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The popularity of online gaming has grown dramatically, driven in part by streaming and the billion-dollar e-sports industry. Online games regularly update their software to fix bugs, add functionality that improve the game's look and feel, and change the game mechanics to keep the games fun and challenging. An open question, however, is the impact of these changes on player performance and game balance, as well as how players adapt to these sudden changes. To address these questions, we use causal inference to measure the impact of software patches to League of Legends, a popular team-based multiplayer online game. We show that game patches have substantially different impacts on players depending on their skill level and whether they take breaks between games. We find that the gap between good and bad players increases after a patch, despite efforts to make gameplay more equal. Moreover, longer between-game breaks tend to improve player performance after patches. Overall, our results highlight the utility of causal inference, and specifically heterogeneous treatment effect estimation, as a tool to quantify the complex mechanisms of game balance and its interplay with players' performance., 9 pages, 11 figures

We study the structure and dynamics of water confined in a nanoporous graphitic carbon structure using molecular-dynamics (MD) simulations. The carbon structure is generated by a reactive MD simulation of oxidation of a silicon carbide nanoparticle. We embed water molecules in the nanopores and study structural and dynamical properties of nanoconfined water as a function of temperature. MD simulation results indicate the presence of high-density water (HDW) and low-density water. Radial distribution functions and spatial density functions indicate that the second solvation shell of the HDW is broken. We calculate the self-diffusion coefficient of confined water molecules as a function of temperature and find a significant decrease in the diffusion of water molecules around $T=190\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The cage correlation function $c(t)$ of confined water molecules at $T=200\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ exhibits stretched exponential decay, $c(t)=\mathrm{exp}[\ensuremath{-}{(\mathrm{t}/\ensuremath{\tau})}^{\ensuremath{\beta}}]$, with $\ensuremath{\beta}=0.43$, which matches exactly with the theoretical prediction $\ensuremath{\beta}=3/7$. Furthermore, the self-intermediate scattering function at $T=200\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ indicates differences in small-scale and large-scale dynamics of water molecules.