Buyback state: which hero can return, and when?
A dead carry and a carry without buyback describe different facts. The first is a temporary absence. The second describes whether a particular return option is available. Mixing them produces a bad late-game model: a lost fight becomes an assumed buyback expenditure, an assumed expenditure becomes a dieback, and the dieback becomes a certain defeat. Record each transition separately. No step in that chain follows automatically from the previous one.
The useful question before a siege is specific: if this hero dies now, can the player buy back, and can the returning hero reach a useful position? A team-wide count cannot answer that alone. Losing the return option on an initiator can matter differently from losing it on a damage dealer or a support with an important save. Hero identity belongs in the state description.
Define availability from observed inputs
Write availability for hero i as Aᵢ = Eᵢ AND Cᵢ = 0 AND Gᵢ ≥ Bᵢ. Here E is eligibility under the active game rules, C is the remaining cooldown, G is usable gold at the relevant moment and B is the displayed cost. The expression is a modeling checklist, not a replacement for the client. A stale gold value or an unverified cooldown makes the result uncertain. Record that uncertainty instead of filling the field from memory.
For an arithmetic example only, choose B = 200 + floor(N/13), where N is net worth. At N = 34,000, this chosen function gives 2,815 gold. Starting with 4,800 gold and spending 3,000 leaves 1,800, below the example's threshold. Spending is therefore relevant even though total net worth may barely change. This example does not establish the current patch's cost rule, rounding convention or treatment of gold after death. Those require current game evidence.
Check the threshold after the event that matters. Gold before an item purchase does not establish affordability after the purchase. Gold before death does not establish the balance after death. Distinguish recorded facts from projected changes, including income while waiting. A chosen safety buffer can be useful for an analyst, but it is neither an official eligibility rule nor a universal percentage discount on the hero's value.
A small state machine can hide essential information
For two tracked heroes, two binary availability flags give four combinations: 11, 10, 01 and 00. Merging 10 and 01 into “one buyback” loses information whenever the heroes have different jobs. Across two teams there are sixteen joint flag combinations before adding whether heroes are alive, their positions, remaining cooldowns or buildings. This is still a simplification. It is more honest than calling a three-state summary a complete Markov model.
The Markov assumption says the chosen current state contains enough information to describe the next transition probabilities. Naming a spreadsheet a state machine does not prove that assumption. Two positions with identical buyback flags can have different futures because one has exposed buildings and the other has protected lanes. Either include those differences, model the transition conditionally, or acknowledge the omitted information. Do not use an attractive diagram to conceal a missing variable.
A siege tree with explicit assumptions
Consider a hypothetical attack. Assume the attackers win the opening fight with probability 0.55. Conditional on that win, defenders use buyback with probability 0.85. Conditional on both events, attackers win the renewed fight with probability 0.40. The four branch probabilities are 0.55 × 0.15 = 0.0825, 0.55 × 0.85 × 0.40 = 0.187, 0.55 × 0.85 × 0.60 = 0.2805, and 0.45. They sum to one.
These branches mean opening win without a defending buyback, opening win followed by a successful recontest, opening win followed by a failed recontest, and opening loss. They do not identify which hero bought back or whether a building fell. In particular, declining to buy back does not mean that buyback was unavailable. The decision could reflect positioning, a planned retreat, an already lost objective or information outside the model. Add observations before assigning a new availability state.
Dieback is dangerous, but it is not absorbing
A death after buyback can leave a hero unavailable for an important defense. It does not make the position mathematically terminal. The hero may respawn; opponents may lack damage, creeps or time; teammates may clear waves or force a retreat. In an absorbing game model, the terminal match result belongs in the absorbing state. A death remains a recoverable game state until the game actually ends. Avoid fixed claims that a dieback loses a stated percentage of professional matches without a documented sample.
Travel and objective timing explain why the same flags can matter differently. Compare the returning hero's observed route, teleport availability and expected arrival with the attackers' ability to reach and damage buildings. A defender need not return instantly to the fight, and an attacker need not walk the entire map. Use actual positions and current abilities. Similarly, a buyback cooldown and a Roshan respawn window start from different events; matching their nominal lengths would not synchronize them.
Price a scenario, then challenge its probability
Suppose an entirely hypothetical price is American +350, equivalent to decimal 4.50. An assumed win probability of 0.34 gives expected profit 0.34 × 4.50 − 1 = 0.53 per unit. At 0.26 the result is 0.17; at 0.20 it is −0.10. The break-even value is 1/4.50, about 22.22%. Buyback observations may change an estimate, but none of those observations independently supplies a calibrated 34% probability. The sensitivity check is the essential part of this example.
Build the observation log around actual purchases, deaths, buyback use, remaining cooldown and eligibility. Record what is unknown on the spectator feed. Review whether the additional state variables improve later predictions over a simpler gold-and-buildings baseline. If they do not, revise the model rather than declaring the bookmaker ignorant. There is no verified claim here about which proprietary inputs a sportsbook uses or how quickly it reacts.
Check the information set before the price
For a live assessment, put the game clock beside the time the information reached you. A broadcast frame, a public scoreboard and an available betting price can describe different moments. Record the source of each observation and keep an unknown field unknown. If the price has already incorporated a fight that your video has not shown, a neat calculation using that video is evaluating an earlier game state. Slow-moving inputs also need this check: a player can spend gold, change position or lose an objective between updates.
Keep a short decision record: event and map, ruleset, roster, relevant state, probability range, quoted odds and observation time. Write the reason before the result arrives. Include the cases you rejected, because studying only placed bets hides selection mistakes. A useful review asks which observation would have changed the decision and whether that observation was actually available at the time. An explanation invented after a win is not a forecast.
Test the estimate, including the decision to pass
Expected profit per unit at decimal odds O is p × O − 1, provided the bet has only win and loss outcomes. Settlement rules can add pushes, voids or partial payouts, so read them before applying that equation. The break-even probability is 1/O. Removing an overround from the offered prices produces a market reference under a chosen allocation method; it does not reveal the true probability. A disagreement with that reference is a research question until the independent estimate has supporting evidence.
Use later matches to test parameters fitted on earlier matches. Split by event or time rather than randomly scattering snapshots from the same map across training and testing. Otherwise the model can recognize a match it has effectively seen already. Check calibration, probability scoring and realized returns with uncertainty, alongside changes in patches and rosters. Closing-line movement is another diagnostic, but a favorable move alone cannot establish accurate probabilities or sustained profitability. When a plausible alternative assumption reverses the expected value, passing is a complete decision. A smaller stake changes exposure; it does not repair a faulty probability.
Related models and reading
These pages explain related methods. Their models do not independently validate the numerical assumptions in this article.
- net worth lead decay math
- buyback state machine derivations on EsportsMath.org
- Esports Odds Converter
- ignoring stream delay mistake
- Dota 2 betting strategy guide
Version context and organizer references
These official references provide patch or event context. They do not establish the hypothetical model coefficients, a current buyback cost formula or a complete ruleset for every event. Check the active client and the specific event rules for operational details.
