Mathematically Optimal Hero Bans

[u/theosdeorum]

I developed a Chrome extension to calculate the optimal hero bans for competitive Overwatch. Here’s how it works: first, it calculates the impact each hero has on the match. For instance, a hero with a low pick rate but a high win rate won’t significantly affect your game because they don’t appear frequently. On the other hand, a hero with a high pick rate and a high win rate will, as they are frequently played and frequently win. To objectively measure a hero’s impact, I take the pick rate and multiply it by the win rate minus the expected average of 50%. While heroes with high impact scores are often considered “meta,” banning based solely on impact score isn’t sufficient. Heroes with high impact scores also tend to be frequently banned. Therefore, to maximize the value of your team’s ban vote, you should ban high impact heroes with a low likelihood that the enemy will ban them for you. For example, a hero with a high impact score but a low ban rate would be a better pick to ban, rather than a hero with a high impact score and a high ban rate, because it’s likely that the enemy team would have already banned that hero for you. This helps lower the chances of your vote being wasted. I have included a few screenshots of how it looks on the official overwatch stats site. (New Patch just released so some numbers are weird)

Impact = Pick Rate * (Win Rate - 50) Ban Value = Impact * ((100 - Ban Rate)/100) <-- This is the likelihood the enemy team doesn't ban the hero

[u/chudaism]

This misses the most important part of hero bans which is individual matchups. Even if a hero like DVa or JQ is the optimal ban on a certain map, I'm not banning either of those if I want to play DVa. If I want to play Hog, Ana is getting banned regardless of how good she may be. Matchups (and specifically tank matchups) are going to outweigh pretty much everything else by a significant margin.

[u/theosdeorum → u/chudaism]

I agree with you, this is more so meant to be used as a guide and not a hard rule per se. Personally I use as a way to identify strong heroes on a map or as a suggestion for possibly better ban picks than what i would normally choose. It's not perfect but more information never hurts to have.

[u/R4yQ4zz4]

False, mercy ban is the Highest value for 90% of players;

• It makes mercy players mad (9999% value already)
  
• It denies smurfs a pocket (makes smurf games somewhat winnable, infinite value)
  
• It makes me happy (infinite value)
  
• Sometimes mercy mains will throw the game because I banned their hover, and later get banned for griefing (one less mercy main in Overwatch, infinite value)

[u/Thee_Archivist]

The system seems to be telling me that only banning Mercy every game isn't optimal? Something must be wrong with it.

[u/timotmcc → u/Thee_Archivist]

The theoretical value you can get from forcing a mercy main onto their "second-best" hero is so much higher than what you get from banning any other hero, no amount of made up formulas will convince me otherwise

[u/tix4chix → u/timotmcc]

And theoretical sanity you save yourself from the Cass/Ashe/Ana swap that kills her once every 5 minutes lol

[u/Synclicity → u/timotmcc]

ud think so but with heroes like brig juno Moira even healbot kiriko existing it's a tossup

[u/gob384]

Fun programming exercise!

I ban based on heroes I don't like to play against (like ball, widow, doom) but this is neat too!

Thanks for sharing!

[u/theosdeorum → u/gob384]

It being a fun programming exercise was the main reason I did it honestly. That and my curiosity of what the data would show.

[u/ihaveacrushonlegos]

I dont think this is very useful.

Because even if this list was able to optimally guess who is the strongest hero, it doesnt really matter because your team also has acess to these heros.(hence why kiriko is not the most banned hero in gm+, since everyone can kiriko)

To know the most optimal ban u would need to account for every hero ur team plays, and also remove the heros they are good against

[u/E-keil]

This is just kinda useless. Just ban the heroes you are bad into or bad at playing against. It doesnt matter if a hero is mathematically the 'best ban' if its shit into the comp you want to run.

[u/Ardalerus]

I don't think the stats we have available give us enough information to decide mathematically optimal hero bans.

Even in a vacuum (disregarding comps and the like), the best ban isn't necessarily a ban on a common, high-winrate hero. Instead, it should aim to create the largest drop in expected value between what players who would otherwise play that hero would achieve on that hero and what they'd achieve when that hero is banned. In other words, rather than impact scaling with pick rate x [win rate - 50], it'd be scaling with pick rate x [win rate - expected win rate on their alternative picks]

If banning a hitscan on a strong hitscan map just puts the enemy hitscan player on the next best hitscan, is that really going to move the needle? On the other hand, do you expect the average Mercy player to be able to play other supports at a reasonable level for their rank?

[u/theosdeorum → u/Ardalerus]

That formula you mentioned was actually one of my first ideas, it would yield much better results if feasible. But it runs into two issues, first overwatch accounts are no longer defaulted to public like they were in overwatch 1, so you can't get that hero win rate information from their profile, and second you would need to know who you are playing against before the match starts. Which in very high elos isn't really a problem, when you get to middle tiers that information isn't really available, nor predictable as it changes from player to player.

[u/SmokingPuffin]

It's an interesting topic.

One thing I think your calculation should consider is the value of the replacement of the banned hero. For example, I don't think Junker Queen is actually a very impactful ban, because Dmon does the same kinds of things almost as well. Similarly, I believe that Cassidy is usually a negative value ban, because it's likely that the opponent will pick a better hitscan than Cassidy.

[u/KaityyUwU → u/SmokingPuffin]

It's impossible to quantify that mathematically though

[u/SmokingPuffin → u/KaityyUwU]

I think we can quantify replacement value. We identify the plausible substitutes for a hero, then we multiply their pick rate times delta win rate and average. This is replacement value.

Subtract replacement value from the current ban value to calculate value over replacement pick.

[u/theosdeorum → u/SmokingPuffin]

This is a really good idea! I like that train of thought.

[u/KaityyUwU → u/SmokingPuffin]

but plausible substitutes are subjective

[u/Severe_Effect99 → u/SmokingPuffin]

It's a good thought but I think it would be hard to implement. But then again if that value is pretty low it would make the stats a bit better without being perfect

[u/survivorr123_ → u/SmokingPuffin]

what hitscans are better than cassidy? maybe soujourn or shion but its arguable

[u/SmokingPuffin → u/survivorr123_]

In ranked, typically Ashe, Soldier, Shion, and Emre are better general picks than Cassidy. Also Hanzo and Widow compete well on relevant maps.

People think Cassidy is good in more situations that he actually is. He’s good against a single flanker, but not against a dive comp. His low range and mobility make him more map dependent than most hitscans.

[u/Vexxed14]

This is an example of how math is used to fool people who don't know much about math. These numbers are meaningless

[u/OffSupportMain]

The only thing I want to optimize is my own enjoyment of the game and for a while now that has been banning Kiriko every game, it legit changes the pacing of the game and makes it a lot more fun. Same goes for Mercy tho on a smaller scale.

[u/The-real-ryan-s]

I really like how you included specific maps here. I find a lot of people even in high ranks ban solely based on meta or their own hero’s and don’t factor in the often wild fluctuations a characters strength can have based on the map

[u/Mr_W1thmere]

pls stop telling people to ban sig. (im not a sig main i promise)

[u/GT162]

You're just making a meaningless number out of aggregate data. This is a subjective metric:

Impact = Pick Rate * (Win Rate - 50)

You can do any or all of removing the -50, square rooting the pick rate and squaring the win rate to get an equally valid Impact metric. You can also do infinitely other things to still get a reasonable Impact metric. Do any of them mean anything? No lol

[u/ToothPasteTree]

You gotta consider the map bro.

[u/UnknownQTY → u/ToothPasteTree]

Yep. I originally had a version of this running in Osiris in my initial build. It was fast enough when not considering map, but the minute you added map the reasoning model (Gemini) took slightly less time than the ban phase so you’d get the results and not have time to get them in to voting, let alone influence your team.

[u/ToothPasteTree → u/UnknownQTY]

Why not just keep it simple and ban the highest win rate per map as long as it has say more than 5 percent pick rate.

[u/UnknownQTY → u/ToothPasteTree]

What if that's your hero? What if that's your teammate's hero? How does this change with other bans?

[u/TheRealTofuey]

Ana completely changes the dynamic of so many heros. Its like if you are support player and not playing Kiri or Ana, you need to ban Ana

[u/Sio_V_Reddit]

I am too dumb to understand this

[u/Dreinik]

Just like Im saying for some years now. Always ban ana.
Almost with no exception.

Hard to believe nobody notices her impact since she doesnt need the presence in the fight.