Competitive Analysis through Conditional Probability — Knowing the Enemy Reveals the Win Rate

"If you don't know the enemy, probability lies. If you know the enemy, probability becomes a weapon."

Introduction: There is no Probability in a Vacuum

Let's say we have a P(Win) = 78.5% calculated in Series Part 1. This number means "our probability of winning this deal." However, one fatal assumption is hidden here — it ignored the presence of competitors.

In reality, there is almost no sales deal without competitors. And depending on the competitor's strength, timing of entry, and strategy, our P(Win) changes dramatically.

"If competitor S enters this deal, how much does our probability change?" — This is the realm of Conditional Probability.

Part 1: Basics of Conditional Probability — Expansion of Bayes' Theorem

1.1 Conditional P(Win)

Conditional win probability when competitor $C$ exists:

P(\text{Win} | C) = \frac{P(C | \text{Win}) \cdot P(\text{Win})}{P(C)}

Where:

$P(\text{Win})$ : Base P(Win) not considering competitors
$P(C | \text{Win})$ : The proportion of past deals we won where competitor C also participated
$P(C)$ : The proportion of total deals where competitor C participates

1.2 Real-World Scenario: Competing with Vinhomes

Let's mathematically break down the situation Park Jun-hyuk faced in the Novel Edition.

Prior Data (Based on SkyLink's past 100 deals):

Overall win rate: P(Win) = 35% (35 deals won)
Proportion of deals Vinhomes participated in: P(C) = 40% (40 deals)
Proportion of the 35 won deals where Vinhomes also participated: P(C|Win) = 20% (7 deals)

P(\text{Win} | \text{Vinhomes}) = \frac{0.20 \times 0.35}{0.40} = \frac{0.07}{0.40} = 0.175 \quad (17.5\%)

The win rate, which was 35% without Vinhomes, drops to half at 17.5% when Vinhomes participates.

Conversely, when Vinhomes does not participate:

P(\text{Win} | \neg\text{Vinhomes}) = \frac{P(\neg C | \text{Win}) \times P(\text{Win})}{P(\neg C)} = \frac{0.80 \times 0.35}{0.60} = \frac{0.28}{0.60} = 0.467 \quad (46.7\%)

Strategic Insight: If Vinhomes enters the competition, the win rate drops from 35% → 17.5%, and without Vinhomes, it rises from 35% → 46.7%. The mere presence or absence of Vinhomes causes a 30%p shift in probability. This is why competitive analysis is necessary.

Part 2: Competition Impact Factor (CIF)

2.1 CIF Definition

We quantify the impact on our P(Win) for each competitor:

\text{CIF}_C = \frac{P(\text{Win} | C)}{P(\text{Win})}

If CIF = 1.0, the competitor has no impact; if 0.5, the probability is halved.

Competitor	P(Win\|C)	CIF	Interpretation
Vinhomes	17.5%	0.50	Strongest competitor. Probability halved
Nam Viet Realty	28.0%	0.80	Average competition. 20% decrease
Hoa Sen Real Estate	31.5%	0.90	Weak competition. 10% decrease
No Competition	46.7%	1.33	Rises when competition is absent

2.2 Combined Effect of Multiple Competitors

What if both Vinhomes and Nam Viet Realty participate simultaneously?

Assuming independence:

\text{CIF}_{combined} = \text{CIF}_{\text{Vinhomes}} \times \text{CIF}_{\text{Nam Viet}} = 0.50 \times 0.80 = 0.40

P(\text{Win} | \text{Vinhomes} \cap \text{Nam Viet}) = P(\text{Win}) \times 0.40 = 0.35 \times 0.40 = 0.14 \quad (14\%)

However, in reality, there is interaction between competitors. If both Vinhomes and Nam Viet participate simultaneously, the customer's psychology of "I have more options, so I will compare more carefully" comes into play, which can cause an additional drop in the probability for all companies.

This is called the Competition Crowding Penalty, and depending on the number of competitors $n$ :

\text{Crowding Factor} = \frac{1}{\sqrt{n}}

In a 3-way competition:

\text{Crowding} = \frac{1}{\sqrt{3}} = 0.577

Final adjusted P(Win):

P_{adjusted} = P(\text{Win}) \times \text{CIF}_{combined} \times \text{Crowding} = 0.35 \times 0.40 \times 0.577 = 0.081 \quad (8.1\%)

Business Interpretation: In a 3-way competition, our expected win rate is 8.1%. We must seriously reconsider whether it is worth investing manpower and costs. On the other hand, if we can eliminate one competitor, the probability rises dramatically.

Part 3: Bayesian Integration of Competitive Signals

In EXAWin, information related to competitors is processed as negative signals (added to β):

Signal	Impact	Reason
"The competitor also conducted a demo"	WN 2.0	Customer is actively comparing
"Competitor's price is 15% cheaper"	SN 5.0	Disadvantage in price competition
"Competitor passed the POC"	SN 5.0	Secured a technical alternative
"Competitor withdrew"	SA 5.0 (Positive!)	Elimination of competition
"Customer requested a reference for the competitor"	WN 2.0	Serious comparison

3.2 P(Win) Simulation based on Changes in Competitive Situation

Scenario: Current P(Win) = 70%. What happens if the following events occur?

Event	Signal	Expected P(Win) Change
Confirmed Competitor A withdrawal	SA 5.0	70% → 78~82%
Competitor B price discount attack	SN 5.0	70% → 58~62%
Customer mentions "Comparing 3 companies"	WN 2.0	70% → 65~68%
Discovered a technical flaw in Competitor C	SA 5.0	70% → 78~82%

Strategic Application: "If Competitor A drops out, P(Win) goes up to 82%" — With this information, you can focus on strategies to eliminate Competitor A (emphasizing differentiation points, resetting the customer's decision criteria).

Part 4: Competitive Advantage Analysis — Putting Math to "Why Choose Us"

4.1 Tracking Differentiation Signals

To win in a competitive environment, differentiation points must be communicated to the customer. EXAWin tracks signals related to differentiation separately:

Area of Differentiation	Customer Reaction Signal	Frequency	Impact
Technology	"The technology is better"	12 times	SA 5.0
Price	"The price is reasonable"	8 times	WA 2.0
Service	"The response is fast"	15 times	WA 2.0
Reference	"The case study is convincing"	6 times	SA 5.0

Based on this data, we can calculate our company's Competition Win Factor:

\text{Win Factor}_k = \frac{\text{Number of deals won due to this differentiation}}{\text{Total number of deals where this differentiation was mentioned}}

Area of Differentiation	Deals Mentioned	Won	Win Factor
Technology	25 deals	18 deals	72%
Price	30 deals	12 deals	40%
Service	35 deals	20 deals	57%
Reference	15 deals	11 deals	73%

Strategic Insight: Technology (72%) and References (73%) show the highest Win Factors. Highlighting these two early in the sales process is a core strategy to increase competitive win rates. Price competition (40%) has the lowest win rate — the data proves that fighting on price leads to losing.

Part 5: Competitive Intelligence Dashboard

5.1 Real-time Competition Board

Deal	Competitors	CIF	Adjusted P(Win)	Strategy
Company A ERP	Company S, Company L	0.45	35.3%	Focus on technical differentiation
Company B Cloud	None	1.33	82.9%	Fast closing
Company C Security	Company K	0.75	63.9%	Target with references
Company D AI	Company S, Company O, Company G	0.25	11.3%	Consider abandoning

5.2 Competitive Scenario Planning

Company D AI deal — Competing against 3 competitors. Adjusted P(Win) = 11.3%.

What-if Scenarios:

If Company S drops out: CIF 0.25 → 0.42, P(Win) = 18.9%
If Company O + Company G drop out (Only Company S remains): CIF 0.25 → 0.50, P(Win) = 22.6%
If everyone drops out (Monopoly): CIF 1.33, P(Win) = 59.9%

"To beat Company S at Company D, what differentiation points must be injected and at what time?" — This is the strategic question provided by conditional probability.

Conclusion: Competition is Unavoidable, but it is Analyzable

The presence of competitors is not an object of fear, but an object of analysis.

Utilizing Conditional Probability and CIF allows you to:

Quantify the impact of each competitor
Simulate competitor elimination scenarios
Verify the effectiveness of differentiation strategies with data
Objectively identify deals to abandon

"If you know the enemy and know yourself, you need not fear the result of a hundred battles." — This classic principle from Sun Tzu's Art of War is reborn in 2026 under the name of Conditional Probability.

In Series Part 4 (Final Part), we will cover Sales Strategy Optimization using Bayesian A/B Testing — "Which sales method is more effective? Probability provides the answer."

Author: EXA Bayesian Research Lab
Published in: EXAWin Technical Series — Vol. 3
Keywords: #CompetitiveAnalysis #ConditionalProbability #CIF #BayesianStrategy #EXAWin

BA04-4. [Series Part 3] Competitive Analysis through Conditional Probability — Knowing the Enemy Reveals the Win Rate

Competitive Analysis through Conditional Probability — Knowing the Enemy Reveals the Win Rate

Introduction: There is no Probability in a Vacuum