How to Choose Fielders in a Sports Game (Cricket Example)

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When developing a cricket/soccer game, one of the key challenges is determining which fielder should respond to the ball based on its predicted location. In this post, we’ll cover two approaches to determine how to score and select the best fielders based on their proximity and alignment with the ball’s path.

Let’s assume the game engine calculates the ball’s velocity and location, and our goal is to select the best fielder(s) for the current play. There are two key factors we can use:

  1. Ball Direction and Fielder Alignment
    The fielder’s alignment to the ball is crucial for how well they can intercept it. We can calculate this by taking the dot product between the ball’s velocity vector and the fielder’s looking direction. Here’s how it works:

    • Dot Product: The dot product between two vectors (e.g., ball velocity vector V_ball and fielder’s looking direction vector V_fielder) gives us a measure of how aligned the two vectors are.
      • If the dot product is close to -1, it means the ball is coming directly towards the fielder (score of 1).
      • If the dot product is close to 1, it means the ball is moving away from the fielder (score of 0).
      • Values between -1 and 1 give us intermediate scores that we can use for more nuanced decision-making.

    Mathematical Function for Dot Product-Based Score:

    score1 = (1 + dot(V_ball, V_fielder)) / 2

    This function ensures that:

    • When the dot product is -1 (perfect alignment), the score is 1.
    • When the dot product is 1 (opposite direction), the score is 0.
    • Intermediate values between -1 and 1 scale the score accordingly.

  2. Proximity of the Ball to the Fielder
    Another key factor is how close the ball is to the fielder. The closer the ball is to the fielder’s position, the higher the score. We can define a minimum distance (e.g., 400 units) where the score would be 1, and anything closer or further would scale the score accordingly.

    Mathematical Function for Proximity-Based Score:

    distance = ||ball_position - fielder_position||  // Euclidean distance
score2 = max(0, min(1, (400 - distance) / 400))

    This function calculates the Euclidean distance between the fielder and the predicted position of the ball. If the distance is 400 units or more, the score will be 0. As the ball gets closer to the fielder (less than 400 units), the score increases towards 1.

Combining Both Scores

Now that we have two scores based on alignment and proximity, we can combine them to get an overall score for the fielder. The combination can be done heuristically by giving weights to each factor based on how important you want each one to be in the selection process.

For example, if we want equal weight (50%) for both the alignment and proximity, we calculate the final score as:

final_score = 0.5 * score1 + 0.5 * score2

This final score can then be used to rank multiple fielders and select the best ones (for instance, the top 3 or top 2 based on the highest scores).

Accounting for Ball Movement

Rather than using the ball’s current position, we use the predicted position of the ball after some time (e.g., 5 seconds). This can be calculated using the ball’s velocity and projectile motion formulas (for airborne balls) or Newton’s laws of motion (for grounded balls). In Unreal Engine, you can use the built-in Predict Projectile Path function to simulate the ball’s trajectory.

  • For airborne balls, you can predict the future position using the projectile motion equations.
  • For grounded balls (when the ball is moving with little vertical velocity), you can apply Newton’s laws to calculate how the ball will travel on the ground.

Example Workflow in Unreal Engine

  1. Predict the ball’s position after 5 seconds using Unreal’s PredictProjectilePath (for airborne balls) or custom Newtonian motion for grounded balls.
  2. Calculate the dot product score between the predicted ball velocity and the fielder’s looking direction.
  3. Calculate the proximity score based on the distance between the predicted ball position and the fielder’s position.
  4. Combine the two scores using a weighted average, e.g., final_score = 0.5 * score1 + 0.5 * score2.
  5. Select the best fielders based on the highest scores.

Conclusion

By combining the dot product-based alignment score and the proximity-based distance score, you can create a more dynamic and realistic system for choosing fielders in a cricket/football game. You can tweak the weights of each factor to suit your game’s specific needs and even adjust for various types of fielders. With Unreal Engine’s built-in nodes like Predict Projectile Path, you can easily simulate ball movement and make real-time decisions for fielder selection, enhancing the overall gameplay experience.