Personal Delta - Balancing Unit Costs for the Way You Play

[Knight of Scape]

After recently getting reinvolved with the Heroscape-playing sections of the boards (thanks to @kevindola and @Dysole convincing me to try out Online Heroscape), I felt motivated to share about how I've been playing Heroscape at my house all these years. I doubt many people are really looking for a comprehensive overhaul of the way they play a game that's been discontinued for a decade (I don't know if anyone even uses the original Delta system anymore), but maybe some of you will find it interesting.

"Personal Delta" is an idea my brother and I first started using it for our games way back in 2012, inspired by the Heroscape Legacy (later renamed Delta) project on the forums, and other similar efforts (e.g. @dok 's auction draft format). We've been using some form of this system for our games ever since, right up through 2020 (although we've added some other pretty major house rules since then, that I plan to share in a later post).

THE INSPIRATION

Everyone knows that Heroscape is not a completely balanced game. Some units are way better than others, at least for their cost. The simplest way to try to fix this is just to change units costs. This is what Delta/Delta+ tried to do, choosing new costs for every card so that they would be balanced for competitive play. There are some problems with their approach, however:

1. Finding the "right" costs for units is hard. There was plenty of disagreements over the Delta costing, despite the fact that quite a few smart people spent a lot of time into trying to get them just right. Finding the right costs for units is hard, and you're unlikely to find values that everyone can agree on.

2. The "right" price for a unit may not be constant. It depends on the current meta: on what armies other players are playing and on what kind of tournament formats are commonly used. It can also change dramatically as new VC units are released that shake up the competitive landscape. Delta tried to address this by having regular updates to the cost, but that approach magnifies issue 1, it requires a lot of effort on the part of the creators and leads to lots of disagreements about what's fair.

3. Not everyone plays "competitive" Heroscape. Lots of players prefer building maps that are cool-looking to ones that might pass the BoV. Some groups routinely play with 1000+ point armies. Many people don't have all of the figures (and don't feel like proxying all the ones they don't).

For my family, the main motivator was our limited collection. While we had quite a few Heroscape figures, like many players, we had a bunch of 1x copies of commons, because it took us way too long to realize how much better common cards were when you had multiples (I blame RoTV for including only unique squads :P ). We were also missing some key synergies (e.g. thanks to the reprint via wave 10, we have 3xBlastatrons, but we have 0xGlads).

Most common squads are still fun to play if you treat them as uniques (although Marro Drones suck), and many units are still interesting without their usual synergies (Our blasts usually get paired up with X17, but they also have the interesting strategy choices of when it's worthwhile to rush some of them into melee to boost the others' attack). In this context, however, the values of units can be substantially different both from their official prices and from the tournament balanced costs of something like Delta.

What we wanted was essentially a set of point values customized for our own household meta, but coming up with these would probably require being way better at Heroscape than we were, and, as noted above, there isn't even a guarantee that any fixed set of prices would accomplish what we wanted (every unit being picked about equally often).

What I came up with was basically a simple algorithm for repricing units that would update every card's cost after each game to constantly keep our metagame fresh.

THE GOAL

My goal was really simply to make a system where, in the long run, every army card is used in about the same number of games (to be mathy, for any two units, the ratio between the number of games they've each been used in should go to 1 as the total number of games goes to infinity).

You can question whether this is a desirable goal (maybe you want some units to be picked more often, because you're okay with, for example, bonding heroes only getting picked with the units that they bond with), but I think it's a reasonable indicator of balance.

One thing that was not the goal was to arrive at a final fixed cost for each unit. We usually play draft games, and part of the fun is combing through the list of current unit costs the day before a game to look for cards that are currently great deals which your opponent might not have spotted. If you're not into theoryscaping or army building, and just want to throw together a quick army and go, this is probably not going to be fun.

This approach also probably only works if you have a small group of people that you play with consistently. Having costs constantly changing when you haven't even played a game sounds frustrating.

THE SYSTEM

All that the Personal Delta system really takes is a little bit of spreadsheet magic. The spreadsheet that my family actually uses for our games is very messy and has a bunch of complicated math and special cases for tweaks that we wanted to try to customize the approach (some of which were of pretty questionable effectiveness), but the basic system is quite simple.

I put together an example spreadsheet to illustrate how it works, using a series of 10 games with just the RoTV set. Feel free to make a copy and play around with it if the system is interesting to you.

Personal Delta Example

The customizable parts of the sheet are Columns A, D, and H onward, as well as cells F7 and F10.

How it works is you put whatever units you have in column A, and their starting costs in column D. Delete the example values in column H onward, and then every time you play a game, fill in the first empty column on the sheet by putting a 1 in the row of every unit which was picked that game. Even if multiple cards of a common unit were used, only a put a 1 in the cell (don't do this while you're drafting, or the costs of units you've already picked will change mid-draft, which is super confusing).

Note that the spreadsheet assumes that the changes to the costs are incorporated after every single game, so if you enter ten games in a row played with the original costs, you'll get wacky results, because the spreadsheet will think you just kept picking a unit despite it's cost repeatedly going up.

The parameter "Costs must be multiples of" does exactly what it says on the tin. By default I set it to Heroscape's 5, although for my Personal Delta system, we set it to 1 (so units can have costs of 87 or 143). If you're on the other extreme and hate odd number costs, you can set it to 10 so everything is nice and even. This just affects the rounding.

The parameter "Delta" is a little more complicated. In essence it affects how quickly costs change, and therefore also how stable the costs are once they reach relatively balanced values. 10-20 is probably a reasonable range.

More technically, every time a unit is picked in a game, their cost increases by Delta%, and then all costs are rescaled to sum to the same value they originally did (so the total cost of all the units never increases or decreases by more than the margin of error from rounding). This has the effect of slowly driving down the costs of units that aren't picked. If you have a lot of figures and feel that some of them are very overcosted, it might take a very long time for their costs to decrease to a reasonable value.

One thing we've done is start the system with a high Delta value (like 20), and then, once costs have started to stabilize, restart the system with the "original costs" of the units set to their final costs from the last run and the Delta value reduced to 10. Another option would be to just start each unit at a rough guess for what their actual value is (so bump Raelin up and Taelord down for example)

If you assume that each unit has a "true value", and players always pick the unit which is the best deal relative to their true value, then after running the Personal Delta system for long enough, eventually every unit's cost will just fluctuate in the range of their true value plus or minus (Delta/2)% (so with Delta=10, the costs end up staying within about 5% of the unit's true value).

These small fluctuations encourage players to continually be trying new units and army combinations. In theory, every unit should get picked equally often by around the time that every unit has been picked at least once and skipped at least once.

CONCLUSION

Well that was longwinded (as those of you who frequent the CoN forums would expect from KoS).

I'm always interested in tweaking and improving our houserules (this spreadsheet has gone through many iterations), so if any of you all have thoughts or comments on this system, or questions about it, I'd be happy to hear them.

If any of you try this, or if you play with something similar, I'd be interested to hear your stories (is adjusting Heroscape costs for balance even still a thing these days?).

If nobody cares that's okay too. At least now if I get around to posting my customs thread, I have a justification to link to for why I stink at pricing units :P

THE IMPROVEMENT

2020/05/20 EDIT: I created a more advanced version of the spreadsheet.

Personal Delta Version 2

This version can still be used in the same way as the old one if you ignore all of the additions. It takes a little big longer to update the prices after you make changes, but it has some extra features:

1. In addition to the Delta value that you can set for all cards in cell G7, you can set a specific Delta value for each card in column E to cause that card's price to be more or less variable than that of other cards. If you leave a cell in column G blank, that card will use the default Delta value from G7. In particular, note that setting Delta=0 for a card will cause that card's price not to change, more or less (there may still be small variations due to the rescaling to keep the total cost of units consistent). For example, in the sample spreadsheet, I have decided that Agent Carr is perfectly costed, and I want Deathwalker 9000's price to change more rapidly than that of other units.
2. It is now possible to add new units to the sheet or remove old ones without having to reset the whole game record. This is useful if you acquire new Heroscape cards/customs, or sell old ones.
   • If you want to add a unit that wasn't available from game 1, just put "start" in the card's row in the column of the last game before the unit was added. In the same spreadsheet, my custom "Ithariel" was only available starting in game 11.
   • If you want the Delta system to stop considering one of the cards (without messing up the current prices of other cards), type "end" in the card's row in the column of the first game the unit was unavailable for. I recommend also right clicking that unit's row and choosing to hide it. Deleting the row would mess up other cards' costs.
   The spreadsheet will calculate the price of a card based on how that card's number of uses compares to the average unit who was available in the same games.
3. The spreadsheet has a new tab "Sorted Pricesheet", which contains the same price data as the main "Prices" sheet, but sorted alphabetically and by price for easier drafting/army building.
4. The spreadsheet has another new tab "Statistics", where you can see all of the different prices that each card has been purchased at, as well as the average cost of the card when it is purchased and the average purchase costs scaled to sum to the same amount as the original costs. (The spreadsheet also has new tabs "Magic" and "Black Magic" for behind the scenes calculation, but I recommend not interfering with the ancient spells of spreadsheet)

[superfrog]

This is a fun way to play if you like staying in your collection and keeping some variety. Good stuff, KoS!

[flameslayer93]

Really cool! I’ve wondered how a fluctuating prices thing would be done, and it looks like you’ve answered that!

[Alexandros]

Really cool idea! Is there a way someone could lock the costs of certain units at a specific value, to try to rebalance only certain units?

[Ketchupgeek]

Originally Posted by Amarant

Really cool idea! Is there a way someone could lock the costs of certain units at a specific value, to try to rebalance only certain units?

Sounds like you manually changing the starting point cost of that unit should do this, right? It wouldn't lock it, but it'd give it a different value to test from, and then the delta system alters it from there based on picks.

[caps]

Neat system.

[Knight of Scape]

Originally Posted by Amarant

Really cool idea! Is there a way someone could lock the costs of certain units at a specific value, to try to rebalance only certain units?

Sorry for a delayed response, I saw this when I was in the middle of prepping for finals and then I got overwhelmed with school and forgot about it.

If you actually want to exclude some units from the system entirely, the easiest thing would be to just not include them in the spreadsheet/record of games. It doesn't actually have to be your whole Heroscape collection.

If you want to include them in the sheet but ensure that their cost never changes, the easier thing would just be to change the value in column B to be a fixed number, like 100, instead of the formula that's currently there (something like '=IF(ISNUMBER(I2),$G$10*ROUND(I2/$G$10),"")' ).

Alternatively, I've created a new more advanced version of the spreadsheet that kind of incorporates this as a feature:
https://docs.google.com/spreadsheets...it?usp=sharing

(I'm actually planning to use a copy of this exact spreadsheet for my home games going forward. It also has some new features I wanted myself (see the updated OP), and is less messy than what I was previously using)

If you want to keep a unit's cost from changing based on the number of times it was picked, you can set the "individual Delta" for that unit to 0 in column E (for example, in my sample spreadsheet I decided that Agent Carr was perfectly priced just as he was). While this means that the number of times Agent Carr is picked isn't going to affect his price, it doesn't actually quite guarantee that his cost will never change, due to some technicalities of how the formula works, but it will probably keep it within +/-5pts of the original cost.

Personally I'd recommend using some low value (e.g. 2 or 3) instead of 0, because I think that even a perfectly costed unit's value has the potential to change in response to changes in the meta (e.g., if human champions get cheaper, Knights and MacDirks get better, even if they were correctly costed before), but if you want to use this system to price customs or something, I can see where you'd want to fix values (although I can't speak one way or another for how well this works for determining prices for customs while keeping all the existing units' prices fixed, that's not really what I designed it for).

~KoS, belatedly and longwindedly