Target Speed

See Race Mechanics for more information on other phases of the race.

The Target Speed is the Velocity an Uma tries to maintain during any Phase. If the Uma’s Current Speed is below the Target Speed, she will accelerate to reach the Target Speed. Conversely, if the Uma’s Current Speed is above the Target Speed, she will decelerate until she reaches the Target Speed.

The Target Speed is calculated as a function of the Uma’s Style, Skill Activations, and Phase of the race.

Formula

The full formula for Target Speed is:

$$\begin{array}{rl}\text{TargetSpeed}& =(\text{BaseTargetSpeed}\mid \text{LastSpurtSpeed})\\ & \times \text{PositionKeepCoef}+\text{ForceInMod}+\text{SkillMod}\\ & +\text{SlopeMod}+\text{MoveLaneMod}\end{array}$$

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This is, in essence:

1. Base Target Speed – the most consistent factor of an Uma’s velocity. Based on an Uma’s Style and the Race Phase.
2. Last Spurt Speed - In the late-race, if the Uma has enough HP to survive Spurting, she will transition from the late-race Base Target Speed to a much higher Top Speed.
3. Position Keep Coefficient – In roughly the first half of the Race (10 out of 24 sections), Umas are subject to Position Keep based on their Style.

See Position Keep for more details.

4. Other Modifiers – There are four more modifiers:

   1. ForceInMod - A tiny increase in speed in the early-race to help an Uma move into an inner lane when she is more than 0.12 course widths away from the inner lane.
   2. SkillMod - Velocity acquired from Skills.
   3. SlopeMod - Uphills will decrease an Uma's Target Speed, while downhills have a chance based on Wit to increase an Uma's Target Speed.
   4. MoveLaneMod - While under the effect of a Navigation Skill, any lateral movement grants a Target Speed bonus based on Power.

Base Target Speed

Base Target Speed is the core part of an Uma’s Target Speed and contributes the most to her total Target Speed.

$$\begin{array}{rl}\text{BaseTargetSpeed}& =\text{BaseSpeed}\times \text{StylePhaseCoef}\\ & +\text{IsLateRace}\times (\sqrt{500\times \text{SpeedStat}}\times \text{DistanceProf}\times 0.002)\text{m/s}\end{array}$$

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In the early-race (Phase 0) and mid-race (Phase 1), Target Speed is determined by the Track Conditions, Track length, and the Uma’s Style.

In the Final Leg (Phase 2) and Last Spurt (Phase 3), Base Target Speed is additionally affected by the Uma’s Speed stat. The Uma will run at Base Target Speed if she does not have the HP to start her Last Spurt at the start of the Final Leg.

INFO

An Uma’s Speed stat has no effect on her Base Target Speed until the Final Leg.

Base Speed

Base Speed is calculated based on Track distance, and is one of the main components of Base Target Speed. On a given Track, all Umas will have the same Base Speed.

$$\text{BaseSpeed}=20.0-\frac{\text{CourseDistance}-2000}{1000}\text{m/s}$$

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Style Coefficient

An Uma’s Target Speed is also dependent on her Style. Front Runners will start off fast and slow down, while Backliners will speed up over the race.

Style	Early-race	Mid-race	Late-race & Last Spurt
Runaway	1.063	0.962	0.95
Front Runner	1.0	0.98	0.962
Pace Chaser	0.978	0.991	0.975
Late Surger	0.938	0.998	0.994
End Closer	0.931	1.0	1.0

Distance Proficiency

An Uma's Base Target Speed in the Final Leg (Phase 2) and Last Spurt (Phase 3) is affected by their Distance Proficiency.

Distance Proficiency	S	A	B	C	D	E	F	G
	1.05	1.0	0.9	0.8	0.6	0.4	0.2	0.1

Last Spurt Speed

Prior to entering the Final Leg, the Last Spurt Distance and Target Speed are calculated.

$$\begin{array}{rl}{\text{LastSpurtSpeed}}_{\text{Max}}& =({\text{BaseTargetSpeed}}_{\text{LateRace}}+0.01\times \text{BaseSpeed})\times 1.05\\ & +\sqrt{500\times \text{EffectiveSpeed}}\times \text{DistanceProf}\times 0.002\\ & +(450\times \text{EffectiveGuts}{)}^{0.597}\times 0.0001\text{m/s}\end{array}$$

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On entering the late-race, the game checks if the Uma has enough HP to run at the max Target Speed.

1. If she has enough HP, then she runs at her Last Spurt Speed.
2. If not, the game will calculate combinations of delayed Spurting and lower Target Speeds, and rank these by time. The Uma will attempt to roll the best time based on her Wit stat, using the following formula:

$$\text{SpurtRecalc}=15+(0.05\times \text{EffectiveWit})\mathrm{\%}$$

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Depending on the Wit rolls, the Uma could run at a lower Target Speed than the calculated Last Spurt Speed, or delay her Last Spurt until a point in the Race where she has enough HP to increase her Target Speed.

WARNING

The Last Spurt calculation does not include the last 60m of the race: The Uma can still run out of HP towards the end of the race.

INFO

Activating a recovery skill will cause a last spurt speed recalculation, while receiving debuffs do not.

Other Modifiers

Force In

Force In occurs when an Uma is more than 0.12 course widths away from the inner rail in the early-race and there is a spot the Uma can move to. The Uma will slightly speed up according to the formula below.

$$\text{ForceInMod}=\text{Random}(0.1)+\text{StrategyMod}\text{m/s}$$

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Strategy	Strategy Modifier (m/s)
Front Runner	0.02
Pace Chaser	0.01
Late Surger	0.01
End Closer	0.03

Move Lane

When an Uma moves laterally while under the influence of a Navigation Skill, she will increase her Target Speed by the Move Lane speed.

$$\text{MoveLaneMod}=(0.0002\times \text{EffectivePower}{)}^{0.5}\text{m/s}$$

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Slopes(Uphill)

When running up a hill, an Uma loses Target Speed equal to

$$\text{UphillSpeed}=\text{SlopePer}\times \frac{200}{\text{EffectivePower}}\text{m/s}$$

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Slopes(Downhill)

When running downhill, an Uma will roll a Wit check using the DownhillCheck formula. If successful, the Uma's Target Speed will increase by DownhillSpeed, and HP consumption is reduced by 60%. Every second, there is a 20% chance for this effect to end.

$$\text{DownhillCheck}=\text{EffectiveWit}\times 0.04\mathrm{\%}$$$$\text{DownhillSpeed}=0.3+\frac{\text{SlopePer}}{10}\text{m/s}$$

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Section Randomness

Each section, an Uma will roll a Target Speed modifier that is calculated as the Base Speed multiplied by a random number.

This random number is between the following:

$${\text{Modifier}}_{\text{Max}}=\frac{\text{EffectiveWit}}{5500}\times {\log }_{10}(\text{EffectiveWit}\times 0.1)\mathrm{\%}$$$${\text{Modifier}}_{\text{Min}}={\text{Modifier}}_{\text{Max}}-0.65\mathrm{\%}$$

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The Last Spurt speed is not affected by Section Randomness.

Minimum Speed

Umas have a Minimum speed after the initial Start Dash. They will not slow down past their Minimum speed. This can occur when an Uma runs out of HP (i.e. HP = 0) or if Pace-Down mode tries to slow them down below Minimum speed.

$$\text{MinSpeed}=0.85\times \text{BaseSpeed}+\sqrt{200\times \text{EffectiveGuts}}\times 0.001\text{m/s}$$

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Starting Speed

The Current Speed at right out of the Starting Gate is 3m/s.

Blocking

When an Uma is blocked, she can run no faster than the Uma blocking her. An Uma is considered blocked when another Uma is within 2 meters ahead and within a lane gap threshold:

$$\text{LaneGapThreshold}=(1.0-0.6\times \frac{\text{DistanceGap}}{2})\times 0.75\text{LaneWidth}$$

This means the blocking "cone" is wider when the blocker is closer: 0.75 horse lanes when 0m away, narrowing to 0.3 horse lanes at 2m away. If multiple Umas satisfy this criteria, the one with the smallest distance gap is considered the blocker.

While blocked, the Uma's speed is limited to:

$$\text{BlockedSpeed}=(0.988+0.012\times \frac{\text{DistanceGap}}{2})\times \text{BlockerSpeed}\text{m/s}$$

The closer the Uma is to her blocker, the slower she runs. At 0m gap, speed is capped to 98.8% of the blocker's speed; at 2m gap, it's capped to 100%.

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