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Data analysis on 8 million games

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Kraekkling
Profile Blog Joined June 2007
625 Posts
Last Edited: 2023-10-15 18:15:25
October 10 2023 22:16 GMT
#1
Now with MMR data.

I recently delved into a database containing around 8 million replays. A huge thanks to Dakota_Fanning for granting me access to the data from repmastered.app.

Introduction

We're all aware of the slight imbalances in various matchups. For instance, there's a ~53% win rate for Terran in TvZ, with similar minor imbalances in other matchups. While these numbers can vary based on factors like maps, spawn locations, player skill, and the current meta, they are generally recognized and accepted by the community.

With the data at hand, I tried to examine how some of these factors might influence the result of a game. Specifically, I examined how win rates in non-mirror matchups change as the game progresses over time.

In essence, we'll be looking at the win rate segmented into 1-minute intervals.

For example, for the 7-8 minute interval, we only consider games that concluded between 7:00 and 8:00 in-game time. This gives us an idea of the likelihood of a particular race winning at that specific time in the game. By doing this for every 1-minute interval, we can observe the win rate over time.

Before diving into the results, let's understand the data used. You can skip this part if you're only interested in the results.

Data
+ Show Spoiler +


The dataset comprises roughly 8 million 1v1 games played since the start of 2018. It doesn't provide complete information from a replay but rather some extracted data.

Build order or income details were not available.

However, the dataset did include:

  1. Player races
  2. Game winner
  3. Game duration
  4. Spawn locations
  5. Player APM & effective APM


To refine the dataset, a few filters were applied:

  1. Games played after 01.01.2018
  2. Game duration > 2 minutes
  3. Exclude draws
  4. Exclude games with afk players
  5. Exclude games on fastest maps and similar
  6. Exclude games on maps with fewer than 20000 plays


Below is a histogram displaying the frequency of each map after applying these filters. ("13" represents Fighting Spirit 1.3)

+ Show Spoiler +
[image loading]



Win rates vs. game time

As mentioned earlier, the y-axis displays the win rate (colored and linked data points, label on the plot's left side) against game time on the x-axis. A dashed, green line represents the 50% win rate, helping us identify when matchup dynamics shift.

The grey background data, with axis labels on the right, shows how many games conclude in each interval. This helps gauge the frequency of games ending at specific times and how often they progress to certain stages.

PvZ + Show Spoiler +
[image loading]

This particular plot initially sparked my interest, so let's start here. Key observations include:

- Zerg dominates the game's early stages.

- The significant dip around 7-8 minutes can likely be attributed to hydra bust builds. This is the most striking example I've seen in the data so far of a single strategy or build having such a profound impact.

- Protoss takes the lead during the mid-game, peaking around 13-16 minutes. This surge might partly result from the hydra bust builds: games that didn't end earlier are likely ones where Protoss successfully fended off the bust, often securing a favorable position.

- From 16-20 minutes, Protoss's win rate drops, with Zerg taking the upper hand. Several factors might contribute, such as Protoss typically mining out their main and natural bases around 16 minutes, while Zerg continues mining at (at least) three bases until roughly 20 minutes. The shift also reflects Zerg's hive tech coming into play.

- Games extending beyond 30 minutes show a slight uptick for Protoss, but these instances are rare and may not be very significant.

Overall, while there weren't any major surprises, it was nice to quantify these trends. Comparing close spawn vs. cross spawn win rates will be interesting.

A key takeaway is that Protoss might benefit from trying to wrap up games while on two bases, as Zerg seems favored in later stages.


PvT + Show Spoiler +
[image loading]

Breaking this down chronologically:

- Protoss has the edge in the game's very early phases (up to 6 minutes).

- A notable number of games conclude between 6-8 minutes, probably due to Protoss timings.

- Terran seems to have a strong timing around 10-12 minutes, which appears to be an optimal window for them to end the game.

- The small bump in Protoss's win rate around 14 minutes is not completely clear to me; it seems to wane a few minutes later. Maybe it represents games where Protoss successfully defends against Terran's 10-12 minute push?

- After 12 minutes, Terran's win rate starts to decline, with games lasting over 20 minutes favoring Protoss.

PvT is the matchup where I have the least knowledge overall, so maybe someone else will have better insights on this?



TvZ + Show Spoiler +
[image loading]
Again, let's look at this chronologically:

- The first few minutes are dominated by wins due to zerglings

- Terran wins quite a bit at 5-7 minutes, probably mostly sunken busts?

- Zerg has a strong timing at around 7 minutes when lair tech kicks in

- If Terran doesn't lose to zerg lair tech timing, they have a really great time until about 12-13 minutes, when zerg finally gets defilers. This pre-defiler timing is probably the most dominant point in the game out of any matchup - both the win rate for Terran is very high and the number of games which end there is large.

- If Zergs can stabilize, they slowly but surely flip the matchup dynamics at the 12-20 minute period.

- And thus we enter a period of advantage for Zerg after 18 minutes. We should note here, that fewer games come to this point where zerg can reap their advantage.

- However, we also see a clear trend, where, if Zerg is not able to finish out the game once they unlock the full hive tech (defiler + upgraded ultra) at ~20 minutes, as the games drag on, the matchup becomes balanced again.

Here it was cool to see how the matchup flips multiple times. Also, if you just visually compare the shape of the win rate vs time of TvZ and PvZ, you'll see striking similarities. In both matchups, Zerg seems to have strong early timings, then gets dominated in the mid-game, but comes back at a later point.





Influence of spawn locations: close vs cross-spawn

Here we use 4 player maps only and compare the winrate on close spawning positions to the diagonal case. This is of particular interest from a map making point of view, since the rush distances have a big influence on how strong certain builds are.

PvT+ Show Spoiler +
[image loading]
Zealot rushes are strong on close positions, as expected. Looks like Protoss overall prefers diagonal spawns. The longer distance means that it takes longer for the Terran to reach him.

PvZ+ Show Spoiler +
[image loading]
Protoss feels a lot safer in the early game on diagonal spawns. Later in the game Protoss also seems to profit from diagonal spawns.

TvZ+ Show Spoiler +
[image loading]
Early Terran wins due to sunken busts are much more likely on close spawns. Then, for the most part of the game the distances don't seem to matter at all.


Influence of player skill effective apm

No MMR data is available to us as of right now, so we'll be using the effective apm instead to estimate the players skill.
Results in brackets of effective apm. + Show Spoiler +
[image loading]
.

Here we can see a few categories of players and the balance in their games. A lower-level group is defined by taking games where both players are slower than roughly half of all the players, that is effective apm below 150. Those are the red data points.

Then we have two groups where both players are required to be above some certain level: both above 150 in purp, and both above 180 in blue. These are the higher-level groups. Note that one is inclusive of the other here, so we expect a strong correlation.

PvT+ Show Spoiler +
[image loading]
Man wtf is happening at the 5 minute mark in the lower-level group. Is this the delayed Zealot rush hitting? Overall, slow Terrans get punished terribly by slow Protosses.

For the better groups, it seems like if Terran can survive to the 10th minute, they will have a comfortable 10 minutes of advantage to win the game. If they do not manage that, the game tilts towards Protoss again,

PvZ+ Show Spoiler +
[image loading]
Zealot rushes only work in the lower group. Hydras are deadly at all levels. It looks like the lower group Zergs are worse in converting their late-game advantage into a win compared to the higher groups.

TvZ+ Show Spoiler +
[image loading]
Again, Terran profits the most from just "getting better". Looking at the 5-6 minute mark we nicely see that the higher groups gain their wins from sunken busting at an earlier time than the lower group. Terran dominance before defiler looks really scary in the higher groups.


Influence by level of play based on MMR.

Here, MMR data is used to examine the balance. A match-mmr is determined by taking the average MMR of the two players (initial MMR values before the match was played). Several brackets of games are defined and compared. Additionally, a requirement is imposed on the max difference of player MMR, to ensure only games of a meaningful skill difference are taken into account. For example, in red are games with

- match-mmr below 1800, and difference of MMR of both player is below 200

The requirements are somewhat loosened as games of higher level are examined, as can be seen in the labels. Take note of the big error bars in some of the brackets in the later stages of the game; that is don't draw too many conclusions from those data points.


PvT+ Show Spoiler +
[image loading]
The game balance is even at an MMR above 1800 and tils slowly towards Terran the higher we go. At the highest level the matchup is roughly 52% in Terrans favour.

PvZ+ Show Spoiler +
[image loading]
Protoss is behind in all brackets and gets dominated at the highest levels where they achieve an overall win rate of 46%.

TvZ+ Show Spoiler +
[image loading]
Again we see a clear trend where the matchup becomes more favoured towards Terran as player skill increases. It looks like high-level Zerg vs Terran is the hardest matchup in broodwar.

(*^^)(^*)
WorsT21
Profile Joined February 2020
Romania12 Posts
October 10 2023 22:59 GMT
#2
This is fascinating, great work
Suricatta
Profile Joined November 2021
27 Posts
October 10 2023 23:11 GMT
#3
Very interesting. Thanks for the info!
TMNT
Profile Joined January 2021
3118 Posts
Last Edited: 2023-10-10 23:45:16
October 10 2023 23:32 GMT
#4
Thanks a lot for for this. I've always wanted to see this kind of "win probability vs time" analysis.

Regarding PvT
- The small bump in Protoss's win rate around 14 minutes is not completely clear to me; it seems to wane a few minutes later. Maybe it represents games where Protoss successfully defends against Terran's 10-12 minute push?

imo this is probably the result of the 1 Arbiter stasis with max army timing.

After 20 minutes PvT favors Protoss probably because for 90% of the player base, Terrans can't manage to play split map and manage more than 4 bases at a time.

I'm very much waiting for the analysis on player skill influence, as I expect we will some notable changes in the shape of those curves around S rank
Effay
Profile Blog Joined December 2010
United States153 Posts
October 11 2023 00:16 GMT
#5
Fascinating analysis!
Obsession: The weak minded's name for dedication
Monochromatic
Profile Blog Joined March 2012
United States998 Posts
October 11 2023 00:37 GMT
#6
Amazing post.

My big takeaway is that Artosis was right about PvT .

I would love to see a ZvZ plot about game length and frequency. What are the odds of lategame ZvZ? It might be interesting to see for other mirrors as well.

MC: "Guys I need your support! iam poor make me nerd baller" __________________________________________RIP Violet
G5
Profile Blog Joined August 2005
United States2921 Posts
October 11 2023 02:23 GMT
#7
On October 11 2023 08:32 TMNT wrote:
Thanks a lot for for this. I've always wanted to see this kind of "win probability vs time" analysis.

Regarding PvT
Show nested quote +
- The small bump in Protoss's win rate around 14 minutes is not completely clear to me; it seems to wane a few minutes later. Maybe it represents games where Protoss successfully defends against Terran's 10-12 minute push?

imo this is probably the result of the 1 Arbiter stasis with max army timing.

After 20 minutes PvT favors Protoss probably because for 90% of the player base, Terrans can't manage to play split map and manage more than 4 bases at a time.

I'm very much waiting for the analysis on player skill influence, as I expect we will some notable changes in the shape of those curves around S rank



The bump around 14 minutes is probably due to there not being a timing then. The spike for T wins from 9-13 minutes is probably from 2 base timings. 3 base 2-1 timings hit around 14 1/2 minute mark and P usually leaves a little bit after that (if it works) which is why the T spikes again between 16-21 minutes (this is probably just 2-1 timings working well and P scrambling and leaving at different points depending on how the game is going). Then P spikes in winning because at the 22 minute mark, P should know if they're going to win or not based on how bad they got smashed or how bad they held the Terran timing attacks and if they're still in the game beyond 22 minutes, they clearly held and are in a decent enough position to continue.

Overall, pretty impressive research and quite interesting. I feel like I can pin point certain builds as to why most of those are the way that they are but it's interesting for it to not be theory and for it to actually have data to point to. It makes theorycrafting a lot clearer.
TT1
Profile Blog Joined December 2008
Canada10014 Posts
October 11 2023 03:21 GMT
#8
Is it possible to do this with progamer replays or 2500+ ladder games from cwal (the ladder games would prob be way better cus of sample size)? I know the sample size would be way less but the quality of games is way more important for this type of analysis. Thanks for this tho, great work.
ab = tl(i) + tl(pc), the grand answer to every tl.net debate
imBLIND
Profile Blog Joined December 2006
United States2626 Posts
Last Edited: 2023-10-11 04:38:42
October 11 2023 04:37 GMT
#9
On October 11 2023 08:32 TMNT wrote:
I'm very much waiting for the analysis on player skill influence, as I expect we will some notable changes in the shape of those curves around S rank


On October 11 2023 12:21 TT1 wrote:
Is it possible to do this with progamer replays or 2500+ ladder games from cwal (the ladder games would prob be way better cus of sample size)? I know the sample size would be way less but the quality of games is way more important for this type of analysis. Thanks for this tho, great work.



Just to add on to this, and I'm sure someone else has already done this, but could you show TvZ and TvP win rates with and without Flash?
im deaf
Zealgoon
Profile Joined January 2013
China187 Posts
October 11 2023 04:38 GMT
#10
Great work. Confirms my theory that PvZ is massively P favored in the midgame :D
Michael34
Profile Joined October 2023
1 Post
October 11 2023 06:31 GMT
#11
On October 11 2023 12:21 TT1 wrote:
Is it possible to do this with progamer replays or 2500+ ladder games from cwal (the ladder games would prob be way better cus of sample size)? I know the sample size would be way less but the quality of games is way more important for this type of analysis. Thanks for this tho, great work.


Based on OP's description of the existing data, its not. You would need to get new data and I don't know how easy that is to do. The way I would do it is to filter out the lowest effective APM players, maybe the bottom 60% or so, since those are disproportionately going to be the worst players. It's far from a perfect proxy, but it would at least keep a lot of D and C rank games from polluting the data.
Muff2n
Profile Blog Joined March 2009
United Kingdom251 Posts
October 11 2023 07:22 GMT
#12
Very cool!
Dante08
Profile Blog Joined February 2008
Singapore4139 Posts
October 11 2023 07:41 GMT
#13
Thanks this is amazing!

This sort of solidifies the fact TvP is the hardest matchup. There are so many ways Terran can die to Protoss in the early-mid game but not the other way around. Once the game goes past 20 mins it gets favoured for Protoss again due to the number of bases Protoss has and the option to switch to carriers.

If you run it at the top level I would think the early-mid game win rates for Protoss lowers abit but overall it wouldn’t change too much.
angry_maia
Profile Joined August 2020
327 Posts
October 11 2023 09:11 GMT
#14
On October 11 2023 16:41 Dante08 wrote:
Thanks this is amazing!

This sort of solidifies the fact TvP is the hardest matchup. There are so many ways Terran can die to Protoss in the early-mid game but not the other way around. Once the game goes past 20 mins it gets favoured for Protoss again due to the number of bases Protoss has and the option to switch to carriers.

If you run it at the top level I would think the early-mid game win rates for Protoss lowers abit but overall it wouldn’t change too much.


i dont disagree that TvP is the hardest, but this data doesn't really prove that. All of your arguments equally apply to PvZ (easy to die early, and then zerg pulls ahead again in the late game).
Dakota_Fanning *
Profile Joined January 2008
Hungary2359 Posts
Last Edited: 2023-10-11 09:50:10
October 11 2023 09:15 GMT
#15
Amazing job! Nice stats!

Don't throw away your tools you generated the stats with, as we might repeat this with a bigger dataset, which might also include matchmaking stats I'm gathering recently (e.g. MMR).
https://repmastered.icza.net
Branch.AUT
Profile Blog Joined May 2010
Austria853 Posts
October 11 2023 10:05 GMT
#16
On October 11 2023 13:37 imBLIND wrote:
Show nested quote +
On October 11 2023 08:32 TMNT wrote:
I'm very much waiting for the analysis on player skill influence, as I expect we will some notable changes in the shape of those curves around S rank


Show nested quote +
On October 11 2023 12:21 TT1 wrote:
Is it possible to do this with progamer replays or 2500+ ladder games from cwal (the ladder games would prob be way better cus of sample size)? I know the sample size would be way less but the quality of games is way more important for this type of analysis. Thanks for this tho, great work.



Just to add on to this, and I'm sure someone else has already done this, but could you show TvZ and TvP win rates with and without Flash?

Assuming equal distribution between zvp/tvz/pvt, we're talking about 2.3Million games in each matchup. Excluding any one player, no matter the name, shouldn't make a dent. Out of the sheer volume of games analyzed.

Great work OP! It's very interesting to see the winrate evolution over game time.
moktira *
Profile Blog Joined October 2010
Ireland1546 Posts
October 11 2023 10:11 GMT
#17
This is really amazing, well done on doing this, so cool to see how it evolves in time rather than just %winrate.
As a few others have expressed it would be very interesting to see for the higher APM users though to get an idea of what it's like among the top players.
If in doubt, differentiate and set equal to zero
RJBTV
Profile Joined December 2022
194 Posts
October 11 2023 10:14 GMT
#18
I've noticed post 40 PvZ protoss becomes extremely resource efficient compared to zerg as the map mines out and toss gets a chance to use reavers, archons, and high templars to defend their last couple bases at a very very low cost. The zerg on the other hand has to spam large volumes of units trying to break into a fortified position with units that die in the blink of an eye.
TMNT
Profile Joined January 2021
3118 Posts
October 11 2023 10:18 GMT
#19
On October 11 2023 13:37 imBLIND wrote:
Show nested quote +
On October 11 2023 08:32 TMNT wrote:
I'm very much waiting for the analysis on player skill influence, as I expect we will some notable changes in the shape of those curves around S rank


Show nested quote +
On October 11 2023 12:21 TT1 wrote:
Is it possible to do this with progamer replays or 2500+ ladder games from cwal (the ladder games would prob be way better cus of sample size)? I know the sample size would be way less but the quality of games is way more important for this type of analysis. Thanks for this tho, great work.



Just to add on to this, and I'm sure someone else has already done this, but could you show TvZ and TvP win rates with and without Flash?

You already have it. T win rate without Flash is literally the current win rate on eloboard, since the site started around the time he left for military. Then compare it with whatever you have before that point. I looked up a while ago and they're basically unchanged.
Dante08
Profile Blog Joined February 2008
Singapore4139 Posts
October 11 2023 10:27 GMT
#20
On October 11 2023 18:11 angry_maia wrote:
Show nested quote +
On October 11 2023 16:41 Dante08 wrote:
Thanks this is amazing!

This sort of solidifies the fact TvP is the hardest matchup. There are so many ways Terran can die to Protoss in the early-mid game but not the other way around. Once the game goes past 20 mins it gets favoured for Protoss again due to the number of bases Protoss has and the option to switch to carriers.

If you run it at the top level I would think the early-mid game win rates for Protoss lowers abit but overall it wouldn’t change too much.


i dont disagree that TvP is the hardest, but this data doesn't really prove that. All of your arguments equally apply to PvZ (easy to die early, and then zerg pulls ahead again in the late game).


The PvZ win area is much bigger than TvP no?
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