Problem → Inputs → Model → Outputs → Interpretation

Problem

Race-day choices rarely reduce to “pick the favorite.” Value hides in mismatches between public odds, private pace figures, and the track’s takeout policy. For a bettor running a disciplined sheet, the core decision is: given book prices with embedded overround, homegrown pace estimates, and a finite bankroll, what portfolio of dutched bets maximizes geometric growth without exposing the bankroll to catastrophic single-race drawdowns? This tool treats the race as a portfolio allocation problem where each horse is a project with an uncertain payoff. By synthesizing sectional times, going, and draw bias into probabilistic opinions, then filtering them through fractional Kelly sizing, you can stage bets that respect both your edge and your risk tolerance.

Inputs

The calculator takes six global inputs plus per-runner details. Bankroll sets the bankroll constraint. Number of runners builds a dynamic roster—up to twelve entrants, matching typical turf handicaps. Fractional Kelly lets you dial aggressiveness. Overround captures the bookmaker margin by summing 1/odds across the field; enter 1.18 to mimic an 18% margin. Pari-mutuel takeout handles tote pools, shaving payouts proportionally. The correlation dampener tempers dutching stakes because only one runner can win; it shrinks allocations in highly correlated slates. Pace synthesizer weights allocate importance among sectional times, going adjustments, and draw bias when computing normalized pace indices.

Each runner contributes five data points: a label (horse name or post), decimal book odds, an optional personal fair probability percentage, a last-3f sectional time in seconds, a going suitability score, and the draw number. Going is a dropdown anchored at −0.6 for a horse that dislikes the surface, 0 for neutral, and +0.6 for a specialist. The draw number calibrates the pace synthesizer’s spatial bias.

Model

The model performs four transformations. First, it builds pace indices. Sectional times are inverted so faster finishes (lower seconds) score higher; the sectional weight scales the deviation from the field average. Going scores and draw bias feed weighted adjustments. Draw bias uses a simple linear bias: in fields of twelve, low draws often save ground on turf, so the synthetic bias equals $\frac{n/2-d}{n/2}$, normalized between −1 and +1 before applying the draw weight.

Second, the pace indices convert to probabilities via a temperature-controlled softmax. The normalized pace probability for runner i is $\frac{e^{\tau zi}}{\sum {e^{\tau zj}}_j}$, where $\tau$ is an implicit temperature chosen to prevent overconfidence. Third, if you supply a personal probability, the model overrides the softmax with that value (after converting from percent), then renormalizes the full set to sum to one. Fourth, fractional Kelly sizing uses the net profit multiple after takeout. In MathML, the dutching stake fraction for runner i is

$f_i={\lambda }_F·max(\frac{pi·oi-1}{oi-1},0)$

where ${\lambda }_F$ is the fractional Kelly multiplier and $oi$ is the effective decimal odds after takeout. The correlation dampener rescales stakes to prevent the sum from exceeding the bankroll and to reflect mutual exclusivity. Expected return and drawdown risk derive from the discrete outcome distribution of dutching: either one of the backed runners wins with profit $\pi i$, or none do and you lose the total stake.

Outputs

The results panel lists each runner’s pace index, blended probability, raw and dampened Kelly stakes, and net profit if the horse wins. It aggregates expected value, variance, and a 10% bankroll drawdown risk metric. The sensitivity table quantifies how ±5% errors in your fair probabilities impact expected profit. CSV export contains runner-level metrics for offline record keeping.

Interpretation

Because the tool renormalizes probabilities, you immediately see when your opinions conflict with the pace synthesizer—huge manual probabilities force the others to shrink. Overround adjustments reveal whether the bookmaker is taking more margin than usual; if the sum of 1/odds spikes to 1.24, even positive pace signals might not justify bets. The correlation dampener reminds you that dutching four short-priced runners can silently risk 30% of bankroll unless scaled back.

Worked 12-Runner Handicap Example

Consider a summer turf handicap with twelve runners and a market overround of 1.18. Your bankroll is $10,000, and you choose a 0.3 fractional Kelly. The form notes below feed the input grid:

• Runner 1 “Storm Signal”: decimal odds 5.5, sectional 34.1s, going +0.6, draw 3.
• Runner 2 “Harbor Light”: odds 7.0, sectional 34.5s, going +0.3, draw 7.
• Runner 3 “Midnight Ridge”: odds 9.0, sectional 34.9s, going −0.2, draw 11.
• Remaining runners cluster between 10.0 and 26.0 with sectional times 34.5–35.8s and mixed goings.

You manually set Storm Signal’s fair probability to 24% and Harbor Light to 18%, leaving the rest to the pace synthesizer. The tool reports pace z-scores centered at zero, with Storm Signal at +1.1 and Midnight Ridge at −0.6 due to its wide draw and slower sectional. After renormalization, your blended probabilities sum to one: Storm Signal 0.23, Harbor Light 0.17, and the rest between 0.02 and 0.09. Book overround of 1.18 indicates the market expects 18% vigorish, while the takeout of 16% reduces effective payouts.

Kelly fractions before damping suggest staking $1,020 on Storm Signal, $620 on Harbor Light, and between $90 and $260 on three mid-priced closers. The correlation knob trims exposures by roughly 15%, resulting in a total stake around $2,600—still only 26% of bankroll thanks to the fractional Kelly. Expected profit on the portfolio is $310, variance is $9,800, and the probability of losing more than 10% of bankroll on the race is 9%. The sensitivity table shows that overestimating probabilities by 5% boosts expected profit to $520, while underestimating by 5% drops it to $120, underscoring how fragile edge estimates can be.

Comparison Table: Kelly Fractions

This comparison clarifies the growth-versus-volatility trade-off. Moving from 0.3 to 0.4 fractional Kelly only adds $70 of expected profit but increases drawdown risk by four percentage points.

Assumptions, Limitations, and Practical Tips

The synthesizer uses a linear pace model; real races feature pace dynamics, jockey tactics, and in-race trouble that defy deterministic scoring. Overround input assumes decimal odds; fractional odds must be converted before use. Takeout adjustments approximate tote payouts but ignore breakage. The correlation dampener is heuristic—true covariance between horses depends on race shape and entry coupling. Treat outputs as guidance rather than gospel.

Practical tips: (1) record sectional times in the same units for all runners to keep the pace synthesizer honest; (2) recalibrate going scores by track—some surfaces favor wide draws; (3) export the CSV to compare planned stakes with settled results; (4) re-run the tool when scratches alter field size or pace complexion; (5) keep fractional Kelly below 0.4 unless your probability estimates come from a tested model.

Testing Checklist

• Edge cases: zero or negative odds trigger validation warnings.
• Rounding: stakes rounded to the nearest dollar for execution simplicity.
• Performance: recalculates twelve-runner grids without noticeable delay.
• Accessibility: each control labeled; results announced via aria-live.