its weight times the natural logarithm of the probability assigned to it. This page evaluates the relationship directly. The rule is c=−a ln(b). Its input values are outcome weight, predicted probability assigned to outcome, and the main result is log-loss contribution. For example: outcome weight=1 and predicted probability assigned to outcome=0.82 produce log-loss contribution=0.19845093872383832.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated binary log-loss contribution relation over the valid real-number domain stated below. The implemented relation is c=−a ln(b), evaluated from outcome weight, predicted probability assigned to outcome to produce log-loss contribution. A realized outcome contributes minus its weight times the natural logarithm of the probability assigned to it. This page evaluates the relationship directly. A zero predicted probability creates unbounded loss, and probability units must be decimals.
Inputs and valid domain
- outcome weight must be a finite real number.
- predicted probability assigned to outcome must be a finite real number.
Important boundary: A zero predicted probability creates unbounded loss, and probability units must be decimals.
The formula
c=−a ln(b)
How the calculator works through it
It substitutes outcome weight, predicted probability assigned to outcome into the formula and exposes every numerical step above. The main output is log-loss contribution.
Read the result correctly
The log-loss contribution is the direct answer to “calculate log-loss contribution from outcome weight and predicted probability assigned to outcome.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
outcome weight=1 and predicted probability assigned to outcome=0.82 produce log-loss contribution=0.19845093872383832.
Where this model stops being reliable
A zero predicted probability creates unbounded loss, and probability units must be decimals.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Binary Log-Loss Contribution works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Binary Log-Loss Contribution uses c=−a ln(b). You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Probability as a modelled proportion
Probability rules are needed to interpret what the Binary Log-Loss Contribution result says about possible outcomes.
Review this foundation about 5 min
Optional enrichment
- Ordered arrangements
Counting ordered arrangements can extend Binary Log-Loss Contribution to more detailed sample spaces and event models.
Review this foundation about 5 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read outcome weight, predicted probability assigned to outcome.
- Evaluate the principal relationship: c=−a ln(b).
- Return log-loss contribution and check the domain conditions described above.
Python
from math import *
def binary_log_loss_contribution_calculator(a, b) -> float:
return (-(a * log(b)))
assert abs(binary_log_loss_contribution_calculator(1, 0.82) - 0.19845093872383832) < 1e-6 * max(1.0, abs(0.19845093872383832))
C
#include <assert.h>
#include <math.h>
double binary_log_loss_contribution_calculator(double a, double b) {
return (-(a * log(b)));
}
int main(void) {
const double expected = 0.19845093872383832;
const double actual = binary_log_loss_contribution_calculator(1, 0.82);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double binary_log_loss_contribution_calculator(double a, double b) {
return (-(a * std::log(b)));
}
int main() {
constexpr double expected = 0.19845093872383832;
const double actual = binary_log_loss_contribution_calculator(1, 0.82);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double binary_log_loss_contribution_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern log
global binary_log_loss_contribution_calculator
section .text
binary_log_loss_contribution_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-16]
call log wrt ..plt
movsd [rbp-40], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-40]
movsd [rbp-32], xmm0
pxor xmm0, xmm0
subsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = binary_log_loss_contribution_calculator(a, b)
result = (-(a * log(b)));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (-(a * Log[b]));
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Binary Log-Loss Contribution Calculator. MW SysArc Tools. https://math.mwsysarc.com/probability/binary-log-loss-contribution-calculator
MLA 9
MW SysArc. “Binary Log-Loss Contribution Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/probability/binary-log-loss-contribution-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Binary Log-Loss Contribution Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/probability/binary-log-loss-contribution-calculator.
Harvard
MW SysArc (2026) ‘Binary Log-Loss Contribution Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/probability/binary-log-loss-contribution-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_binary_log_loss_contribution_calculator_2026,
author = {{MW SysArc}},
title = {Binary Log-Loss Contribution Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/probability/binary-log-loss-contribution-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Binary Log-Loss Contribution Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/probability/binary-log-loss-contribution-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Binary Log-Loss Contribution do?
Calculate log-loss contribution from outcome weight and predicted probability assigned to outcome.
How does the Binary Log-Loss Contribution work?
The calculator applies c=−a ln(b). A realized outcome contributes minus its weight times the natural logarithm of the probability assigned to it. This page evaluates the relationship directly.
What can I learn from the Binary Log-Loss Contribution?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .