IEM Katowice PvT Blink: 64%. PvT Overall: 61%, a game theoretic analysis

2 weeks ago, IEM Katowice showed off some sick games. My favorite was sOs’s Phoenix into Colossi into Carriers on Alterzim Stronghold, but the biggest news apparently was Blink Stalkers in PvT. After several crushing games by HerO and sOs, it really looked like Blink was imbalanced in this matchup. The most insightful analysis I saw was from bwindley, and now I have had a chance to label data and crunch numbers, here’s my take on the situation with a few numbers, a little analysis, and some game theory.

The easiest point to make here is the raw win rates. In 33 PvTs, Protoss went Blink Stalkers in 11 of them. The overall PvT win rate was 20-13 for 61% (ref). In games where Protoss went Blink, the win rate was 7-4 for 64% (ref).

For comparison, in Spawning Tool, the overall PvT win rate is 804-767 for 51% (ref). In games where Protoss researched Blink before 6:00, the win rate is 71-58 for 55% (ref).

So Blink wins slightly more than normal, but it’s pretty dang close. One would hope that different strategies would have different win rates, or else the meta-game had stagnated as no strategy would confer an advantage over any other (more on this below).

Of course, IEM Katowice is a small sample size, and the data is biased. I haven’t run the numbers, but I doubt that the difference is statistically significant. Even if we did get a lot of samples, tournaments naturally bias the data since the best players are over-represented by playing deeper into the tournament. In other words, it’s kind of hard to generalize from one tournament of the world’s best Protoss players (sOs and HerO) using a strategy.

In fact, according to game theory, one would expect the Blink win rates to look close to global win rates. Basically, if we assume that professional players have internalized the different options available, they’re picking their builds so that they all roughly win the same amount in the current meta-game.

Mixed Strategies and the Meta-game in StarCraft

The idea of the meta-game is closely tied to an idea in game theory called “Mixed Strategies“*. In a game where a player has multiple choices, it can be optimal to pick randomly between different options. The simplest example is “Rock, Paper, Scissors”, where you (listen up Dustin Browder) probably don’t want to become predictable and go Rock every time. In the case of StarCraft, this means you should mix up your builds. If you know that a 6 Pool usually beats a 15 Pool and loses to a 10 Pool, but a 15 Pool usually beats a 10 Pool, there’s some happy mix between them (maybe 33%-33%-33%) that works best. If you only play greedy builds (Greg), it is probably going to catch up to you. The exact ratio depends on the specific strategies and how good you are with them, but generally, mixing is good.

The funny consequence is that given time to optimize these ratios (as progamers do over thousands of practice games), the win rates should even out regardless of the specific strategy chosen. For any build, opposing players should increase the ratio of games where they play to counter it until it’s back in equilibrium. For example, let’s say that I (StoicLoofah) am twice as good with 10 Pools as 6 Pools and start out with a 80% and 40% win rate, respectively. My naive opponent might mix evenly between all strategies to begin with, but over time, they will learn that they should 15 Pool more often to counter my 10 Pool. Because of that, my 10 Pool win rate will plummet until it matches my 6 Pool win rate, and we will continue to tweak from there.

These changing ratios of builds represents one main point of a meta-game shift (the other being that you can directly become better with a strategy). When nothing big happens, shifts can be slow as the community jointly optimizes our strategy mix. Occasionally, however, we discover a new strategy, or some pro popularizes a strategy, either of which can quickly change the ratio of strategies. After that, the win rates for each strategy might be different, but they will draft back again.

So this looks pretty grim. If all strategies are going to get you the same win rate, why even bother having so many options? Why not just have everyone stand around and play Rock-Paper-Scissors or a simpler RTS? Well, StarCraft is generally a lot more exciting, but more importantly, the presence of a strategy can bend the mixing ratios. The win rates don’t change, but what we actually see game-to-game changes in what strategies players pick, and that (and not the win rate) is what we actually experience.

For example, remember pre-nerf Infestors with non-projectile Fungal Growth and upgraded Infested Terrans? In the long run, it wouldn’t suck because Patch Zergs were winning too much: it would suck because it would become totally boring with only 1 way to play Zerg and 1 way to play against it. In short, we as a community will figure out how to beat any strategy: it just might end up being a really boring game.**

So what does this mean for Blink Stalkers? I think we should wait to see what happens***. There was one tournament where we saw a lot of it, but it was a small, biased sample size. The win rates, in truth, were in line with the rest of the tournament, so it’s possible that players have already adjusted for it, but maybe there is more meta-game development ahead. The more important question is how you like the game as it is. If you’re seeing more Blink Stalker play on the ladder or in tournaments than you would like in the long run, that’s a problem. But there’s also a chance that Blink Stalkers will just meld in as part of the toolbox, and this will be temporary in an ever-changing meta-game.

In summary (or TL;DR),

  1. The win rate for Blink in PvT isn’t that different from PvT as a whole, but that should be expected
  2. It was a small sample size
  3. The question shouldn’t be, “Are Protoss players winning too much PvT with Blink Stalkers?”
  4. The question should be, “Are Protoss players using Blink Stalkers too much in PvT?”

* Disclaimer: I don’t actually know that much about game theory. If you want to learn more, I recommend this class from Yale.

** As an extension, you can actually think of picking your race as another game in itself. If all we really cared about was win rates, we would pick our race to match optimal mixing as determined by Blizzard’s balancing. The truth, however, is that we pick races based on what’s fun, and so we hope that Blizzard balances the races so that our win rates line up with our preferences

*** Alternatively, Blizzard could do things like Valve with Dota 2. Blizzard depends on game-to-game mixing. Valve constantly change the game balance so that the meta-game intrinsically shifts to keep things fresh. Both can work

(For more analysis, follow @spawningtool. Or do your own analysis using data at http://spawningtool.com )

2 thoughts on “IEM Katowice PvT Blink: 64%. PvT Overall: 61%, a game theoretic analysis

  1. Hi Kevin,

    I really love your post analysing Blink from a purely statistical data point of view. The data never lies! For sure there’s no arguing the fact that Blink does seem to be unfairly targeted towards the current metagame shift toward Protoss being more favored in this match up.

    I do think that the reason that Blink has been targeted is that Terrans feel that this build is just way too hard to defend covering all areas (although I would love to see more sensor tower usage) whilst at the same time being too flexible for Protoss to transition to another tech or macro behind.

    It seems, that this build more then others, has a good advantage in map control and aggression, and not so much of a disadvantage when not enough damage is dealt. This has always been the formula for all builds that aren’t favoring economy.

    On the flipside with Terran realising its Blink, will have to get bunkers up in the main and natural, divide up his army and basically be soft contained (at best) until stim and medivacs are ready. Finding out what Protoss is doing is hugely problematic, scanning is never guaranteed when mules are, reapers don’t work in midgame, and even dropping can be difficult due to Blink and Photon Overcharge.

    Looking at the data here is the most obvious choice of action to see what is going on. But the numbers like you say is from a rather small sample size. What I would compare it to though, is more like Innovation pre Hellbat nerf period. He was the best at using Hellbats, but Terrans themselves weren’t necessarily crushing TvP. So in the same way, whilst Blink might not be getting the most outrageous winrates, the very best Protosses are basically unstoppable using this strategy ($O$, Parting, both Hero’s).

    • Thanks for the thoughtful reply! I think you bring up a lot of good points here.

      That’s a good point about the Hellbat nerf: there was definitely a huge advantage for top level pros like Innovation who could drop in 2 places. I can’t quite remember the entire circumstance, but I remember it being particularly brutal in TvT over the other matchups. If I think back, though, I think players were figuring out how to defend it: it just required a really big commitment to defense (Bunkers in mineral lines, Spores EVERYWHERE) that twisted the meta-game in a strange way. The question is whether Blink will have such a big effect.

      As far as the flexibility of it, I think your point draws attention to a bias in the community. Builds like Blink favor the aggressor, and one possible shift we might see is that Terran players try to be more aggressive in the early game. I don’t know enough to say whether it’s possible or not (the Mothership Core really put a damper on it), but I think there’s a general bias to say that aggressive, “cheesy” strategies aren’t as fun to watch or play against as more economic strategies.

      Of course, this is the fun part of game design where you have the draw the line between the whining every player will have about their own race and legitimate concerns about the game. I think the StarCraft is a sufficiently complex game with enough strategies that we can eventually work out ways to deal with every strategy, but it might just be a coin-flippy, aggressive game, and it’s totally valid if that’s not what people want.

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