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How Gold to Make the Golden Snitch: Designing the "Game Changer" in Esports

Zhihuan Huang, Yuxuan Lu, Yongkang Guo, Yuqing Kong

TL;DR

The paper addresses how to design a Game Changer reward to maximize audience surprise in esports, using a Quidditch-based Markov-chain model and extending to MOBA games with data-driven calibration. It develops a belief-based surprise objective, derives closed-form expressions for belief, visits, and total surprise, and provides an analytical upper bound for the optimal Snitch score $x^*$, showing $x^*=0$ for symmetric matches and a value that scales with game duration and strength difference in unbalanced cases. The MOBA analysis uses real LOL and DOTA 2 data to estimate dynamics (wealth growth, teamfight win probability, endgame risk) and finds that the optimal reward grows with increasing strength inequality, while even balanced MOBA matches can benefit from nonzero rewards due to dynamic probabilities. Overall, the work offers design guidelines for Game Changers grounded in a rigorous stochastic framework and illustrates practical implications for audience engagement and game balance in competitive esports.

Abstract

Many battling games utilize a special item (e.g. Roshan in Defense of the Ancients 2 (DOTA 2), Baron Nashor in League of Legends (LOL), Golden Snitch in Quidditch) as a potential ``Game Changer''. The reward of this item can enable the underdog to make a comeback. However, if the reward is excessively high, the whole game may devolve into a chase for the ``Game Changer''. Our research initiates with a Quidditch case study, a fictional sport in Harry Potter series, wherein we architect the Golden Snitch's reward to maximize the audience's surprise. Surprisingly, we discover that for equally competent teams, the optimal Snitch reward is zero. Moreover, we establish that under most circumstances the optimal score aligns with the game's expected duration multiplied by the teams' strength difference. Finally, we explore the correlation between the ``Game Changer's'' reward and audience surprise in Multiplayer Online Battle Arena (MOBA) games including DOTA 2 and LOL, finding that the optimal reward escalates with increasing team strength inequality.

How Gold to Make the Golden Snitch: Designing the "Game Changer" in Esports

TL;DR

The paper addresses how to design a Game Changer reward to maximize audience surprise in esports, using a Quidditch-based Markov-chain model and extending to MOBA games with data-driven calibration. It develops a belief-based surprise objective, derives closed-form expressions for belief, visits, and total surprise, and provides an analytical upper bound for the optimal Snitch score , showing for symmetric matches and a value that scales with game duration and strength difference in unbalanced cases. The MOBA analysis uses real LOL and DOTA 2 data to estimate dynamics (wealth growth, teamfight win probability, endgame risk) and finds that the optimal reward grows with increasing strength inequality, while even balanced MOBA matches can benefit from nonzero rewards due to dynamic probabilities. Overall, the work offers design guidelines for Game Changers grounded in a rigorous stochastic framework and illustrates practical implications for audience engagement and game balance in competitive esports.

Abstract

Many battling games utilize a special item (e.g. Roshan in Defense of the Ancients 2 (DOTA 2), Baron Nashor in League of Legends (LOL), Golden Snitch in Quidditch) as a potential ``Game Changer''. The reward of this item can enable the underdog to make a comeback. However, if the reward is excessively high, the whole game may devolve into a chase for the ``Game Changer''. Our research initiates with a Quidditch case study, a fictional sport in Harry Potter series, wherein we architect the Golden Snitch's reward to maximize the audience's surprise. Surprisingly, we discover that for equally competent teams, the optimal Snitch reward is zero. Moreover, we establish that under most circumstances the optimal score aligns with the game's expected duration multiplied by the teams' strength difference. Finally, we explore the correlation between the ``Game Changer's'' reward and audience surprise in Multiplayer Online Battle Arena (MOBA) games including DOTA 2 and LOL, finding that the optimal reward escalates with increasing team strength inequality.
Paper Structure (45 sections, 1 theorem, 35 equations, 10 figures)

This paper contains 45 sections, 1 theorem, 35 equations, 10 figures.

Table of Contents

  1. Introduction
  2. This paper
  3. Results overview
  4. Related Work
  5. Problem Statement: Quidditch
  6. Optimization Goal
  7. Belief curve
  8. Maximizing the expected overall surprise
  9. Time-homogeneous Markov Chain
  10. State space
  11. Transitions
  12. The recurrence relationship of belief
  13. Method Overview
  14. Step 1 (Solving recurrence relationship of belief)
  15. Step 2 (Belief $\rightarrow$ Surprise)
  16. ...and 30 more sections

Key Result

Theorem 3.1

In Quidditch, there exists a closed-form formula for the overall expected surprise. For all $0<p\leq \frac{1}{2}$, $q\in(0,1)$This assumption does not lose generality since we can exchange two teams.,

Figures (10)

  • Figure 1: Belief curves with low/high overall surprise
  • Figure 2: Transitions when the Snitch's score is $0$ and $1$
  • Figure 3: Optimal score and numerical estimations
  • Figure 4: Transitions of the MOBA game in one round
  • Figure 5: Winning probability of a teamfight when $\lambda=1$: Left subfigures are the empirical winning frequency estimated from the real-world data. The right subfigures are the winning probability calculated from our model with fitting parameters.
  • ...and 5 more figures

Theorems & Definitions (6)

  • Definition 2.1: Surprise ely2015suspense
  • Theorem 3.1: Main theorem
  • Claim 3.2
  • Claim 3.3
  • Claim 3.4
  • proof : Proof of Claim \ref{['claim:surp01']}