Rules and Regulations for the Pinball Rating System
---------------------------------------------------
last update: Nov. 9, 1995
The Pinball Rating System is a way of determining the relative strength of
any two players, if they were to meet in a head-to-head match. It can be used
to determine seedings in a tournament, or to help a player find others at
his or her approximate level.
This system is closely based on the rating system used by the US Chess
Federation. Information about the USCF's system is due to a post on rec.
games.pinball by Mark Phaedrus in May 1994, so many thanks goes out to him for
help.
There are two types of ratings used in the system.
Provisional Ratings & Unrated Players
-------------------------------------
A new player is considered "unrated" until they have played four matches
against other opponents. A match between a player with an Established Rating
and an unrated player will not affect the Established player's rating.
The four matches may be played against any other player, even other unrated
players. After the required four matches have been played, the player is
given a Provisional Rating, based on the average rating of his/her opponents,
and his/her performance in those matches.
The provisional rating is determined by a formula:
Provisional Rating = (Avg. of Opponents' Ratings) + 200((W - L) / (Matches))
(For the purposes of computing a Provisional Rating, any other Provisional or
Unrated player is considered a 1400 player.)
This means that if a player wins all his matches, his rating will be
200 higher than the average of the opponents. If he loses all of them,
it will be 200 lower.
Example: Keith plays his first rated matches. His first three matches are
against unrated players, and he beats them all. His fourth match is against
Kevin, who has an Established rating of 1800. He loses that match, as well as
his fifth match against Dave, who has a Provisional rating of 1600.
To compute the rating, first find the average opponent score. Dave is
considered a 1400 player, since he is not Established yet. The average is
(1400 + 1400 + 1400 + 1800 + 1400) / 5 = 1480.
Keith's record is 3-2 over 5 matches, so his record changes his rating by
200 * (3 - 2) / 5 = 40.
Keith's new rating is 1480 + 40 = 1520.
Another way to figure out this rating is to use an effective rating for each
game, and dividing that by the number of games played. To do this, add or
subtract the 200 before averaging the scores.
For the situation above:
1400 + 200 = 1600
1400 + 200 = 1600
1400 + 200 = 1600
1800 - 200 = 1600
1400 - 200 = 1200
----
7600 / 5 matches = 1520.
For provisional players, the rating is displayed as "1520/5", which shows that
Keith has a 1520 after 5 matches. This is used to show that the rating is
not Established.
The Provisional Rating is used for the first 10 matches of any new player.
After that, the Provisional Rating becomes an Established Rating. If a player
should go over 10 matches within a multi-player group, then the Provisional
Rating rules apply to all the results of that match.
The opponents' average is determined by the opponent's rating at the
time of the match. If two Provisional players play, their effective
rating (for the other player) is always 1400, regardless of the opponent's
actual Provisional Rating.
Established Ratings
-------------------
After 10 matches, a player's rating is "established", and a different
formula is used to determine their rating change in matches.
If two Established players face each other, each has to pay a certain
number of rating points (RP) to enter the match. The winner
takes all the points (always 32). In case of a draw, the original
ratings are _not_ returned; instead, each player receives 16 points. (Of
course, there is not likely ever to be a draw in the near future.)
The scaling is used to give players no particular advantage in choosing their
opponents. If a player is 90% likely to win a match, he should have to wager
9 times as many rating points as his opponent. If players are equally matched,
they should have to wager the same number of points.
The system is designed to even ratings out over time; if two players were to
play each other many times over, they would eventually reach a point where
neither player's rating changes much. If a player is overrated or underrated,
time will work it out eventually.
The chart gives the scale of points to pay for matches.
If the difference The better player And the lesser
in rating is... puts up ... player puts up
points, ... points.
Less than 12 16 16
12 -- 33 17 15
34 -- 55 18 14
56 -- 77 19 13
78 -- 100 20 12
101 -- 125 21 11
126 -- 150 22 10
151 -- 176 23 9
177 -- 205 24 8
206 -- 238 25 7
239 -- 272 26 6
273 -- 314 27 5
315 -- 365 28 4
366 -- 445 29 3
446 -- 525 30 2
526 -- 715 31 1
716 or more 32 0
This second chart gives a list of the expected percentages for victory for
the better player.
Rating difference Score % Rating difference Score %
0 points 50% 300 points 85%
50 points 57% 350 points 88%
100 points 64% 400 points 91%
150 points 70% 500 points 95%
200 points 76% 600 points 97%
250 points 81% 800 points 99%
(The 99% for a gap of 800 points explains why the better player should have
to pay 32 points to zero in that situation.)
This is a logarithmic scale, built so that a difference
of 400 points is equivalent to a tenfold increase in
skill. Other point levels in between are adjusted accordingly.
Note that if the rating gap is more than 715, the better player
cannot gain any rating points from the match.
Example: Lyman (rating 2000) plays Bowen (rating 1800). According
to the chart, Lyman has to put up 24 RP to participate, and Bowen
only has to put up 8. The winner of the match gets 32 points --
if Lyman wins, his resulting rating will be 2000 - 24 + 32 = 2008,
and Bowen's is 1800 - 8 = 1792. If they were to immediately play
a second match, Lyman would have to put up 25 points and Bowen 7,
as the rating gap has increased to 216.
For the purposes of an Established player playing an unrated player, the
Established player's rating is unchanged. For the purposes of an Established
player playing a Provisional player, the Established player's rating changes
as it does against any other Established player. (The Provisional's rating
changes according to the earlier scheme.)
Example: Bowen (rated 1785 after losing to Lyman again) plays Neil,
a fairly new player with rating 1600/5 (Provisional). Bowen needs to
put up 24 points to enter the match, since the effective difference
in rating is 185 (1785 - 1600). Bowen loses again, so his rating is
reduced to 1761. If Bowen had won, his new rating would be 1761 + 32 =
1793.
To figure out Neil's rating after this match, we can use the system above.
Multiplying the rating by the number of matches brings up the old sum total.
Previous total: 1600 * 5 = 8000
+ this match: 1785 + 200 = 1985
-----
9985 / 6 = 1664 (rounded).
Neil's new rating is listed as 1664/6.
Multi-Player Matches
--------------------
A multi-player match is taken just as the lump sum of several two-player
matches. The same rules for Provisional and Unrated players apply.
Example: Marc (2000), Neil (1900), and Bowen (1800) play (all Established).
How many points should each put up in each match?
Marc vs. Neil : Marc pays 20, Neil pays 12 (gap 100)
Marc vs. Bowen: Marc pays 24, Bowen pays 8 (gap 200)
Neil vs. Bowen: Neil pays 20, Bowen pays 12 (gap 100)
Totals: Marc pays 44, Neil pays 32, Bowen pays 20.
Note that in 3-player matches, this total is always 96 (32 x 3 sets), and
in 4-player matches, this total is always 192 (32 x 6 sets).
In the three-player situation, the winning player earns 64 points (2 x 32),
second gets 32, third gets 0. In a four-player situation, the winner gets 96,
then 64, 32, 0.
In the above situation, if the final standing is "Neil, Marc, Bowen", the
resulting ratings are:
Neil : 1900 - 32 (pd) + 64 (won) = 1932
Marc : 2000 - 44 + 32 = 1988
Bowen: 1800 - 20 + 0 = 1780
As always, no points are gained or lost overall. Note that Marc, the highest-
rated player in the group, lost rating points despite a 1-1 record in the
match.
If you'd rather not worry about how many points each player has to put up,
great. Send your results to Bowen, who will handle the computations for you.
"Sanctioned Events"
-------------------
Any match is "sanctioned". A league night, a national tournament, or two
friends meeting at a bar. Each game played is a "sanctioned" one (assuming
all players agree to it ahead of time), and affects the players' rating.
Note that each game in a series counts toward the rating (this is especially
noteworthy for league play).
Ground Rules
------------
Anything that players will agree to is acceptable. Any tournament situations
will have their own rules, and any tournament scores are certainly acceptable
for submission.
If two players cannot agree to a match situation, the following rules apply.
- No extra balls or buyins. If you should score an extra ball in the course
of play, you may line up a Skill Shot, but you may not touch the flippers or
nudge the machine in the course of the extra ball.
- 3-ball game only, unless the machine can only be played as a 5-ball game
(most old EMs).
- No bang backs, no death saves. A Lazarus ball (lucky bounce death save) is
fine, but absolutely no influence can be put on the ball.
- For machine and order of play, flip a coin. The winner chooses either the
machine or the order of play; the loser chooses the other. For multiple
game sets, the loser of the previous game has first choice for the next
game.
If there are any other rules that you feel should be included, please let me
know. The system is designed mostly for easy use and flexibility, which is
why there are few rules prescribed here.
How to Join
-----------
Just let me know, either by email or phone. I will need a home address as
well as your name and email (if any). Of course, the more, the merrier, and
it's easier to become Established if there are friends to play.
Questions & Comments; How to Report Matches
-------------------------------------------
This type of system can certainly be confusing. If there are any questions,
please feel free to email me at bowen@leland.stanford.edu (effective until
December 1996), or call (415) 497-0512.
If you have matches to report, email them to me, or Snail Mail to PO Box 9215,
Stanford CA 94309. Please give the date of the match, and machines and scores
of games (optional, but I'd like to be able to post noteworthy scores).
Thanks a lot, and I hope to be hearing from you.
Bowen
-----
bowen@leland.stanford.edu