The Economics of Match Events

February 24, 2025

Nearly all economic activity in match-based or “saga”-based metas follows the fundamental relationship:

[ text{Revenue}_{i} = text{Gold Sink}_{i} = text{Attempts}_{i} cdot text{Gold Sink Per Attempt}_{i} ]

where,

(bullet) (text{Revenue}_{i}) is the revenue for the (i)th player. (\) (\) (bullet) (text{Attempts}_{i}) is the number of attempts made by the (i)th player. (\) (bullet) (text{Gold Sink Per Attempt}_{i}) is the average of gold spent per attempt by the (i)th player. (\)

(\) Holding (text{Gold Sink Per Attempt}) constant, an increase in (text{Attempts}) leads to higher (text{Revenue}). Similarly, increasing the (text{Gold Sink Per Attempt}) while holding (text{Attempts}) constant also raises (text{Revenue}). Many innovations in match economies operate within this framework. For instance, a “super light ball” mechanic increases (text{Attempts}) but reduces the (text{Gold Sink Per Attempt}). Events follow the same structure.

Basic Match Model

At the aggregate level, revenue across all players is:

$$ text{Revenue} = sum_{i}bigl(text{Attempts}{i} cdot text{Gold Sink Per Attempt}{i}bigr) $$

Event Uplift

Events affect revenue by shifting the number of attempts or the gold sink per attempt. The marginal uplift from an event ((e)) is given by:

$$ text{Event Uplift}{e} = Delta text{Attempts}{e} cdot Delta text{Gold Sink Per Attempt}_{e} $$

where (Delta text{Attempts}) and (Delta text{Gold Sink Per Attempt}) are increases due to the event.

Effective Rewards

Events also distribute rewards, which function as a gold source in a simple gold-only economy. The effective rewards generated by event ((e)) are:

$$ text{Effective Rewards}{e} = sum{s} Bigl(text{Reward Amount}{s,e} cdot text{Win Rate}{s,e}Bigr) $$

where: () (bullet) (text{Effective Rewards}{e}) is the effective gold rewards from event ((e)). () (bullet) (s) indexes different reward tracks, or stages in the event. () (bullet) (text{Reward Amount}{s,e}) is the gold amount granted at stage ((s)) of event ((e)). () (bullet) (text{Win Rate}_{s,e}) is the probability that a player reaches stage ((s)) and claims the reward in event ((e)).

Generally, games find that engagement is also strongest when the effective rewards are highest. Tracking either progression speed (win rate) or reward amounts amplify any event’s effect.

Event Effect: Net Source or Sink

The net economic effect of an event is determined by subtracting the total effective rewards from the total event uplift:

$$ text{Event Effect}_{e} = text{Event Uplift}_{e} – text{Effective Rewards}_{e} $$ (\) (\) If (text{Event Effect}_{e} > 0), the event acts as a net sink, removing more gold from the economy than it introduces. Whereas, if (text{Event Effect}_{e} < 0) the event acts as a net source, introducing more gold than it removes.

Not all events need to be net sinks. Events can function as planned gold sources, offsetting reductions in base saga rewards to maintain long-run economic stability. In this scenario, base saga victory rewards are reduced while event rewards compensate, ensuring that the total gold sourced per attempt remains stable but with different sources.

How Many Events to Run

For a series of events that act as net sinks, running multiple events concurrently increases total gold sink. However, each additional event faces diminishing returns in increasing either (text{Attempts}) or (text{Gold Sink Per Attempt}), while (text{Effective Rewards}) remains relatively stable, or monotonically increasing (win rate is generally pushed upward as rewards rise, even though the rate of increase declines at every +1 event).

[ text{Event Effect}_e = gamma^{(e-1)} cdot Bigl(text{Base Uplift} – text{Effective Rewards}_eBigr) ]

Where, () (bullet) (text{Base Uplift}) is the uplift if the event ran alone. () (bullet) (text{Effective Rewards}_e) is gold distributed by the event. () (bullet) (gamma) controls how quickly subsequent events’ net effect diminishes. () (bullet) As (e) increases, (gamma^{(e-1)}) becomes smaller, reflecting diminishing returns for each additional event. () () The optimal number of concurrent events occurs when:

[ sum_{e=1}^{n} text{Event Effect}_e = 0 ]

Beyond this point, an event is a net source, which is not sustainable in the long run without other economic adjustments. This should be how teams assess event stacking! Set up A/B tests to find this zero point; by all means, Royale Match suggests 5-6 events.

Conclusion

Match events should be rigorously modeled to understand their economic effects. Contrary to common belief, an event’s effectiveness is not solely determined by its ability to act as a net sink. Structuring events as alternative sources of rewards can be LTV-positive compared to embedding the same rewards in saga progression.

Balancing reward scalars—designing an event with the same Event Effect but significantly higher uplift and effective rewards—creates different economic trade-offs. Remember, these two are causally linked: offering more rewards increases attempts. Or consider experimenting with holding the effective rewards constant, increasing the win rate but lowering the prize.