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The Luck Meter

Introduction

As many of you have seen, JavaBBowl shows a number in the titlebar called Luck. As with any statistical figures, it is very important to understand exactly what they represent.

The luck value is a semi-statistical figure that represents the outcome of your rolls compared to the statistically expected average.

Please take a moment to re-read what you just read, and consider what it really means. Given that the value is based on the dice rolls made by the player in question, there is no proper way of comparing the luck values of the two players involved in the game.

As the luck value is not carried over between games (or even reloads), the value is highly inaccurate for the first few rolls that are being made for a player. This is evident by the highly erratic behaviour of the value in the first few turns of a game. The number of rolls required before the luck value has stabilized varies a bit depending on the difficulty level of the rolls being made. A player that attempts a lot of very difficult or a lot of very easy dice rolls will need more rolls to make the value stabilize than if the player had made rolls with a 50% success rate.

The math

Each dice roll is categorised into one of three possibilities:

Success
The dice roll was a success. For example, a block roll that manages to take the defender down without causing a turnover (ie, the blocker is still standing).
Failure
The dice roll failed. For example, a block roll where the blocker is knocked over.
Neutral
The dice roll was neither a success or a failure. In the case of a block, a pushback is considered neutral.

For each dice roll made, the probabilities of each of these outcomes is calculated. Let's call these pSuccess, pNeutral and pFailure. Note that the sum of these numbers is always exactly 1.0 (or 100%) but that one or more of them can individually be 0.

In order to get a luck value between 0 and 100%, a simple division is made:

Luck = Nominator / Denominator

The Nominator and Denominator values are updated for each dice roll outcome as follows:

Success
Nominator is increased by 1 / (pSuccess + pNeutral / 2)
Denominator is increased by 1 / (pSuccess + pNeutral / 2)

This will increase the luck value, but never take it above 1.0.

Failure
Nominator is unchanged.
Denominator is increased by 1 / (pFailure + pNeutral / 2)

This will decrease the luck value, but never take it below 0.

Neutral
Nominator is increased by 1 / (2 * pSuccess + pNeutral)
Denominator is increased by 1 / (2 * pSuccess + pNeutral) + 1 / (2 * pFailure + pNeutral)

This will make the luck value strive towards 0.5.

The outcomes of the rolls are categorised as follows:

Armour rolls

  • Success: Armour was broken.
  • Failure: The defender was left prone.

Block

  • Success: The defender went down, without causing a turnover (ie, attacker is still standing).
  • Failure: The attacker went down, causing a turnover. Whether the defender went down or not is irrelevant.
  • Neutral: The defender is still standing, and no turnover happened.

Catch

  • Success: The player caught the ball.
  • Failure: The player dropped the ball.

Dauntless

  • Success: The dauntless roll was successful.
  • Failure: The dauntless roll failed.

Dodge

  • Success: The player managed to dodge.
  • Failure: The player failed the dodge.

Going for it

  • Success: The player succeeded with the roll.
  • Failure: The player fell over.

Injury Rolls

  • Success: A casualty was caused.
  • Failure: The player is only stunned.
  • Neutral: The player is Knocked Out.

Pass

  • Success: The pass is accurate.
  • Neutral: The pass is inaccurate.
  • Failure: The pass is fumbled.

Pickup

  • Success: The player picked up the ball.
  • Failure: The player failed to pick up the ball.

In addition to these actions, there is a standard "d6" roll which covers the rest of the actions, such as shadowing. Naturally, a successful roll is considered a success and a failed roll is considered a failure in these cases.

The luck formula has the following characteristics:

  • The order of the dice rolls is irrelevant.
  • Rolling statistically average rolls will result in a luck value of 50%.

Note: The actual implementation in the JavaBBowl client is slightly modified based on this explanation. A few actions have been added, but this covers the basics and is the version that Christer sent to SkiJunkie? for inclusion in the client.

Last update: March 1, 2008