Simple Playoff Probabilities

Hello all! In this installment of J-Cook’s one look, I decided to try my hand at predicting who will/won’t make the playoffs. I used two different methods, and hope to add a third that steals some methods from computational materials science (namely using a probability proportional to a psuedo-Boltzmann factor with energy replaced by average point differential).

The first approach I used was just to see what happens if everybody scores the same points as they did on average in the first 9 weeks.

Standings are below (only with W-L records, sorted by theoretical PF)

  1. Johnson (9-4)
  2. Chasen (9-4)
  3. Amunrud (9-4)
  4. Charbs (9-4)
  5. Hart (8-5)
  6. Jonathan (6-7)
  7. Stock (5-8)
  8. Ventura (5-8)
  9. Paul (3-10)
  10. Melton (2-11)

The next method I used, which lets us see the effect of the final schedule, uses a 50-50 split odds for each game (as stated above, I plan on introducing a way to change this factor). I used 1000 trials to calculate this figure.

Standings with average W number in ()

  1. Johnson (8.55)
  2. Chasen (8.48)
  3. Jonathan (7.52)
  4. Amunrud (7.499)
  5. Charbs (7.486)
  6. Ventura (6.536)
  7. Hart (6.472)
  8. Stock (5.46)
  9. Paul (3.507)
  10. Melton (3.489)

I’ve also included the probabilities of each W-L record that was the basis for the above average calculations.

Okay, so I did it the fancy way, with the probability of winning for the player with higher average porportional to an exponential. When the difference in average points is 0, the win% is 50%. When the difference is 25 points, the player with the higher average will win 80% of the time. The exact formula for the higher scoring player to win is Prob=1-0.5*exp[-(higher-lower points)/27.28]

This definitely had an impact on the rankings at the playoff cutoff, which are now below:

  1. @Alex (8.8405)
  2. @chasenrogers (8.769)
  3. @ianamunrud (8.3131)
  4. @IanC (8.1991)
  5. @gbhart (7.1587)
  6. Jonathan (6.9155)
  7. @ventura (5.9945)
  8. @mikeastock (5.2591)
  9. @PaulDawg (3.0041)
  10. @awmelman (2.5785)

And another nice table, which now shows you a win-loss distribution that is not as evenly distributed, indicating that the 50% rule is off for certain matchups (ie Melton against anybody, as he went from having less than 3 wins 14% of the time, to having less than 3 wins >50% of the time).