In my opinion, one of the weaknesses in the APBA Hockey game is the penalty system.  Unfortunately, the original system doled out too many penalties and each successive version has tried to kludge the system rather than just starting from scratch.  This article will go into how the system works, how to calculate what numbers a player should receive and a brief exploration of a better system.

The Current System

The play numbers 33 to 40 are used to dole out the trips to the sin bin, and essentially go in order from least severe (33) to most severe (40).  Assuming that the average player spends 80% in Forecheck 2, 5% in Forecheck 1, 5% in Forecheck 3, 5% in Power Play and 5% in Shorthanded, each number should produce the following assuming you use none of the enhancements:

• A 33 is a coincidental penalty in Forecheck 2 72% of the time and a minor in Forecheck 3 and power play, so this will produce a coincidental penalty 58% of the time and a minor 10% of the time.
• A 34 is a minor penalty in Forecheck 2, a coincidental penalty in Forecheck 1 and shorthanded, and a coincidental penalty 72% of the time in Forecheck 3 and power play.  This is a minor penalty 80% of the time and a coincidental penalty 17% of the time.
• A 35 is always a minor
• A 36 is a flight 72% of the time in Forecheck 2 and always a fight in Forecheck 3 and power play, producing a fight 78% of the time.
• A 37 is a fight in Forecheck 2, 3 and power play, or 90% of the time.
• A 38 is a fight in Forecheck 2, 3, power play and a fight 72% of the time in Forecheck 1 and shorthanded, or 97% of the time.
• A 39 is a fight
• A 40 is a major 42% of the time in Forecheck 3, 28% of the time in Forecheck 2 and 8% in Forecheck 1, otherwise it is a fight.  This returns a fight 73% of the time and a major 27% of the time.

Players also receive a minor, major and misconduct rating.  These are the typical ranges seen in all APBA Games (11-66 or 0).

Any fights or coincidental penalties involve checking the correlated penalty rating (minor or major) of all of the players on the other time and finding an opponent.  For minors, after one check through if no opponent can be found it converts to a minor penalty.  For fighting, after one check for a major opponent you then convert the penalty to coincidental minors.  Major penalties do not have an opponent.

If you play via this method, it becomes quickly apparent that the players with the fight numbers receive too many penalty minutes.  So in the second and third versions of the game, there are modifications offered to get the numbers better in line.  This involves canceling a 33 for low-minor rated players or adding minors on some fight numbers.  The third version streamlined some of the rules of the second version, which had results checking for penalties on non-penalty numbers.

Figuring out the Ratings

So what determines what penalty numbers players get?  To do this, you need to find out the number of minors, majors and misconducts (both 10-minute and game).  These numbers are available on the NHL site for recent seasons.  You will also need to know the total ice time for the player, which is the game ice time times game.  For this example, I’m go to explore the 2010-11 card of Justin Abdelakder of the Detroit Red Wings.

• Abdelkader played 12 minutes a game for 74 games, totaling to 888 minutes.  Dividing 888 by 60 gives us 14.8.  We’ll refer to this as “per 60 minutes” in later calculations.
• He had 61 minutes in penalties from 21 minors and 3 majors.  Note that the math here (21 * 2) + (3 * 5) only produces 57 minutes.  The NHL considers a double minor as one minor, when for these calculations should be counted as two minors.  So we will use 23 minors and 3 majors.
• Take the number of minors and divide by the “per 60 minutes” figure: 23 / 14.8 = 1.55.
  • To determine the Minor rating, take the figure above, multiply by 8.2, remove the decimal and subtract 2: (1.55 * 8.2) = 12.71, subtract 2 and round which leaves us 11.  In the base-6 APBA-world we change that number to 25, as it is the 11th possible dice roll.  A player can not be below 0 or above 66.
  • To determine the play numbers, we associate the 1.55 figure with this chart:
    • 0.00-0.51: 33
    • 0.52-0.73: 33-33
    • 0.74-1.10: 33-34-35
    • 1.11-1.47: 34-34-35
    • 1.48-1.75: 34-35-35
    • 1.76-2.25: 35-35-35
    • Add additional 35s for each .50 above 2.25
  • So at the moment, Abdelkader has 34-35-35.
• Take the number of majors and divide by the “per 60 minutes” figure: 3 / 14.8 = .20
  • To determine the Major rating, multiply the number above by 26 and convert to base 6: .2 * 26 = 5.2 or 15.
  • To determine the play numbers, we use the Major rating and assign the following numbers:
    • 0-14: nothing
    • 15-23: 36
    • 24-35: 36-36
    • 36-42: 36-36-36
    • 43-56: 36-36-37
    • 61-64: 36-37-39
    • 65-66: 36-37-37-37-37
    • For numbers for players who would have received something beyond 66, 36-37-37-39-39 is used as a base and then additional 37 through 40 numbers are added.  At this point there are not enough cases to figure out a set pattern, but basically it’s an extra number per additional .50.  In the set I looked at, the largest number was 4.17 for Aaron Voros (Anaheim).  He received 3 37s, 6 38s, a 39 and a 40.
    • If the player received a 35 in the minor step, the first fight number replaces the 35.  All of the other fight numbers are then added.  Since Abdelkader did receive a 35, the last one is replaced with a 36 (since he has a 15 Major rating).
• For the Misconduct rating, use the same method as the Major rating (misconducts divided by the “per 60 minutes” and multiply by 26, and then converting to base 6).

Making it Better

While in the current version the majors work pretty well, there are still way too many coincidental minors.  Also, misconducts are improperly rendered, as the rating should be the number of misconducts into majors.  Here’s what I do:

• If the play result is 33, reroll the dice and combine:
  • 11-26: Coincidental minors (X)
  • 31-36: Minor (X)
  • 41-46: Check for misconduct, otherwise NZFO (X)
  • 51-66: NZFO (X)
• If the play result is 34: Minor (X)
• If the play result is 35, reroll the dice and combine:
  • 11-62: Minor (X)
  • 63-64: Double Minor (X)
  • 65-66: Double Minor plus coincidental minor (X)
• If the play result is 36, reroll the dice and combine:
  • 11-45: Fight (X)
  • 46-66: Coincidental minors (X)
• If the play result is 37, 38 or 39, reroll the dice and combine:
  • 11-52: Fight (X)
  • 53-66: Coincidental minors (X)
• If the play result is 40, reroll the dice and combine:
  • 11-56: Fight (X)
  • 61-66: Coincidental minors (X)
• Only check for misconducts on fights.  Do not check on coincidental minors.
• On Forecheck 1, One Man Up or One Man Down, subtract one from the play number (e.g.: 34 becomes a 33).
• On Two Men Up or Two Men Down, subtract two from the play number (e.g.: 38 becomes a 36).
• If the designated fight opponent has a Major rating of 11-14, check for a possible conversion.  Reroll the dice and combine:
  • 11-21: Opponent Major 11 converts both to coincidental minors
  • 22-32: Opponent Major 11 or 12 converts both to coincidental minors
  • 33-43: Opponent Major 11, 12 or 13 converts both to coincidental minors
  • 44-54: Opponent Major 11, 12, 13 or 14 converts both to coincidental minors
  • 55-66: Keep as fight

If I Really Had My Way

Baseball cards sometimes have two columns.  Football has three, bowling has two.  Why can’t hockey have two?  I would envision a chart that would be something like:

• 1-25: various minors (i.e.: 1-hooking, 2-tripping, 3-interference, 4-holding, etc.)
• 26-32: various coincidental minors or double minors
• 33-39: various fights
• 40: no penalty

The number of times a card is played through varies depending on the player’s Shot Frequency.  For the purposes of this exercise, I’ll just pull a number out of my hat and say Abdelkader’s card would be hit 4.5 times a game assuming he plays his 12 minutes.  Of his 23 minor penalties, 2 were double minors and 3 were paired as a coincidental, leaving 16 true minors.  The other penalties he needs are the 2 double minors, half of the 3 coincidentals and half of the 3 majors, or 22 penalty events.  He played 74 games and at 4.5 passes per game he would receive a dice roll 333 times, or 9.25 card passes.  He has three penalty numbers, so those numbers would be hit 27.75 times.

We would create a second column that would be triggered off any of the penalty numbers.  We would then see a card like this:

It would be fun to play.  It would also be a nightmare to calculate.