SS healer mmr modeling

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tl;dr i built a naive monte carlo model for the ‘grenade in a lobby’ scenario and it demonstrates that ‘grenade in the lobby’ affects healer win rates more negatively than dps win rates

because of stupid forum trust level bs, here is the plot

imgur . com / gGxcnid

Recently there was a long-winded but well-founded post on these forums claiming that healers are disproportionately hurt when there is a ‘grenade in the lobby’ compared to dps. A ‘grenade in the lobby’ is a player who significantly underperforms (ie 0-6 or 1-5).

The original post by the author claims that under uniform probability where the ‘grenade’ player could be any one of the six players, healers ON AVERAGE are hurt more by this than dps simply due to how the team combinations are constructed. DPS only have to play with the grenade player twice whereas healers have to play with them three times, resulting in more 4-2s for dps and more 3-3s for healers.

I take this a step further and try to naively model this over 2 variables that are commonly discussed on these forums: healer agency and having a grenade player in your lobby.

The meaning of the variables is pretty self-explanatory. Healer agency is truly how much influence the healer can have over the match relative to the dps agency which is fixed, and the grenade skill ranges from being -1 (abysmal) to 1 (comparable skill to teammates).

The method behind my model is pretty simple and trivial. By no means am I claiming that it captures all complex interdependencies so take it with a grain of salt. The gist of the method is that I build two teams and randomly replace one of the players in the lobby with a grenade with uniform probability. Then I simulate tens of thousands of matches using a simple probability model. A winner of each match is selected by a weighted random choice. Each team’s contribution is the sum of the agency*skill for each player on the team. Then the team1 and team2 contributions are normalized and used as weighted probabilities for np.random.choice.

the result can be summed up with this visualization

imgur . com / gGxcnid

The interpretation of this plot is simple. Assuming equal probability of the grenade being any player in the lobby, ON AVERAGE, dps will have higher win expectation than healers do. The effects of this are more profound if the grenade is especially bad, or if healer agency on the game outcome is worse.

This is inline with the original post from Why 3-3 should count as a 4-2 for healers

Now I will be the first to say and reiterate that this is an extremely simple model and the choices of scales and values for this are hand-wavy. Some people might argue that healer agency is equal to dps agency, where as others argue that healers might only have have the agency that dps do. Whether or not the scales are exactly correct is not the point. The point is that dps benefit the most when there is a grenade in the lobby because that grenade is more likely than not another dps.

AKA as many have pointed out

“it’s harder to climb as a healer”

This is corroborated by the MMR disparity between dps and healers.

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As someone with 2 degrees, including a Master’s, I appreciate strong minds. Thank you for coming to the aid of a lowly Healer :slight_smile:

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great post. fix healers mmr

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Love that you added math to this. I hope this perks a devs ear and they actually take action. Healers NEED to be able to climb easier than DPS for queues to go down.

I feel like another way of describing this model is that if there are 6 players there is a 1/6 chance for each one to be the “bad grenade”. Because there are only 2 healers and 4 dps and they are in different MMR brackets. The healers have higher probabilities of being in lobbies with a bad grenade Dps rather than. A bad grenade healer. Thus more healers will go 3-3 than DPS. this combined with a smaller healer sample size leads to mmr discrepancy

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+1 great post

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Thanks for taking the time to read it.

They definitley need to fix this and the solution could be simple. What I would do if I were them is I would start issuing points for healers when they 3-3 and i would do this until the cumulative distribution function of healer mmrs matches that of dps mmrs. I think the system would be stable. If a healer can 3-3 until 2400 for example, it means that they are performing sufficiently well to break even at that rating. When the healer can no longer perform well enough to break even, they will lose cr. It seems very simple and I cannot see why this wouldnt be a stable solution.

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This is the smartest thing I’ll read this year

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Good post, thanks for typing all that out and doing the math. Can you possibly explain how we’re supposed to read the graph you included? Feeling a bit dumb cause I’m not sure what I’m looking for. I don’t think I’ve seen a graph like this one before.

Hopefully blizzard takes some note of this and includes it in future mmr changes, to whatever extent this actually effects our games. Idk how common 6-0/0-6s are in solo shuffles. Feels common, but I’m sure they have the real numbers to compare.

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Lame.
That model isn’t even riding on spinners.

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as a grenade i take this personally

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Certainly can help explain it.

The difference between this graph and most common graphs is that it allows you to visualize the value of something versus 2 input variables instead of only one. Most common graphs are y vs x (or y=f(x)) but this graph is y vs x1, x2 (or y = f(x1, x2)). In this graph the two input variables are the ones on the ‘ground plane’ and the output value is the height of the mountain at any point.

In terms of interpretting the graph, the height of the mountain at any point is the ratio of dps wins to healer wins. In a perfectly balanced game, this wouldn’t be mountain shaped at all, it would be totally flat meaning there is no advantage to playing dps over healing.

You can see where the mountain is the highest (also color coded yellow) is where healer agency is low (0.3) and the grenade is really bad (-1) skill. This plot basically shows that if healer agency is low and one person is the lobby underperforms (which most lobbies have) that this starts to favor DPS win expectations to be more than healer win expectations, which is totally unfair to healers, and is a possible explanation to why healer mmr is so jank right now.

This model suggests that DPS can win up to 12% more often than healers. This could be a possible explanation of why 92% of the top 100 players are DPS and only 8% are healers, when it really should be 66% of the top 100 players are DPS (because teams are 2/3 DPS).

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yeah this checks out. also i’m a way better healer than a dps yet my dps are always far higher in rss so yknow

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Instead of adding spaces, put ` on either side of your links, it’s the button to the left of 1 (on most keyboards).

So they look like this:

imgur.com/gGxcnid

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Good work, keep it up.

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If anyone in the lobby had an equal chance of being the grenade, wouldn’t the spread just be even?

Game H1 H2 Dps1 Dps2 Dps3 Dps4
1 6 0 3 3 3 3
2 0 6 3 3 3 3
3 3 3 0 4 4 4
4 3 3 4 0 4 4
5 3 3 4 4 0 4
6 3 3 4 4 4 0
Total Wins 18 18 18 18 18 18

In both cases, queueing as dps or queuing as a healer, even if you remove the possibility of you yourself being the grenade, you will end up the same. 18-18 if you can grenade, 18-12 if you cannot.

Healer grenading is more impactful but will be less likely to occur with everything else being constant. It’s not constant though so ultimately assuming an even spread of grenades is pretty meaningless in practice.

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Wasn’t going to comment because I’m not going to put in the work to actually go against the OP, but it appears as if he went through a bunch of trouble to visualize the fact that healers go 3-3 more often, which no one disputes. DPS have a higher grenade-based “win expectation”, while healers win harder when they do get their own beneficial grenade. The net freebie rounds remains the same.

The actual question is if there’s a meaningful difference between between 1x 6-0 and 3x 3-3 vs. 3x 4-2 and 1x 3-3. It’s possible that more forced matches that solidify your MMR is damaging to a player’s net velocity, but it’s also possible that the freebie 6-0 spike counterbalances this. It depends on how much the algorithm increases MMR elasticity for larger wins vs. smaller wins, and how much it reduces it for going even.

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Saying something is ‘meaningless in practice’ is kinda meaningless in and of itself. There’s nothing wrong with assuming a uniform distribution for a random variable when there is no strong evidence indicating another prior distribution is more appropriate.

Yes, if you simply sum the win expectation as you did trivially, it does indicate equal win expectation. But you conveniently/deliberately excluding the second variable and a large point of the model, which is healer agency. If a DPS is the grenade, healers have very little agency to compensate/carry that player and force a non 3-3 outcome. But if the healer is the weak link, and if DPS has more agency than healers do (which no one should debate), it’s very easy to work out that DPS win expectation will be higher. This was like literally the whole point.

And if this doesn’t explain the clear and obvious divergence of mmr between healers and dps, what do you think does? I’m not seeing you attempt to explain it.

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Plebzgosplat you wrote an amazing post.

In all honesty you are great and I appreciate you for taking your time to explain this model and logic.

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This seems like it’s missing the point. You made a model where, assuming healers have a harder time (less agency), they have less wins. As the poster above said, with uniform prior the expected number of wins for healers and DPS assuming every game has a grenade is the same. I’m not sure something like an aff lock has any more agency than an Rdruid. Some classes are clearly better at carrying (e.g. ret/rogue who can make up for poor healer), but healers can also carry through controlling the strongest dps.

An easy explanation for divergence of healer/dps MMR is just number of players in the relative MMR pools (more people in the DPS MMR pool). An elo system requires you to push down the people less skilled than you to climb. If there’s more people below your skill level to push down you can climb faster.

https://twitter.com/FlorinBilbiie/status/1522908522467532802/photo/1

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Lol, right?

It reminds me of Lord Farquad from Shrek, furiously pushing to curate a ‘perfect world’.