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SKILL.md
Innovation Management Guide
A skill for conducting research on innovation management, technology strategy, and R&D performance. Covers innovation measurement, technology forecasting, diffusion modeling, patent-publication linkage, and bibliometric analysis of research portfolios.
Innovation Measurement
Key Innovation Metrics
Metric
Definition
Data Source
R&D intensity
R&D spending / Revenue
Annual reports, Compustat
Patent count
Granted patents per year
USPTO, EPO
Citation-weighted patents
Patents weighted by forward citations
PatentsView
New product revenue share
Revenue from products < 3 years old
Internal data
Time to market
Concept to commercial launch
Project records
Innovation efficiency
Revenue from new products / R&D spend
Combined internal data
Building an Innovation Scorecard
import pandas as pd
import numpy as np
def compute_innovation_scorecard(firm_data: pd.DataFrame) -> pd.DataFrame:
"""
Compute a multi-dimensional innovation scorecard for firms.
firm_data columns: firm_id, rd_spend, revenue, patents_filed,
patents_granted, citation_count, new_product_revenue, employees
"""
scorecard = pd.DataFrame()
scorecard["firm_id"] = firm_data["firm_id"]
# Input metrics
scorecard["rd_intensity"] = firm_data["rd_spend"] / firm_data["revenue"]
scorecard["rd_per_employee"] = firm_data["rd_spend"] / firm_data["employees"]
# Output metrics
scorecard["patent_yield"] = (
firm_data["patents_granted"] / (firm_data["rd_spend"] / 1e6)
)
scorecard["citation_impact"] = (
firm_data["citation_count"] / firm_data["patents_granted"].clip(lower=1)
)
scorecard["new_product_share"] = (
firm_data["new_product_revenue"] / firm_data["revenue"]
)
# Efficiency
scorecard["innovation_efficiency"] = (
firm_data["new_product_revenue"] / firm_data["rd_spend"]
)
# Normalize to percentile ranks within the sample
for col in scorecard.columns[1:]:
scorecard[f"{col}_rank"] = scorecard[col].rank(pct=True)
# Composite score (equal weights)
rank_cols = [c for c in scorecard.columns if c.endswith("_rank")]
scorecard["composite_score"] = scorecard[rank_cols].mean(axis=1)
return scorecard.sort_values("composite_score", ascending=False)
Technology Diffusion Models
Bass Diffusion Model
The Bass model is the foundational framework for forecasting technology adoption:
from scipy.optimize import curve_fit
def bass_model(t: np.ndarray, p: float, q: float, m: float) -> np.ndarray:
"""
Bass diffusion model for cumulative adoption.
t: time periods (0, 1, 2, ...)
p: coefficient of innovation (external influence)
q: coefficient of imitation (internal influence)
m: market potential (total eventual adopters)
Returns cumulative adoption at each time period.
"""
return m * (1 - np.exp(-(p + q) * t)) / (1 + (q / p) * np.exp(-(p + q) * t))
def bass_incremental(t: np.ndarray, p: float, q: float, m: float) -> np.ndarray:
"""Bass model incremental (new adopters per period)."""
F = bass_model(t, p, q, m) / m
f = (p + q * F) * (1 - F)
return m * f
def fit_bass_model(adoption_data: np.ndarray) -> dict:
"""
Fit Bass diffusion parameters to observed adoption data.
adoption_data: cumulative adoption counts per period.
"""
t = np.arange(len(adoption_data))
try:
popt, pcov = curve_fit(
bass_model, t, adoption_data,
p0=[0.01, 0.3, adoption_data[-1] * 2],
bounds=([0, 0, adoption_data[-1]], [1, 2, adoption_data[-1] * 10]),
maxfev=10000,
)
return {
"p_innovation": round(popt[0], 6),
"q_imitation": round(popt[1], 6),
"m_potential": round(popt[2], 0),
"peak_period": round(np.log(popt[1] / popt[0]) / (popt[0] + popt[1]), 1),
"q_p_ratio": round(popt[1] / popt[0], 2),
}
except RuntimeError:
return {"error": "convergence_failed"}
Typical Bass Parameters by Technology Category
Technology
p (innovation)
q (imitation)
q/p ratio
Consumer electronics
0.01-0.03
0.3-0.5
10-50
Enterprise software
0.005-0.02
0.2-0.4
10-80
Medical devices
0.001-0.01
0.1-0.3
10-300
Social media platforms
0.03-0.10
0.5-0.8
5-25
Bibliometric Analysis of R&D Portfolios
Publication Portfolio Analysis
def analyze_research_portfolio(publications: pd.DataFrame) -> dict:
"""
Bibliometric analysis of an organization's research portfolio.
publications columns: doi, title, year, journal, citations,
fields (list), authors (list), affiliations (list)
"""
# Publication trend
annual_pubs = publications.groupby("year").size()
# Citation impact
citation_stats = {
"total_citations": publications.citations.sum(),
"mean_citations": publications.citations.mean(),
"median_citations": publications.citations.median(),
"h_index": compute_h_index(publications.citations.values),
}
# Research field distribution
all_fields = []
for fields in publications.fields:
all_fields.extend(fields)
field_dist = pd.Series(all_fields).value_counts().head(20)
# Collaboration patterns
collab_rate = publications.affiliations.apply(
lambda x: len(set(x)) > 1
).mean()
return {
"total_publications": len(publications),
"annual_trend": annual_pubs.to_dict(),
"citation_impact": citation_stats,
"top_fields": field_dist.to_dict(),
"collaboration_rate": round(collab_rate, 3),
}
def compute_h_index(citations: np.ndarray) -> int:
"""Compute h-index from an array of citation counts."""
sorted_cites = np.sort(citations)[::-1]
h = 0
for i, c in enumerate(sorted_cites):
if c >= i + 1:
h = i + 1
else:
break
return h
Technology Forecasting Methods
S-Curve Analysis
Technology performance typically follows an S-curve pattern:
Emergence phase: Slow initial growth, high uncertainty
