Alternate Pythagorean Wins

[Mike G]

As of yesterday morning, the Bulls were 6-5 with an average score of 93.5-90.5
Their Pythagorean Wins, given their +3.0 ppg over 11 games, were 6.64 (and 4.36 pL)

Then they lost by 39 to the Clippers.

Now their point averages are 92.5-93.1 , yielding pW = 5.75 (and 6.25 pL)
Somehow, by being blown out in their 12th game, they earned minus-0.89 pW

If your average score is 82-121, then your pyth W% is about .005 -- you should win one game in 200 or so.
There's no such thing as a negative probability of a win.

If the first game of the season is a 82-121 loss, then you have earned .005 pW
But if it happens later than that, you have earned negative pW for the same game.

Obviously, if you have lost by 40 or by 1, you have a zero likelihood of having won the game. Yet we can still assign a pW% to each game. Here are the Bulls' 12 games in order of their pW earned:

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.opponent            Chi  Opp    pW
Utah Jazz             97   73   .98
Toronto Raptors       96   80   .92
Cleveland Cavaliers   96   81   .91
Indiana Pacers       110   94   .89
Charlotte Bobcats     86   81   .69
New York Knicks       82   81   .54
Philadelphia 76ers   104  107   .41
Portland TrailBlazers 95   98   .40
Denver Nuggets        87   97   .19
Miami Heat            95  107   .17
Indiana Pacers        80   97   .07
Los Angeles Clippers  82  121   .01
.total/avg          92.5  93.1  6.16

A win is a win, and a loss is a loss, whether by 1 or by 40. They still have a pW of 5.75; but when you add their game-by-game pW, they are at 6.16

Here are all teams, ranked by the amount that traditional pythW% overrates them, relative to game-by-game (Alternate) pW%

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diff    Tm     W%    pW%   AltpW%      diff    Tm     W%    pW%   AltpW%
.087   Min   .533   .706   .618       -.003   Sac   .308   .374   .377
.063   LAC   .667   .641   .578       -.006   Was   .385   .427   .432
.069   SAS   .923   .833   .764       -.018   Orl   .308   .409   .428
.060   GSW   .571   .644   .584       -.022   Det   .385   .428   .450
.051   Mia   .769   .771   .720       -.021   Cha   .500   .427   .448
.050   NOP   .500   .582   .532       -.030   Mem   .538   .423   .453
.039   Ind   .923   .798   .760       -.035   Chi   .500   .479   .514
.025   Tor   .462   .542   .517       -.040   LAL   .500   .425   .465
.023   Okl   .750   .651   .628       -.038   Bos   .333   .318   .356
.016   Hou   .643   .629   .613       -.046   Uta   .067   .159   .205
.015   Por   .857   .686   .671       -.065   Mil   .167   .202   .266
.014   Dal   .643   .598   .585       -.062   Brk   .231   .265   .326
.013   Atl   .571   .585   .572       -.067   NYK   .250   .309   .375
.011   Phx   .538   .582   .571       -.068   Cle   .286   .240   .308
.001   Den   .500   .500   .499       -.072   Phl   .400   .330   .402

OKC led Utah by 32 after 3 quarters yesterday, and the eventual difference was 22.
The Clipps led the Bulls by 23 after 3, and a 25-9 4th Q made it a 39-pt difference.

Losing by 39 may or may not be an ominous portent of serious problems with the Bulls. More likely, IMO, it's "just one loss".
Close to zero added win chances, not some huge (and impossible) negative number.

[kclough]

While the model you have built clearly outperforms traditional Pythagorean wins at "predicting" current records, it only works given knowledge of the results of individual games. The value of Pythagorean wins is in its ability to predict records given no knowledge of individual games. It allows us to translate aggregate information (point margin over a period of time) into wins without knowledge of the individual game's results.

Given that your model requires us to know the outcomes of the past games (game by game point margin), a better model of past expected wins would simply be the team's record.

It may or may not outperform Pythagorean wins at predicting how the rest of the season will turn out. That is something I would be interested in seeing.

[Mike G]

... The value of Pythagorean wins is in its ability to predict records given no knowledge of individual games. ..

Well, game scores are one of the most enduring of all NBA records.
In 1969, Bill Russell's last season, the Celtics finished 4th in the East, 48-34, barely making the playoffs. Then they won the Finals, going 12-6 in the playoffs.
They also had almost the best MOV in the league, 5.57 ppg. Their pWins were 54.6

Game by game, their Alt pW sum to 48.6 . Obviously, this does not predict their postseason success. I'm just demonstrating that I can generate this info in a few minutes.

While winning 58.5% of their games, they had 3 losses of 20+ points. They had 15 wins of 20+ points, including 3 of 40+ pts.
So it seems their MOV was rather inflated by 'piling on' points during some easy wins.
Just as a 48-point victory doesn't get you more than 1 win, it shouldn't predict much more postseason success than, say, a 24-pt win.
http://www.basketball-reference.com/box ... 90BOS.html

[Yooper]

Does any method attempt to define a boundary for the absolute MOV consider to be meaningful? I would say this is somewhere around 20 points or so.

[Mike G]

There might be a rapidly diminishing value to margin of victory. But pushing the lead from 20 to 30 in the final minutes may indicate that your team has great depth of players trying hard to make a favorable impression.

In normal pythagorean W%, every 10 points of margin allegedly improves your chances equally; in the proposed alternative, game by game, it's like the final column here:

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Pts  oPts  MOV   pW   delta
100  100    0   .500    ---
105   95   10   .791   .291
110   90   20   .935   .144
115   85   30   .982   .047
120   80   40   .995   .013
125   75   50   .999   .003
130   70   60  1.000   .001

I'm only aware of one instance of one team doubling the score on the other, for 48 minutes. At that point, the losing team's competitiveness is vanishingly small.

[mystic]

Code: Select all

diff    Tm     W%    pW%   AltpW%      diff    Tm     W%    pW%   AltpW%
.087   Min   .533   .706   .618       -.003   Sac   .308   .374   .377
.063   LAC   .667   .641   .578       -.006   Was   .385   .427   .432
.069   SAS   .923   .833   .764       -.018   Orl   .308   .409   .428
.060   GSW   .571   .644   .584       -.022   Det   .385   .428   .450
.051   Mia   .769   .771   .720       -.021   Cha   .500   .427   .448
.050   NOP   .500   .582   .532       -.030   Mem   .538   .423   .453
.039   Ind   .923   .798   .760       -.035   Chi   .500   .479   .514
.025   Tor   .462   .542   .517       -.040   LAL   .500   .425   .465
.023   Okl   .750   .651   .628       -.038   Bos   .333   .318   .356
.016   Hou   .643   .629   .613       -.046   Uta   .067   .159   .205
.015   Por   .857   .686   .671       -.065   Mil   .167   .202   .266
.014   Dal   .643   .598   .585       -.062   Brk   .231   .265   .326
.013   Atl   .571   .585   .572       -.067   NYK   .250   .309   .375
.011   Phx   .538   .582   .571       -.068   Cle   .286   .240   .308
.001   Den   .500   .500   .499       -.072   Phl   .400   .330   .402

Assuming w% is the actual win percentage of the teams, pW% is the pythagorean win percentage (not quite sure which exponent was used) and AltpW% is your suggested alternative (average of the game-to-game pW%), I'm not quite sure what you really want to say here, because the RMSE of the AltpW% is bigger than that of the pW% (0.078 vs. 0.086), when compared to the actual win percentage.

Btw, if you check for predictive power of the overall team results, you will notice that the best prediction is based on the full dataset without any cutoffs for blowouts. Matter of fact is good teams aren't getting blown out by 39 points, unless there are circumstances like injuries to important players; in the case of the Bulls to Derrick Rose and Jimmy Butler. Which in turn means, if you have a realiable player metric, a prediction based on the player metric while taking minutes played into account should exceed the predicitive power of a pw%-based predicition.

[Mike G]

Assuming w% is the actual win percentage of the teams, pW% is the pythagorean win percentage (not quite sure which exponent was used) and AltpW% is your suggested alternative (average of the game-to-game pW%), I'm not quite sure what you really want to say here, because the RMSE of the AltpW% is bigger than that of the pW% (0.078 vs. 0.086), when compared to the actual win percentage..

You got it right on the column headers.
I used 13.3 as the exponent for pythW%

The RMSE is perhaps of interest and will likely evolve as the season lengthens. It's not central to the inquiry, though. Yes, predicting (or postdicting) wins would offer some validation, but as someone else noted, Win% is the best "predictor" of Win%.
I think both pW% and the alternative should be of some value.

... if you check for predictive power of the overall team results, you will notice that the best prediction is based on the full dataset without any cutoffs for blowouts.

There's no sharp cutoff. You'll see in an earlier post that succeeding strata of 10-point margins have steeply reducing benefits. In traditional pW%, all points are equally important.

Matter of fact is good teams aren't getting blown out by 39 points, unless there are circumstances like injuries ...

Well, the 2000 Lakers were blown out by 33 in Game 5 of the Finals, before closing out the Pacers in Game 6. Phil said something like, "Champions shouldn't lose by 33 points ..." But they did, and yet they were.

In the 2005 Finals, Detroit lost by 15 and 21, then beat the Spurs by 17 and 31. Maybe neither was a good team? But the last 3 games were great.

And of course, last year Miami lost Game 3 by 36 points. They never did catch up with the Spurs in total series points, thus lost the PythWins battle.
It prompted this earlier appearance of what I'm now calling Alternate Pythagorean Wins:

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.     score     pyth wins    cumulative
G   Mia   SA    Mia    SA     Mia    SA
1    88   92    .36   .64     .36    .64
2   103   84    .94   .06    1.30    .70

3    77  113    .01   .99    1.30   1.70
4   109   93    .89   .11    2.20   1.80
5   104  114    .23   .77    2.42   2.58

6   103  100    .60   .40    3.02   2.98
7    95   88    .74   .26    3.76   3.24

viewtopic.php?f=2&t=8253&start=25
Through 7 games, Miami takes the majority of 'cumulative game pWins'. This in spite of the Spurs' +0.7 ppg advantage.

It just doesn't matter that Danny Green et al hit a bunch of extra shots in game 3. It was still just one win for SA.