Playoff series predictions

[J.E.]

Just wanted to get things started.

Not a single matchup is yet set in stone, but OKC and NOP rate pretty much the same in the team metric I'll use (http://fivethirtyeight.com/datalab/nba- ... off-power/), so here are my predictions for a GSW vs. NOP/OKC series (OKC with a healthy Ibaka)

GSW in 4 : 25.8 %
GSW in 5 : 32.5 %
GSW in 6 : 18.9 %
GSW in 7 : 13.1 %
NOP/OKC in 4 : 0.6 %
NOP/OKC in 5 : 1.5 %
NOP/OKC in 6 : 3.7 %
NOP/OKC in 7 : 3.8 %

GSW wins series: 90.4 %
NOP/OKC wins series: 9.6 %

Will post more once we know what the matchups are (and will update in case injury news come out)

[ampersand5]

stupid question, but I never learnt how to do this before.

How do you predict the winning probabilities for a game based on SRS (or whatever other team ranking metric you want to use)?

something based on this? G * (Tm PTS14 / (Tm PTS14 + Opp PTS14))????

[ampersand5]

so using the 538 numbers for GS and OKC, you would have: (112.5^14 / (112.5^14 +103^14))

which would give GS a 77.47% chance of winning a game ???

which is then converted into a 7 game series how?

[J.E.]

Not a stupid question

I am indeed using the WPyth formula, but with a lower exponent. 14 is used for games that have already been played. To "predict" the future you need something lower. I'm using 10.5, based on past tests I did I think that's close to optimal

Then, you also need to account for home court advantage. So, when playing in SF, GSW's rating will be higher than 12.5 (HCA is usually around 3 - 3.5 PTS)

If you got all that you can just simulate (10000 or how many times) with a random number generator

[ampersand5]

Not a stupid question

I am indeed using the WPyth formula, but with a lower exponent. 14 is used for games that have already been played. To "predict" the future you need something lower. I'm using 10.5, based on past tests I did I think that's close to optimal

Then, you also need to account for home court advantage. So, when playing in SF, GSW's rating will be higher than 12.5 (HCA is usually around 3 - 3.5 PTS)

If you got all that you can just simulate (10000 or how many times) with a random number generator

Thank you for your assistance!

[ampersand5]

For fun, I just ran the numbers for a raptors - wizards series using the Hollinger power ranking formula.

0.063636364 raps winning in 4
0.2 raps winning in 5
0.154545455 raps winning in 6
0.272727273 raps winning in 7

for a total chance of winning the series of 69.1%

[AcrossTheCourt]

Not a stupid question

I am indeed using the WPyth formula, but with a lower exponent. 14 is used for games that have already been played. To "predict" the future you need something lower. I'm using 10.5, based on past tests I did I think that's close to optimal

Then, you also need to account for home court advantage. So, when playing in SF, GSW's rating will be higher than 12.5 (HCA is usually around 3 - 3.5 PTS)

If you got all that you can just simulate (10000 or how many times) with a random number generator

Thank you for your assistance!

Here's a post that details a method of prediction:
http://statitudes.com/blog/2013/11/12/h ... using-srs/

But there are a couple of important tweaks you need for the playoffs, and there are better team rating systems than SRS, of course.

[ampersand5]

using the 538 rankings, I ran 1000 simulations on 7 game series and the Raps have a 64.2% chance of beating the Bucks.
61.4% chance of beating the Wizards.
36.4% chance of beating the Hawks.
19% chance of beating the Cavs.

[mystic]

which is then converted into a 7 game series how?

I just "rewrote" my old Matlab script to use it in R:

Code: Select all

a=12.5
b=3

hca=3
e=10.5

ha=(100+a+hca)**e/((100+a+hca)**e+(100+b)**e)
ab=1-ha

aa=(100+a)**e/((100+a)**e+(100+b+hca)**e)
hb=1-aa

awin4=ha**2*aa**2
bwin4=ab**2*hb**2

awin5=2*(ha**2*aa**2*ab)+2*(ha**3*aa*hb)
bwin5=2*(ab**2*hb**2*ha)+2*(ab**3*hb*aa)

awin6=(ha**3*aa*hb**2)+3*(ha*aa**3*ab**2)+6*(ha**2*aa**2*ab*hb)
bwin6=(ab**3*hb*aa**2)+3*(ab*hb**3*ha**2)+6*(ab**2*hb**2*ha*aa)

awin7=(aa**3*ha*ab**3)+(ha**4*hb**3)+9*(ha**3*aa*ab*hb**2)+9*(ha**2*aa**2*ab**2*hb)
bwin7=(hb**3*ab*ha**3)+(ab**4*aa**3)+9*(ab**3*hb*ha*aa**2)+9*(ab**2*hb**2*ha**2*aa)

awins=awin4+awin5+awin6+awin7
bwins=1-awins

a is the rating for the team with HCA (this time the value for GSW), b for the other team (here the value for OKC/NOP). e is the exponent used. I found 10.7 to be the best for prediction some time ago, but that isn't really different than the 10.5 J.E. proposed.

That would be the exact solution for the problem at hand and it is not too difficult given that there is a limited number of possible outcomes.

[J.E.]

CLE in 4 : 20.4 %
CLE in 5 : 29.9 %
CLE in 6 : 19.7 %
CLE in 7 : 15.6 %
BOS in 4 : 1.0 %
BOS in 5 : 2.4 %
BOS in 6 : 5.5 %
BOS in 7 : 5.5 %
CLE wins series: 85.6 %
BOS wins series: 14.4 %

[mystic]

J.E., two things:

1. Can you clarify whether RPM is using a prior for 2014 and/or 2015?
2. Would you mind putting your numbers for other series in the op in order to not get lost in the rest of the thread?

[NateTG]

stupid question, but I never learnt how to do this before.

How do you predict the winning probabilities for a game based on SRS (or whatever other team ranking metric you want to use)?
...

Here's a somwhat more naive approach:

Often, a rating system corresponds to a sort of regression where you're picking constants to minimize the error in the predictions of a particular model. If that's the case, then a natural approach is to use that model to make the predictions.

SRS, for example, corresponds to the assumption that a game's score differential corresponds to the difference in team strengths plus some normally distributed random variable. (Actually calculating normal distributions is a bit of a chore, so we like to offload that to computers.) For the NBA, the standard deviation of scoring is around 12 points.

So, pulling the SRS ratings from basketball reference I get GSW at 10.06 and OKC at 2.29. I'll also account for home field advanage as around 3.21 points.
That means we estimate that the Warriors are 10.06-2.29+3.21=10.98 points better at home, and 10.06-2.29-3.21=4.56 points better on the road.
Now, I can use Excel or something similar to calculate win probabilty estimates:
GSW home win: NORMDIST(0,10.98,12,TRUE) = 0.82
GSW road win: NORMDIST(0,4.56,12,TRUE) = 0.65

Now, we can estimate the chance of GSW in 4:
0.82*0.82*0.65*0.65=0.28

The chance that GSW wins in 5 is a bit more complicated since they could drop any of the first four games:
0.18*0.82*0.65*0.65*0.65+
0.82*0.18*0.65*0.65*0.65+
0.82*0.82*0.35*0.65*0.65+
0.82*0.82*0.65*0.35*0.65=0.28

Similar calculations give GSW in 6 as 0.25, and GSW in 7 as 0.12

The formulae that mystic showed below correspond more closely to a 'pythagorean' type model.

There are, of course various reasons to think that this isn't a particularly accurate approach, but it's relatively nice mathematically speaking.

[J.E.]

1. Can you clarify whether RPM is using a prior for 2014 and/or 2015?

Not sure if I understand the question 100% correctly, but RPM uses a BoxScore prior. The RPM version that's on ESPN doesn't use any data from last season

[mystic]

Yeah, the phrasing of the question wasn't very good as I meant to ask whether the prior would contain previous season data. Well, you answered that anyway. Thanks.

[ampersand5]

Splitter is hurt - crazy to think that the Spurs might not be favourites to win in the first round anymore.

This brings me to a much more important point - how much did certain teams (like potentially Chicago) cost themselves (in terms of both wins and total revenues) yesterday by not selectively tanking?
Truly astounding to see so many teams act without regard for what's ahead of them.