Wins vs Pythagorean Wins

[Mike G]

A few years ago, I noticed that older teams tend to win their close games. And over the course of a season, this meant more wins than their point-differentials (MOV)would project.
At b-r.com, we see Pythagorean Wins (PW) alongside Wins in their Miscellaneous Stats table:
https://www.basketball-reference.com/le ... misc_stats

The 2015-16 Dubs had a nice MOV for the year of +10.8. This would normally win about 65 games of 82. But they won 73, and their (W-PW) of +8 is largest for any team in the last 5 seasons at least.
In that interval, 150 team-seasons, the 10 teams with W-PW = 5+, avg age is 28.3; the bottom 10 avg age was 25.4
Correlations between (W-PW) and some Misc. Stats:

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correl.    
.259    Age
.209   Attend.
.173    eFG%
.159    TS%
.107   NetRtg
.107    MOV
.092    ORtg
-.073  OpeFG%
-.062   DRtg
.050   OpTO%
.022    3PAr
-.009   Pace
.020    TO%
-.027  OpFT/FGA
-.042   FT/FGA
-.053   FTr
-.099   DRb%
-.102   SOS
-.124   ORb%

So we may surmise that rebounding helps your pt-diff, but it isn't so important in a short game. And defense is nice, but great shooting wins the nail-biters.
Age is the biggest difference-maker -- and then home crowd size!

[Crow]

Has the correlation sign for Def Rtg and some other opponent stats been reversed to reflect where lower on that is better?

This is not on your topic but has anyone looked at player performance for the 4 factors by age? Age curves tend to be presented for overall performance to my memory. It could be useful to look at factor level to see when players can be expected to advance or decline af specific skills that may be especially important to a team or lineup.

I normally have thought that W - PW had at least something to do with coaching. Could run a list of criteria for coaches- career w-l, mov, age, yrs of experience, avg. factor or stat level or performance, etc.

If you wanted to push further (and maybe check on attendance correlation further), could do W-PW for home and away. And top / bottom halves or thirds of opponent quality.

Doing this for playoffs would probably involve calculating PW legwork but it would be even more important to know what variables correlate higher or lower there vs. regular season. Is age even more important? I'd guess yes. The GMs trying to win big in playoffs with younger teams than the historically successful title teams are implicitly voting against this and are almost always wrong at least in terms of getting to a title. And they do it again and again to the same effect. Talking about you Sam Presti for one.

[Mike G]

Has the correlation sign for Def Rtg and some other opponent stats been reversed to reflect where lower on that is better?...

Yes, kinda, thanks for asking. It's perpetually confusing. I left the signs on and inserted them in their proper order -- just now -- maybe.

It looks like this season busts out of the previous trend, so I re-ran the correlations without this year.
One year isn't much of a sample size for this kind of analysis, but 5 years is; and year by year could be.
Average age of teams at least 2 Wins above or below PythWins each year; numbering 6 to 11 of each per year.

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year    +2+    -2-
2014   26.5   26.0
2015   27.8   26.6
2016   27.7   25.2
2017   26.1   25.5
2018   26.8   26.3
2019*  25.7   26.6

The greatest difference is in 2016. Then older teams lost their advantage. And younger teams then lost their disadvantage.
This year there is no overall correlation with either age or attendance. Has the league endeavored to stop favoring the veterans and the home team? Is it tied to the increased pace and offensive efficiency?
The avg player has also gotten younger, from 26.7 in 2016, to 26.3 this year.

We should check back when the season has concluded, after all the tanking and such.

[Crow]

Thanks for the work.

Could be interesting to compare simple volatility of these criteria to the W-PW correlations. Some of the correlation of W-PW to criteria is related to relative size / importance of the criteria (with shooting being the biggest factor) and some of it is relative to the degree of volatility of the criteria.


Unusually strong / weak draft classes alone or in combination could have an effect on the W-PW trends. Which draft classes have the most players who are 25-27 now? I guess it is probably the ones 5-7 years ago. There are variances in draft class strength that may be affecting this but I found only 3-5 guys per class with a career average over BPM plus 2. I'd rather see RPM but there probably are not many difference makers by any metric. Most first rounders even lottery ranked are not becoming differencemakers.

Player peak age may vary by position and by individual box score metrics vs RPM.

[Crow]

I now see playoff PWs at BRef. So no calculation necessary for that.

[Crow]

For the last 7 champions the average age for starters by position varies some. For PG thru PF the avg ages vary by only about 1 yr- 27 to 28.

Centers average 31. Probably more for salary cap reasons and avoiding a center who screws it up but major experience at the back of the defense is probably helpful too. Which contenders are going eith younger centers? Sixers, Rockets, Nuggets, Jazz, Blazers, Thunder. Most should be fine but might bite one or more.

The average age for recent titlist starters is about 28. 6 of 9 top contenders are close and between 27-29. But most are younger than the titlist average. Boston, Denver and OKC are at or below 26. Thunder the youngest, with Ferguson making the difference. Many have young, perhaps too young benches.

[xkonk]

When are these stats calculated relative to the win differential? Like if the Dubs are +8 in 2015-16, is their age from the beginning of the 2015-16 season? The end? Is it minute-weighted or anything? Basically, I'm curious if the correlation is an artifact of teams that are having bad luck (and thus maybe a lower/negative win differential) giving their rookies and young guys more run, trading vets during the season, something like that.

Also, it looks like MOV has a .1 correlation? After Pythag wins is already based on MOV, right? Is this a sign that Pythag wins should have the MOV term further adjusted somehow? Is it just noise and telling us that anything up to (at least) a .1 correlation should be seen as unreliable?

[Mike G]

When are these stats calculated relative to the win differential? Like if the Dubs are +8 in 2015-16, is their age from the beginning of the 2015-16 season? The end? Is it minute-weighted or anything? Basically, I'm curious if the correlation is an artifact of teams that are having bad luck (and thus maybe a lower/negative win differential) giving their rookies and young guys more run, trading vets during the season, something like that.

At b-r.com, player 'age' for the season is at Feb. 1, roughly middle of the season. It's arbitrary, but it applies equally to all teams. Unless a team has lots of players born in winter or in spring, it's not too big an influence.
Yes, it's weighted by the minutes for each player. Thus, average age on the court, over the course of the season.

Negative correlation with youth could indeed be in part an artifact of younger teams tending to be developing, rebuilding, or even tanking.

Also, it looks like MOV has a .1 correlation? After Pythag wins is already based on MOV, right? Is this a sign that Pythag wins should have the MOV term further adjusted somehow? Is it just noise and telling us that anything up to (at least) a .1 correlation should be seen as unreliable?

It may be related to the previous question about how players are used on rebuilding teams. And how about the correlation with crowd size? Is that referee bias creeping in? If so, maybe in a very close game, they tend to side with the team they think is better?

Some have argued for a bigger exponent in pythWins, which would seem to be supported by the MOV bump. In playoffs, we might see better refs and less correlation..

[Mike G]

I lined up the 80 playoff team-seasons with their regular season selves, and found a formula that 'predicts' their playoff wins based on their RS wins.
W = (RSW-38)/2.37
So a team that sneaks into the playoffs at 38-44 can be expected to be swept in round one. Similarly:
RS - PO
40 - 0.8
45 - 3.0
50 - 5.1
55 - 7.2
60 - 9.3
65 - 11.4
70 - 13.5
Applying this simple straight-line formula to all playoff teams, then their over/unders are found and have correlations with the same set of stats.
Interestingly, RS pythWins do not correlate as well to playoff wins. So I went with actual RS wins.

Without flipping any signs to indicate better or worse:

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POW/xW  RSW/pW    
.348    .041    TO%
.320    .182    eFG%
.311    .155    TS%
.219    .183    NeFG%
.164    .001    3PAr
.141    .054    ORtg
.116    .249    Attend
.111   -.062   DRtg
.104    .296    Age
.092   -.071   OpeFG%
.064   -.011    Pace
.042    .078    NRtg
-.064   .097   OpTO%
-.067  -.103    FT/FGA
-.071  -.149    DRb%
-.082  -.112    FTr
-.109  -.015   OpFT/FGA
-.143  -.160    ORb%

I include for comparison the correlations in RS from pythW to actual W.
Age and attendance are now middling factors in playoffs.
Turnovers are not a good thing; but in playoffs they tend to diminish. So whatever your RS record, if it's tempered by above-avg TO, you're really better than that. (?)

[Crow]

Looks like your expected playoff win formula doesn't allocate the last of the 16 wins needed for a title. Still, 50 wins equals should make it to 2nd round. Over about 57 should make conference finals. Over 65 wins should make finals. Maybe teams over 55 out perform the linear formula a bit?

Do both teams that should make finals tend to be good enough to win it? There are probably some years where it is lopsided by conference but these results would suggest generally yes or at least that it can't tell.

If you want to try even more, what about playoff predictions based on difference in regular season record, PW or SRS? Which is best? Which combo?

Apply to current playoff seeding? Justin Jacobs on twitter has done this by some private method.

Some say give a bonus for the team with the best player. Or ding any team without a top 5 guy. By RPM, Harden appears to be top guy... but hasn't been in past playoffs. With estimated errors hard to separate the top 10 candidates for top 5 player by RPM alone. That and past playoff performance would be better.

[Mike G]

In fact, 50 wins in the West is not as good as 50 in the East, as far as what you are likely to do in playoffs.
This 5 year survey basically covers the Warriors/Cavs era; and 5 of the 6 most-overachieving playoff teams were LeBron's 5 trips (one @ Miami).

When I strip out Cle and GSW from the field, the correlations remain: If two evenly matched teams meet in the playoffs, don't bet on the team with good rebounding that forces turnovers; go with the team with higher TO and eFG%.

[Crow]

W-PW is affected by team behavior in blowout conditions, for and against. Some run up score, some ease back. Some fight every uphill fight, some give in... late or sometimes early or from the beginning because of scheduling, load management, etc.

[Mike G]

That is true. A team might win half of its close games and also indulge in inflating blowout wins, and look "bad" in W-pW.
But I haven't seen that as a pattern. Coaches tend to use blowout time as experimental time, at least when they're winning.

Here are those biggest disparities in the last 5 years:

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tm   yr    W   PW       tm  yr    W   PW
Dal  18   24   33      GSW  16   73   65
Min  14   40   48      Cle  18   50   43
Min  17   31   38      Mem  16   42   35
Det  15   32   38      Brk  14   44   38
Phl  16   10   16      Hou  15   56   50
Uta  16   40   46      Bos  17   53   48
Cha  17   36   42      Brk  15   38   33
Cha  18   36   42      Mem  15   55   50
Uta  18   48   53      Chi  16   42   37
Mil  14   15   20      Orl  17   29   24
Sac  14   28   33               

Actually there's probably a disincentive for coaches to run up scores. If the Mavs last year "should have won" 33 games according to some inflated stats, but Carlisle only got 24 out of those talented players, that doesn't help his case.

On the other side, the Dubs of 2016 were so good they could rest their stars and cruise in with an 8 to 10 point win that they were in no danger of losing, and could/should have been 15 to 20 pt win.

[bbstats]

Hi! This is literally all I care about these days (figuring out why and how some teams beat their Net Rating in terms of win%).

Some thoughts:
1. Something is awry if Net Rating has a +.107 correlation. How is that possible? Should be removed from the equation really...just want to measure Net Rating vs. Win%.

2. Opponent FTR wasn't in the dataset but it should be - there's a (relatively) good correlation there. It makes sense though - if you're down at the end of the game you'll likely increase your fouling.

3. The age thing is very interesting - is this weighted by minutes?

4. I'll add that if you measure the quality of your 5-most-played players there's a high correlation with win% above expected (my patrons @ www.patreon.com/bbstats know this!). This is because you can play your best players in crunch time.

[Mike G]

1. NetRtg has a smallish additional correlation (beyond the 100% assumed) to Win%, suggesting the PythWins exponent is too low, or some teams have been blowing up MOV and/or cruising to victory.

2. Opp FT/FGA is almost identical to Opp FTr and has a -.11 corr. This suggests an additional disadvantage to fouling a lot, beyond the MOV cost.
The corr. between RS wins and PO wins is essentially zero. Likely because your high-fouling bench isn't playing so much.

3. Yes, b-r.com calculates Age according to minutes on the floor.

4. I think all these correlations support your theory and can be explained by it.
Whether by referee bias, or lineup management, or some interactions between the two.