Moneydice | Heroscape Sabermetrics

[Chris Perkins]

A recent conversation inspired me to come up with some ideas for Heroscape Sabermetrics (advanced Baseball stat type stuff).

Came up with one to start, and wanted to start this thread to see if anyone else had ideas for cool/innovative stat ideas.

Tbh, these are probably more for fun than for actual value, but I do think there might be useful metric ideas hidden in here.

Here's a running list of the ideas posed in this thread so far:

Point Efficiency Per Squady (PEPS)
Goal: Measure the efficiency of the squad contribution of your army for a given point/figure format restriction.
Formula: (∑ Squad Points / # Squad Figures) / (Max Format Points / Max Format Figures)
Ex. Delta, 510 points, 18 figure max, Rule of 12
Army: Micro x2, PK x4
(490/18 ) / (510/18 ) ~= .98 = 98% efficiency

Meta-Health Index (MHI)
Goal: Measure the health of the meta of a given tournament by using the amount of point-overlap between armies as a proxy.
Read More

Lifense
Goal: Measure the survivability of a given figure
Formula: # Lifes x # Defense

Wound Efficiency Value (WEV)
Goal: Measure how efficient each figure is at dealing damage, either in a single game or over a larger sample size.
Formula: (∑ (targetPoints/targetLives) * woundsDealt) / points
Ex. Major Q10 deals 3 wounds to Grimnak and kills 6 Heavy Gruts. WEV(Q10) = [(120/5)*3 + (70/4)*6] / 150= 177 / 150 = 1.18.

[Sir Heroscape]

Oooo, what an interesting concept! I like this. I've always felt like there are "deeper" concepts like this that exist in the game the more that I've played. This is definitely an example of something I've done before but never "operationally defined" it. That is, optimizing the max number of squads in a given format is definitely something people do...but this puts a more direct measurement on army building that could help players evaluate matchups or just how they build their armies in general.

That is, if someone has a higher PEPS value when compared to their opponent...in theory, they have a more efficient army.

[Sir Heroscape]

I'll add to the list, something I heard somewhere but don't know who to give credit to (maybe dok?):

LIFENSE
Essentially it's a measure of survivability by multiplying the Life Stat X Defense Stat.
ex. Moriko has better Lifense than Deathwalker 9K (4def X 4life = 16Lifense, 9def X 1life = 9 Lifense)

Kinda helps put into perspective how units can be expected to survive. Hence why DW9K is so easy to kill all the time because he has such low lifense when compared to even the "simplest" of units.

[Shurrig]

I think the "Batting Average" sabermetric for Heroscape would be how many points a unit kills/wounds in a game over how many points said unit costs. If there isn’t a name for this already, I’d dub it as the Wound Efficiency Value [WEV(Δ)].


WEV/WEVΔ Equation

Much like batting avg., WEV(Δ) is a simple division equation. IE, If Major Q10 puts 3 wounds on Grimnak [24 points per wound x 3= 72) and kills 6 Heavy Gruts (105), your WEV for Q10 is 177/150= 1.180 (Δ is 219/170=1.288).


This stat does have its limitations, as it is not truly representative of every unit’s true value. Defenders like Rats/Raelin will not usually kill their point total and therefore will often average a lower WEV than a Nilfheim or Stingers. Inversely, units like Isamu or Marcu can easily hit way above their points due to their low point total/variance. Nonetheless, I think it’s a fun stat to track and still has its use cases for several types of units.

[ryguy266]

There was a discussion between @Chris Perkins and myself about a tournament evaluation metric, known for now as the Meta Health Index. With some time on my hands yesterday, I worked up an equation for assessing how healthy a tournament meta was, or essentially "how many different viable armies?" were there for the given format and is on a scale from 0 to 1, with 1 being the highest achievable score and 0 being the lowest. A healthy meta should fall within the .8-1 range.


The equation is loosely based on Jaccard similarity. The equation also weights higher ranking armies better, so that if the top 8 armies were all different but the bottom 8 were all identical, the MHI won't be as negatively affected as if the opposite were true. It again weights based on "player skill" represented by the players' all-time win-loss ratios on .org. Because the M values are point-based, the equation can be applied across all formats.

As an example of the MHI in action, I worked out the scores of Lincoln Seasonal IV and the top 4 of OST S6 Kaiju Wars by hand. I did the top 4 because I didn't want to code it out and it took a while, so the MHI is a little high because there were different lower-ranking armies. But it still serves as a good example.

Lincoln Seasonal IV MHI: 0.953.
Kaiju Wars Top 4 MHI: 0.127.

To reiterate, this is a little unfair to Kaiju Wars. But part of a healthy meta is that there are a wide variety of armies that do well, not just a wide variety of armies. And so while there were hounds armies and soulborg armies and Hydra armies, they would be given much less weight under the tournament placement factor, and so I don't expect that the MHI would increase by much.

I think this equation could serve as a useful tool for tournament directors. Generally, formats with low MHI scores lead to less interesting tournaments and less fun experiences for players. No one wants to play a mirror match. This is also something that would be fairly easy to implement as this information is all freely available on .org, but I would like to refine the MHI first.

I know we have tons of engineers, mathematicians, and statisticians in the community who are much smarter than I am. I would appreciate any feedback on this equation. I'm well aware it's not perfect, especially because there are extreme edge cases that would fall outside the bounds of 0 and 1. (But you don't need to mention that I used J and j in the same equation...blame Jaccard, not me.) ((And yes, I used Word's equation editor to type this up. Sue me.))

If people feel that this is worth its own thread, I will move it to its own thread. In my opinion it would be extremely helpful as a TD to have MHI scores for various formats at various point totals and variations. I would also be fascinating as a player and a scaper to evaluate the MHI of VCheese over the years.

[ryguy266]

A mistake in the equation has been pointed out already by the illustrious Chris Perkins. The Ra term should be *Ra, not *1/Ra.

[Chris Perkins]

I spent way too much time yesterday working on this with Ryguy But it was fun.

The upside is we got an altered version of the formula that was implementable on .org, and is now available in production. On the page of any finished tournament on .org, below the standings, it shows the MHI value, with a link to a PDF explaining the calculation in full.

The gist of the formula is the same as Ryguy's original, but I had to alter the weights considerably because the old scale was not actually bound to [0, 1], and we were seeing some values like -4.5 in practice/production with the original formula.

You can read more here if you're interested:
https://heroscape.org/documents/MHI%...h%20Index).pdf

[superfrog]

Does the heroscape.org implementation freeze results as of the tournament date?

i.e. does it use delta point values correct as of the event (seems like it definitely should), and does it update player strength values after the event (could make an argument either way)?

FYI the MHI for CCL Season 1 Qualifier #2 will not load for me.

[Chris Perkins]

Originally Posted by superfrog

Does the heroscape.org implementation freeze results as of the tournament date?

i.e. does it use delta point values correct as of the event (seems like it definitely should), and does it update player strength values after the event (could make an argument either way)?

No, it does not. It re-calculates upon each load.

I hadn't thought of the wrong delta points issue. Definitely not ideal. They don't change drastically over time, so it's probably not too much noise, but it's a good point/issue regardless.

It uses current player strength values, which I think is a good thing?

Originally Posted by superfrog

FYI the MHI for CCL Season 1 Qualifier #2 will not load for me.

Ooh, good catch.

That tournament had some players drop before it started, and their lack-of-armies was breaking the algorithm. Just updated it to exclude such players from the calculation.

Should be fixed now (might require force-refresh to get latest).

As a side note, this scale isn't incredible in the sense that it doesn't really go [0, 1] in practice. I suspect you picked CCL #2 because of the decent overlap in armies. I'm seeing MHI=0.9462 for it, and it obviously had a few clear army duplicates (and 4-5 units that showed up frequently aside from that).

I'm open to suggestions as to how to possibly scale the final value, since from what I've seen it rarely dips < 0.7, which leaves most of that [0, 1] scale unused in practice. But I decided to publish an un-scaled version first since it more directly correlates to the actual percent of overlap.

[lucasd21]

Love this thread idea. I kept stats for about a year during games, but trying to pin down value of certain characters was difficult due to the different uses (cheerleader, shark, bread and butter, etc.). I used something like the Wound Efficiency Value as a way to measure offensive output. However, to measure a card's value outside of strict attacking output I used what I'll call the Support Value.

It goes something like this:
(Number of order markers placed on a card)/(Number of times a card's power is used successfully).

The closer to 0, the more passive a unit is and does not require order markers. The closer to one, the more order markers a unit requires to support your army.

For example: Anytime a figure successfully defends an attack using raelin's aura, it counts as one in the first half of the equation. If a figure does receive a would, despite raelin's aura, her card was not successfully used. Let's say her aura successfully defends 20 attacks per game, and she had two order markers on her over the course of the game.
2/20 = .01 SV

Another example: Bonding. This scores very well because you are often not putting order markers on bonding heroes. However, in order to use bonding, it requires an order marker on the bonding squad. This results in bonding heroes receiving a lot of Support Value. Let's say you take 15 turns with the knights, and Finn bonds with them for 10 turns before he dies. Finn never had an order marker placed on him, then gets one more card power used for the post death attack bonus.
0/11 = 0 SV

One more: Rats. Ideally, you only need 1-3 order markers on them per game and are just using scatter the rest of the time. If you place 2 order markers in the beginning of the game to develop your rats and then move only using scatter 10 times, that's 2/10 = 0.2 SV

In contrast, an offensive figure like Q9 would score very poorly, although multiple attacks per order marker helps (possibly a flaw). Maybe over the course a game, 15 order markers are placed on him while the rats do the dirty work. His special attack was successfully used (dealt a wound) 18 times, but only with an order marker on it. 15/18=0.83.

There are definitely flaws in this. For example, anytime a unit never has an order marker on them the result is 0. The larger the number for the latter half of the equation the better the Support Value, despite the number of supporting actions potentially being 0. Non-zero values for successful power usage do not receive a score.

I'm sure there are ways this could be developed further, but just something I came up with a couple years ago.

[lucasd21]

Realizing now that some of the stuff in my Raelin example is wrong, so disregard the parts that are incorrect. The general idea is hopefully still easy to understand.