Esports Math Glossary
Authoritative mathematical definitions, analytical formulations, and empirical worked examples for 25 foundational concepts in esports probability, game theory, and in-play market trading.
Rating Systems & Volatility
(4)Elo Rating System
#P(A) = \frac{1}{1 + 10^{(R_B - R_A)/400}}, \quad R_A' = R_A + K \cdot (S_A - P(A)) A zero-sum skill rating algorithm calculating comparative win probabilities based on point differentials. Used as the historical foundation for CS2 and Dota 2 team power rankings.
Glicko-2 Rating System
#g(\text{RD}) = \frac{1}{\sqrt{1 + 3 q^2 \text{RD}^2 / \pi^2}}, \quad q = \frac{\ln(10)}{400} An advanced Bayesian rating framework created by Mark Glickman that expands classical Elo by modeling uncertainty through Rating Deviation (RD) and skill volatility (sigma).
Rating Deviation (RD)
#\text{RD}' = \sqrt{\text{RD}^2 + c^2 \cdot \Delta t} A measure of confidence in a player or team's estimated rating, equivalent to one standard deviation in a Gaussian distribution. RD inflates over inactivity intervals and collapses after matches.
K-Factor Calibration
#\Delta R = K \cdot (S - E) The sensitivity multiplier determining how many rating points are transferred per match outcome. High K-factors (32+) provide rapid reactivity but excessive noise; low K-factors (16) provide long-term stability.
Map Pool & Veto Game Theory
(4)Map Pool Depth Metric
#\text{MPD} = \sum_{m \in \text{Pool}} \mathbf{1}_{\{WR_m \ge 0.50\}} \cdot \ln(N_m + 1) Quantitative index measuring the breadth and statistical viability of a team across the 7 Active Duty maps, weighted by sample volume and winrate thresholds.
Permaban Optimization
#\text{BanRate}_m = \frac{N_{\text{bans}, m}}{N_{\text{drafts}}} \ge 0.85 The map a team systematically vetos in the first ban phase across all official fixtures, eliminating exposure to low practice hours and forcing opponents into contested ground.
Veto Minimax Game Theory
#\max_{p \in \text{Picks}} \min_{b \in \text{Bans}} \mathbb{E}[\text{WinProbability}(p, b)] The algorithmic game-theoretic sequence where each team makes ban and pick decisions that maximize their worst-case series payoff against a rational opponent.
Best-of-Series Compounding Probability
#P(\text{Bo3}) = p_1 p_2 + p_1 (1 - p_2) p_3 + (1 - p_1) p_2 p_3 The binomial path summation calculating the overall probability of winning a Bo3 or Bo5 series from individual map win probabilities.
In-Play Momentum & Economy
(7)Pistol Round Cascade Factor
#P(\text{MapWin} \mid \text{WinBothPistols}) \approx 0.742 The structural multiplier where winning a pistol round triggers high-probability conversion of the subsequent anti-eco round, producing an immediate 2-0 score momentum.
Economy Reset
#\text{LossBonus} = \min(3400, 1400 + 500 \cdot L) A situation where a team loses a round immediately after winning one, capping their loss bonus at $1,400 and forcing an eco round, creating sustained multi-round EV swings.
Force Buy Equity
#P(\text{Win} \mid \text{Force vs Full}) \approx 0.288 A high-risk tactical investment where a team spends all remaining funds on sub-optimal rifles and pistols instead of saving, yielding ~28-32% upset conversion.
Eco Round (Save Round)
#P(\text{Win} \mid \text{Eco vs Full}) \approx 0.176 A designated concession round where a team spends minimal funds (<$500) to build a maximum loss bonus bankroll for the next round.
Map Side Bias Asymmetry
#\text{Bias}_{\text{CT}} = \frac{N_{\text{rounds, CT won}}}{N_{\text{total rounds}}} - 0.50 The structural map design skew that causes round win probabilities to deviate from 50% between Counter-Terrorists and Terrorists (e.g. 54.8% CT on Ancient vs 52.6% T on Anubis).
Half-Switch Momentum Reset
#\text{Round}_{\text{switch}} = 13 \quad (\text{CS2 MR12}) The mandatory role reversal at round 13 in CS2 MR12 regulation where economies reset to $800 pistol baseline and map asymmetry inverts.
Comeback Probability Factor
#P(\text{Win} \mid \text{Score } 4\text{-}8) = f(\text{SideBias}, \text{PistolProb}, \Delta \text{Elo}) The conditional probability of overcoming a substantial half-time deficit (e.g. 4-8 or 3-9) based on map side asymmetry, pistol conversion, and rating skill delta.
Player Impact & Fantasy Props
(5)Average Damage Per Round (ADR)
#\text{ADR} = \frac{\sum_{r=1}^N \text{Damage}_r}{N} The mean health points subtracted from opponents per round played. Unlike KPR, ADR captures assist contribution and chip damage, correlating with true win share at r=0.74.
KAST Percentage
#\text{KAST} = \frac{N_{\text{Kill } \cup \text{ Assist } \cup \text{ Survived } \cup \text{ Traded}}}{N_{\text{total rounds}}} \times 100\% The percentage of rounds in which a player achieved at least one Kill, Assist, Survived, or was Traded within 4 seconds of dying. Measures baseline consistency.
HLTV Rating 2.1 Composite
#\text{Rating 2.1} = f(\text{KAST}, \text{KPR}, \text{DPR}, \text{ADR}, \text{Impact}) The industry-standard composite index evaluating competitive CS2 performance by integrating KAST%, KPR, DPR, ADR, and Impact Rating into a centered distribution around 1.00.
Role-Adjusted Rating (RAR)
#\text{RAR} = \frac{\text{Rating} - \mu_{\text{role}}}{\sigma_{\text{role}}} A Gaussian z-score standardizing individual performance against specific tactical roles (Anchor, Entry, AWP, IGL, Lurker), removing systematic role bias.
Carry Potential Index (CPI)
#\text{CPI} = \left(\frac{\text{Damage}_{\text{player}}}{\text{Damage}_{\text{team}}}\right) \cdot \left(\frac{\text{Rating}_{\text{player}}}{\overline{\text{Rating}}_{\text{rest}}}\right) A metric quantifying the degree of statistical reliance a team has on a single star player. High CPI (>1.35) highlights teams vulnerable to solo target-banning and bad individual form.
Quantitative Betting & Risk
(5)Expected Value (EV)
#\mathbb{E}[X] = \sum_{i=1}^n x_i \cdot P(X = x_i) = (P \cdot b) - (1 - P) The probability-weighted average payout of a wager over an infinite horizon. In esports betting, positive EV (+EV) represents a mathematical edge where model probability exceeds bookmaker implied probability.
Bookmaker Overround (Vig)
#\text{Overround} = \left(\sum_{i=1}^n \frac{1}{\text{Odds}_i}\right) - 1 The cumulative margin extracted by a sportsbook by pricing reciprocal outcomes below true fair odds. Low overround (sub-4%) preserves player capital, while casual books extract 8-12%.
Return to Player (RTP)
#\text{RTP} = \frac{1}{1 + \text{Overround}} \times 100\% The percentage of total wagered turnover mathematically returned to bettors across balanced market distributions. 1win Esports markets benchmark at ~96.8% RTP versus ~92.5% across industry averages.
Variance & Maximum Drawdown
#\sigma^2 = n \cdot p \cdot (1 - p), \quad \text{MDD} = \max_{t \in [0,T]} (H_t - B_t) Statistical dispersion of betting returns around mathematical expectation and the maximum observed peak-to-trough bankroll contraction. Esports live markets exhibit elevated variance due to sudden economy eco resets.
Kelly Criterion (Fractional Kelly)
#f^* = \frac{p \cdot b - q}{b}, \quad f^*_{\text{half}} = \frac{f^*}{2} The mathematically optimal fraction of bankroll to wager on a positive-expectation proposition to maximize logarithmic capital growth. Half-Kelly (f*/2) and Quarter-Kelly (f*/4) are recommended in esports to hedge against hidden map pool variance.