Probabilities of winning the snowpool as of Nov 6 2008
Total snow to date = 0.1 inches
6.3 Gail Phillipps 6.73%
7.1 Ted Terpstra 3.04%
10.0 Gera Stenchikov 2.94%
10.3 Suba Krishnan 0.59%
10.5 Geoff Vallis 0.59%
10.8 Tom Delworth 0.60%
11.0 Bernie Siebers 0.41%
11.1 Sherri West 1.46%
12.3 Alda Austin 1.72%
12.6 Bart DeCorte 0.44%
12.7 Gayle Wittenberg 0.89%
13.3 John Lanzante 1.35%
13.8 Sarah Dunne 0.92%
14.0 Adi Benito 0.93%
14.5 David Hurlin 1.41%
15.2 Tatiana Stenchikov 0.95%
15.3 Jamie Palter 0.48%
15.5 Marlene Stern 3.41%
18.0 Steve Griffies 3.73%
18.5 Bill Shearn 1.01%
18.8 Joan Tuleya 0.76%
19.0 Rosemary Weatherington 0.76%
19.3 Cathy Raphael 0.76%
19.5 Dick Wetherald 0.76%
19.7 Bess Ward 0.76%
20.0 Kirsten Findell 1.01%
20.4 Anna Johansson 1.01%
20.6 Leo Donner 0.76%
20.9 John Austin 0.51%
21.0 Gabriel Lau 0.25%
21.1 Michele Marchok 0.25%
21.2 Steve Mayle 0.51%
21.5 Carole Umscheid 0.51%
21.6 MaryAnne Knutson 0.25%
21.7 MaryJo Dixon 0.50%
21.9 Susan Wilson 0.50%
22.0 Charles Stock 0.50%
22.2 Amy Lowenstein 0.75%
22.4 Ryan Coyle 0.50%
22.5 Bob Hallberg 0.75%
23.0 Stewart Samuels 1.00%
23.3 Ni-Zhang Golaz 0.75%
23.5 Gabe Vecchi 0.99%
24.0 Dave Weatherington 0.74%
24.1 Bruce Wyman 0.49%
24.3 Carol Broccoli 0.74%
24.5 Bill Hurlin 0.98%
25.0 Michelle Lau 0.97%
25.2 Laura Rossi 0.73%
25.4 Songmiao Fan 0.72%
25.6 Bud Moxim 0.48%
25.7 Jeff Flick 0.24%
25.8 AM2 AM2 0.48%
26.0 Jake Mayle 0.95%
26.5 Larry Horowitz 0.95%
26.8 CM2 CM2 0.71%
27.0 Arlene Fiore 0.70%
27.3 Lisa Lancaster 0.47%
27.4 Jim Sentman 0.46%
27.6 Amy Langenhorst 0.69%
27.9 Terri Kurtzberg 0.46%
28.0 Dianne Smith 0.68%
28.4 Marian Westley 1.13%
28.8 Carol Shearn 0.90%
29.0 Rich Gudgel 0.45%
29.1 Brian Gross 0.44%
29.3 Jeff Ploshay 1.54%
30.4 Lori Sentman 2.56%
31.7 John Dunne 1.45%
31.8 Alistair Adcroft 0.61%
32.3 Tim Marchok 0.80%
32.5 Bill Stern 0.60%
32.7 Eric Galbraith 0.59%
33.0 Bonnie Samuels 0.59%
33.3 Alan Robock 0.77%
33.7 Linda Terpstra 0.57%
33.8 John Wilson 0.38%
34.1 Jon Trudel 0.75%
34.5 Chris Golaz 0.74%
34.7 Jim Byrne 0.37%
34.8 Ann-Marie Delworth 0.37%
35.0 Cassie Hallberg 0.54%
35.3 Will Cooke 0.54%
35.6 S. Ramaswamy 0.71%
36.0 Lou Umscheid 0.52%
36.1 April Cruz 1.37%
37.6 Martha Ploshay 1.32%
37.7 Loyda Friedenreich 0.32%
38.0 Brendon Field 0.48%
38.2 Charlene Moxim 1.10%
39.2 Russ Sinclair 1.06%
39.4 Maria Flick 0.45%
39.7 Dan Schwarzkopf 0.59%
40.1 Larry Perfetto 1.28%
41.3 Tony Broccoli 1.63%
42.4 Tony Gordon 1.03%
42.8 Bob Tuleya 1.12%
44.0 M. Ramaswamy 0.95%
44.3 Keith Dixon 1.57%
46.8 Stuart Friedenreich 2.96%
50.2 Mary Gross 2.25%
52.0 Isaac Held 0.89%
52.4 Mary Fan 0.42%
53.0 Joann Held 1.83%
58.0 V. Balaji 1.69%
59.5 Peter Phillipps 0.48%
60.2 Andrew Wittenberg 0.37%
61.3 Bob Smith 0.93%
65.3 David Pinkus 2.24%
81.0 Luciano Rossi 0.98%
85.0 Tom Knutson 0.66%
Probabilities are based on a probablistic model for the amount of snow to fall in the remaining part of the snowfall season.
The model uses the Poisson distribution for the number of snowfall events.
The Poisson distribution is:
P(n) = m**n * exp(-m) / n!
Where n is the number of events
m is the mean number of events
(! denotes factorial)
The mean number of events for the remaining part of the season is adjusted as the season progresses.
More about this below.
The model uses an exponential function for the amount of snow falling in a single event.
R(1,x) = exp(-x/M) / M
Where x = amount of snow in a single event
M = mean snowfall for a single event
This function was chosen for two reasons:
1) It is more likely that an event will be light than heavy. This function has this property.
2) It makes the rest of the work more mathematically tractable.
From this one can derive the probability density function for multiple events.
R(n,x) = x**(n-1) * exp(-x/M) / (M**n * (n-1)!)
Where x = amount of snow in "n" events
Combining this with the Poisson distribution yields the expression for snowfall in the remaining part of the season.
__
\
T(x) = / P(n)*R(n,x) Summed from n=1 to infinity
--
This expression does not integrate to 1.0 over all x because it does not include the probability of no snow at all.
No snow at all requires that n=0, so the probability is simply P(0). T(x) integrates to 1.0 - P(0)
The mean of T(x) = m*M
The variance of T(x) = 2*m*M**2
The model is fitted to the observed snowpool data for all past snowpool years.
This results in values of M and m. (m for the entire season)
m is adjusted as the season progresses but M is not.
m is adjusted by assuming that the frequency of snow events follows a gaussian distribution in time.
Fitting a gaussian distribution to some monthly snowfall data for New Brunswick N.J., the peak is on Jan 31
and the standard deviation is 32 days. (A snow event is equally likely on Dec 30 and Mar 4)
Fitting the model to the observed mean and standard deviation of snowpool data requires that:
mean snowfall per event = M = 4.97 inches
mean number of events per season = unadjusted m = 5.84
The resulting value of M seems a bit too high, and m too low, but the resulting seasonal snowfall
probability function looks reasonable despite this.