Predicting basketball RPI
What is RPI?
• Ratings Percentage Index
• Based on win/loss percentage throughout the
season.
• Not necessarily a predictor of a stronger team.
How is RPI Calculated?
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Weighted wins, losses
Wins worth 1.4 away, 1 neutral, .6 at home
Losses worth 1.4 at home, 1 neutral, .6 away
Two parts:
– Win pct (wins/(wins+losses)
– Strength of schedule
• Opponents unweighted win pct
• Opponents’ opponents unweighted win pct
What is RPI used for?
• Estimator of team strength, as it factors in
strength of schedule
• Helps to seed the NCAA tournament.
• Helps selection committee/analysts determine
quality of wins.
The Selection Committee
• 10-person committee that determines who will
receive an at-large bid and seeding for the
tournament
• 5 year Tenure
• Use multitude of selection tools
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Win/loss
Conference strength
How a team won
Voodoo
Apparently, more random numbers than me.
Decidedly NOT just RPI.
How can RPI be predicted?
• Predict outcomes of games
• Run through season
• Rinse, repeat (Monte-Carlo!)
Kenpom statistics
• Statistics on all division 1 basketball teams
– Offensive Efficiency
– Defensive Efficiency
– Tempo
• Average possesions per game: FGA-OR+TO+.42 FTA
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Meteorologist from Salt Lake City, Utah
Basketball stats just a hobby, no background
Stats referenced by ESPN, wall street journal
Season averages
Step 1: Predicting games
• Generate scores: compare and mark
• Home games:
– xscore<round(x[8]/100*rnorm(1,1.05,.2)*(((x[4]+y[4])/2)*
rnorm(1,1.1,.2))+((y[12]*rnorm(1,1.05,.2))/80))
– yscore<round(y[8]/100*rnorm(1,.95,.2)*(((y[4]+x[4])/2)*r
norm(1,.9,.2))+((x[12]*rnorm(1,.95,.2))/80))
Step 2: Recording data
• Compare scores
• Higher score wins
• Mark wins/losses in appropriate places
Step 3: Run through season
• 5284 division 1 vs division 1 games.
• Import list of all games, which team is home,
away, to be called and put into game function.
• Run 1 of three game situations based on court
(1 is home, 2 is away, 3 is neutral).
• Each team plays approximately 30 games.
Step 4: Compile RPI, rank, repeat!
• After season is done, run through game list to
grab opponent’s win-losses.
• Next, re-run through game list to grab
opponent’s opponent’s win-losses by.
What do these results mean?
• Interesting estimator, but cannot be taken too
seriously.
• True Top 25 RPI missed by average of 13
places.
• My top 25 missed true RPI by average of 11.
• Kansas, WVU right where they should be!
• Villanova ranked 18, therefore project should
be considered a success.
Is the RPI reliable?
• [252]Wake Forest(7.4%), [202]DePaul (9.9%)
more likely to make tournament than nearly
200 other teams based on RPI alone.
• Too much weight placed on who you play, not
how you play.
• Still only one factor in determining NCAA
tournament.
Interesting Oddities
• Program took over 15 hours to run.
• In 10,000 simulated seasons, 31 teams will not
receive an at-large bid (will not be in the top 37
RPI at the end of the season)
• Of those 31 teams, half of them would likely end
up as a play-in team going to the final four.
– VCU received at large bid with RPI rank of 49 (to fill
36th-38th at large bid), Harvard with RPI rank of 35
denied tournament bid
Are these results reliable?
• Maybe?
• Only 2 teams predicted correctly in top 25.
• Season averages inaccurate for day-of play,
but might average out over whole season.
• Effect of random variables should eventually
absorb things like suspensions, injuries, team
morale.
• Possible that one of the seasons actually
matches this season perfectly.
Theoretical/Technical Issues
• Unable to account for mid-season
tournaments, changes in schedule, delayed
games.
• ‘Labor Intensive’ program – 5 trillion
calculations.
• Still near-impossible to seed mock
tournament without just taking 68 highest RPI
(which might not be a bad idea)
March Madness
• There are about 14,757,395,260,000,000,000 different
brackets of the NCAA tournament (but only 1 winner!)
• Over 6 million brackets were submitted to ESPN.com
this march in competition.
• Of those brackets, the best bracket, just 1 of 6 million,
got 52, or 77.6% of their picks correct.
• This year was the first time 2 11 seeds made the sweet
16, and the first time no 1 or 2 seeds made the final 4.
• Most even field the tournament has ever had, no great
teams
My terrible bracket
• My original bracket:
– 33.6th percentile on ESPN at 480 pts (4-millionth
place) Champion: Notre Dame
– No final four team, only 2 elite 8 (UNC, Uconn)
Basically, terrible. Last place in every pool I was in.
Can I make my bracket any better?
• This year, no, but next year? Maybe!
• Goal: create a bracket based on Kenpom
rankings, and see if it does any better.
Results:
• Worth twice as many points on ESPN, enough
to put me in the 92nd percentile!
– Beat 5,520,000 brackets!
• Still had no final 4 team.
Is it a reliable method? Votes for no:
• Highest championship percentage was less than 6%, only
4% better than flipping a coin.
• Many games were decided by less than a percentage point
• Doesn’t take into account injuries, coaching, stage fright,
‘home field,’ streaks, incredible ability to lose the lead, or
recruiting violations. Examples:
– Georgetown and St. Johns both had their star players hurt going
into the tournament and lost in the first round.
– Tennessee head coach Bruce Pearl was hit with school and
NCAA sanctions the day before the game and lost by 30 points.
– George Mason entered the tournament on an 11 game wnstreak
Votes for Yes:
• Randomness exists to account for the issues
previously mentioned.
• Anything can happen, this season could have
been that 1 in 10,000 chance for VCU, data
could be reliable.
• 55.2% of the bracket picked correctly, up
from… well, zero-ish.
Oddities and anecdotes
• First trial of the tournament I ran (before looping)
yielded Butler over Uconn, with Kentucky and Kansas in
the final 4.
• Defeated teams sometimes more likely to advance:
Notre Dame has a higher chance of making the
championship game over Wisconsin, 8.47% over
8.38%, but Wisconsin is more likely to win the
championship, 4.90% over 4.76%
• VCU had only a 51.5% chance of winning it’s first game,
a 22% chance of advancing past Georgetown, and a
2.64% chance of advancing to the final 4.
Conclusions: RPI
• Can RPI (remember RPI?) be predicted for a
season using Monte-Carlo methods?
– Decent yardstick, but not perfect
– Since RPI is just a yardstick anyway, should work
okay.
• Can it be used to seed a tournament?
– Difficult but yes, would need to run through 31
conference tournaments and determine an Ivy
league AQ as well.
Conclusions: NCAA tournament
• Can Monte-Carlo methods be used to predict
the NCAA tournament?
– Better predictor than me and better than a coin
flip.
– Good for calculating odds but not for absolute
winner.