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• ... think ... Assuming reduced minutes-per-player is the result of increased competition, that seems to be the consensus. Getting a sense of dilution would
Message 1 of 14 , Jun 4, 2001
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--- In APBR_analysis@y..., "Dean Oliver" <deano@t...> wrote:
> So a concentration factor > 1 means a net influx of talent? I
think
> that is what this all means. (Please correct me.) Actually the
> concentration factor is a measure of net influx of talent, but not
> dilution. Right?

Assuming reduced minutes-per-player is the result of increased
competition, that seems to be the consensus.

Getting a sense of dilution would mean comparing
> the concentration factor increase to the increase in the number of
> teams or the number of players. So the 2.85 factor over the last
50
> years (when the league has gone from 10 teams to 29) means that
> talent isn't all that diluted (2.85/2.9 ~1). It should have gone
up
> by a factor of 2.9 to keep up with the number of teams.

I don't think so. Increasing the number of teams (expansion) has
only reduced the talent concentration during that year, and it is
immediately made up in the next year or two. What I am reading is
that a player from 1965, transported to 1985, would only get half as
many minutes. This is, of course, an average; a Wilt or an Oscar
would still get beaucoup minutes, but a Bob Ferry might get only 1/4
the minutes.

On the other
> hand, the number of players you are calculating this for went from
59
> to 271, an increase of 4.5. So maybe it's diluted a lot
(2.85/4.5).
> I'm not sure which is the more relevant comparison.

I think, by comparing individuals' year-to-year minutes, we are
immune to such factors as # of teams or # of players. The proof is
in the pudding.
>
> I hope I'm right in my interpretations because, with this
> understanding, I really do think you have something there. And I
> wasn't sure there was a way to measure dilution. So simple yet so
> apparently reasonable.

Simple enough, when you have Excel. Yet I have overlooked its
significance.

> What players do you calculate the values for? Do you think we need
> to correct for the number of games played, too (which change from
> year to year, esp. early on)?
>
Fewer games early on means I get scalped some more, for beating up
on the old-timers. I counted everyone who played for one team in 2
consecutive years. Not counting players traded midseason should not
add up to anything in the long run, but I can't prove this. Partly,
I was concerned about guys getting 88 games, but mostly I didn't have
• I am responding to my own earlier post. I am editing some of this chart to factor in the changing schedule, from 66 games in 1952, to 82 games by 1967. In
Message 1 of 14 , Jun 5, 2001
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I am responding to my own earlier post. I am editing some of this
chart to factor in the changing schedule, from 66 games in 1952, to
82 games by 1967.
In this version, ABA seasons are not included, though the effects
on the NBA are measured.
I also completed the analysis from 1996-2000, previously missing.

--- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:
> A chart showing players who played in 2 consecutive seasons,
> listing the year, number of players qualifying, minutes from
previous
> season, minutes from year indicated, ratio of minutes
> (previous/current), and cumulative factor. The cumulative factor
is
> the given year's "concentration factor" multiplied by the previous
> cumulative factor.
> Players who played for more than one team during either year are
> not eligible in this list. That's just the way I did it.
>
> Here is the complete listing, as it now stands:
>
> concentration
> year players prev. min. factor cumul. expansion/contraction
> 1953 59 1777 1928 .977 .977 9 teams to 10
> 1954 56 1981 1928 1.057 1.033 10 teams to 9
> 1955 51 2080 1910 1.089 1.125 9 teams to 8
> 1956 58 1944 1817 1.070 1.20
> 1957 54 1783 1682 1.060 1.28
> 1958 54 1944 1817 1.047 1.34
> 1959 66 1781 1799 .990 1.32
> 1960 68 1797 1725 1.086 1.44
> 1961 66 1797 1825 1.037 1.49
> 1962 65 1914 2036 .952 1.42 8 teams to 9
> 1963 75 2091 1908 1.096 1.55
> 1964 75 1943 1827 1.064 1.65
> 1965 68 1836 1763 1.041 1.72
> 1966 68 1892 1846 1.025 1.76
> 1967 66 1975 2122 .942 1.66 9 teams to 10
> 1968 93 1682 2045 .849 1.41 10 to 23 (11 ABA teams)
> 1969 155 1955 1982 .962 1.36 23 to 25 (11 ABA)
> 1970 172 1949 1893 1.045 1.42
> 1971 185 1971 2070 .953 1.35 25 to 28 (11 ABA)
> 1972 208 2001 1867 1.069 1.44
> 1973 205 2069 1974 1.063 1.54 28 to 27 (10 ABA)
> 1974 220 1888 1834 1.007 1.55
> 1975 214 1897 1827 1.016 1.57 27 to 28 (10 ABA)
> 1976 216 1864 1719 1.022 1.61 28 to 25 (7 ABA)
> 1977 189 1890 1645 1.142 1.84 25 to 22
> 1978 164 1892 1859 1.017 1.87
> 1979 171 1906 1860 1.024 1.91
> 1980 170 1894 1800 1.052 2.00
> 1981 169 1883 1888 .997 2.01 22 teams to 23
> 1982 196 1825 1708 1.069 2.14
> 1983 198 1731 1655 1.046 2.24
> 1984 204 1780 1768 1.007 2.26
> 1985 227 1767 1667 1.060 2.39
> 1986 223 1761 1690 1.042 2.49
> 1987 220 1724 1659 1.039 2.59
> 1988 211 1687 1665 1.013 2.63
> 1989 224 1532 1553 .986 2.59 23 teams to 25
> 1990 223 1751 1778 .985 2.55 25 teams to 27
> 1991 247 1750 1675 1.045 2.66
> 1992 253 1710 1674 1.022 2.72
> 1993 271 1736 1611 1.078 2.93
> 1994 263 1666 1577 1.056 3.10
> 1995 271 1664 1576 1.056 3.27
> 1996 271 1584 1600 .990 3.24 27 teams to 29
1997 266 1615 1596 1.012 3.28
1998 265 1658 1597 1.038 3.40
1999* 277 1637 1572 1.041 3.54
2000 298 1640 1554 1.056 3.74

* 1999 minutes adjusted for short season
• ... this ... Fascinating stuff, this really is utilizing the minutes played statistic for all it s worth. A couple of minor suggestions: 1. It looks like
Message 1 of 14 , Jun 8, 2001
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--- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:
> I am responding to my own earlier post. I am editing some of
this
> chart to factor in the changing schedule, from 66 games in 1952, to
> 82 games by 1967.

Fascinating stuff, this really is utilizing the minutes played
statistic for all it's worth. A couple of minor suggestions:

1. It looks like you're literally looking at total minutes played;
I'd suggest minutes per game instead. For two reasons: it
automatically corrects for the "games per season" problem that
you've been wrestling with. And it will help correct for injuries,
and comebacks from injuries, which can cause a player's minutes
to seemingly plummet or skyrocket. Injuries will also affect minutes
per game, but less so than total minutes.

2. The issue of players' minutes changing due to their individual
improvement or aging is a potentially important but complex one.
You mentioned that it sort of evens out, as young players improve
and old players decline, but that assumes a sort of long run
equilibrium. I can imagine that there have been times when the
NBA was in the middle of a period of influx of new talent (probably
most all the time) or conversely a period of decay in which old
players declined but failed to get replaced by an equal amount of new
talent (probably much rarer, except maybe when an unusual "baby boom"
of talent, such as 1984, starts aging).

Are the concentration factors based on players' total minutes?
That might be the best way to do things, but it might cause the
concentration factors to be overly influenced by the star players
who get the most minutes. E.g. if 2 players both doubled their
minutes from 400 to 800, but one superstar diminished from 3,200 to
2,800, the grand total is unchanged and the concentration factor would
be 1.0. But I wonder if we should instead give each of the three
players equal weight, with individual concentration factors of 2.0,
2.0, and .875, for an average of 1.625. (This is assuming I've got the
correct formula for calculating concentration factors.)

That example shows a danger of my suggestion, as there will be a lot
of marginal players with tiny minutes whose individual concentration
factors can be huge or tiny, and which might unduly influence the
overall index.

Maybe there's an intermediate way... logarithms, medians instead of
means or totals, etc.

I won't be reading email for almost a month, so I regrettably won't
be able to participate in this discussion for much longer, until July.

It occurs to me that my minutes-per-game suggestion might be
problematic when players change their number of games played, in
addition to their number of minutes per game ... a lot here to think

--MKT
• ... to ... minutes ... One problem with using minutes-per-game is that, while mathematically compensating for the player who was injured, in fact that player s
Message 1 of 14 , Jun 8, 2001
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--- In APBR_analysis@y..., tamada@o... wrote:
> --- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:
> > I am responding to my own earlier post. I am editing some of
> this
> > chart to factor in the changing schedule, from 66 games in 1952,
to
> > 82 games by 1967.
>
> Fascinating stuff, this really is utilizing the minutes played
> statistic for all it's worth. A couple of minor suggestions:
>
> 1. It looks like you're literally looking at total minutes played;
> I'd suggest minutes per game instead. For two reasons: it
> automatically corrects for the "games per season" problem that
> you've been wrestling with. And it will help correct for injuries,
> and comebacks from injuries, which can cause a player's minutes
> to seemingly plummet or skyrocket. Injuries will also affect
minutes
> per game, but less so than total minutes.

One problem with using minutes-per-game is that, while
mathematically compensating for the player who was injured, in fact
that player's minutes are picked up by other players; and so there
would be a skewed total for his team, and for the league.

> 2. The issue of players' minutes changing due to their individual
> improvement or aging is a potentially important but complex one.
> You mentioned that it sort of evens out, as young players improve
> and old players decline, but that assumes a sort of long run
> equilibrium. I can imagine that there have been times when the
> NBA was in the middle of a period of influx of new talent (probably
> most all the time) or conversely a period of decay in which old
> players declined but failed to get replaced by an equal amount of
new
> talent (probably much rarer, except maybe when an unusual "baby
boom"
> of talent, such as 1984, starts aging).
>
Completely valid points. But wouldn't a mass retirement or mass
influx be evened out over a few years at most? If there were serious
ups and downs not attributable to league expansion, I would wonder
about this, yet as the sample size grows in later years, the trend is
invariably toward talent concentration.

> Are the concentration factors based on players' total minutes?
> That might be the best way to do things, but it might cause the
> concentration factors to be overly influenced by the star players
> who get the most minutes. E.g. if 2 players both doubled their
> minutes from 400 to 800, but one superstar diminished from 3,200 to
> 2,800, the grand total is unchanged and the concentration factor
would
> be 1.0. But I wonder if we should instead give each of the three
> players equal weight, with individual concentration factors of 2.0,
> 2.0, and .875, for an average of 1.625. (This is assuming I've got
the
> correct formula for calculating concentration factors.)
>
> That example shows a danger of my suggestion, as there will be a
lot
> of marginal players with tiny minutes whose individual
concentration
> factors can be huge or tiny, and which might unduly influence the
> overall index.
>
> Maybe there's an intermediate way... logarithms, medians instead of
> means or totals, etc.
>
> I won't be reading email for almost a month, so I regrettably won't
> be able to participate in this discussion for much longer, until
July.
>
> It occurs to me that my minutes-per-game suggestion might be
> problematic when players change their number of games played, in
> addition to their number of minutes per game ... a lot here to
think
>
>
> --MKT

Again we have reached more agreement than I am comfortable with!
I wish we could find some holes in the logic, or at least some seams.
Even casually asking my acquaintances seems to produce the same
response, intuitively or analytically: players must be getting
better.
• ... I agree with your conclusion on player improvement. I was trying to think of a way of independently verifying that point. The one way that it struck me
Message 1 of 14 , Jun 8, 2001
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--- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:

> Even casually asking my acquaintances seems to produce the same
> response, intuitively or analytically: players must be getting
> better.

I agree with your conclusion on player improvement. I was trying to
think of a way of independently verifying that point. The one way
that it struck me to do this is to check players' best years and see
whether their peaks coincide with the generally believed development
of players (ie rising production from 21-27/28 and then gradual
decline). Indeed, it did seem that an inordinate number of players
hit their statistical peaks in 61-62 well before we might believe
they would. I have not looked at this thoery in depth but its just a
thought.
• ... to ... see ... development ... a ... Another suggestion (offline) has been that players have longer careers these days. Whereas 13 years was about the
Message 1 of 14 , Jun 9, 2001
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--- In APBR_analysis@y..., harlanzo@y... wrote:
>
> I agree with your conclusion on player improvement. I was trying
to
> think of a way of independently verifying that point. The one way
> that it struck me to do this is to check players' best years and
see
> whether their peaks coincide with the generally believed
development
> of players (ie rising production from 21-27/28 and then gradual
> decline). Indeed, it did seem that an inordinate number of players
> hit their statistical peaks in 61-62 well before we might believe
> they would. I have not looked at this thoery in depth but its just
a
> thought.

Another suggestion (offline) has been that players have longer
careers these days. Whereas 13 years was about the limit for players
entering before 1965, there are now quite a few players who go for 15-
20 years. In general, their last few seasons would consist of
minutes diminishing below that of their rookie seasons.
Which brings me to another point: I don't think it matters where
in your career you peak (early, middle, late), in terms of league-
wide averages. Rather, it matters how many minutes you played as a
rookie, and how many you play in your last season, and that is all.
While a good many players hang on to the bitter end, perhaps
winding up their career with a 100-minute season, there are very few
who get 100 minutes as a rookie, and build up to major minutes
later. Most good, long-career players are good as rookies.
So, regardless of the intervening years, only one's first and last
seasons really add up to anything in the league totals. If you get
2000 minutes as a rookie, you may peak at 3000 or 2500, or whatever;
if you play 10 years and end up with a 500 minute season, you lost
1500 minutes over 10 years. When you are looking at large numbers of
players, the curve smooths out everyone's peaks and valleys, and it
looks as though every year it is tougher to get minutes; but at least
part of this measurement is bogus.
Now we come to another sticking-point; we could figure everyone's
rookie minutes, final-season minutes, and career length, to get an
average annual minutes-lost number. But this would not distinguish
between an aging factor and a competition factor.
So these numbers may mean nothing. Or they may mean something.
Anyone?
• Responding to one of my own posts, again. I went ahead and tabulated the careers of some 1500 players, using seasons spent with a single team. I have broken
Message 1 of 14 , Jun 22, 2001
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Responding to one of my own posts, again.
I went ahead and tabulated the careers of some 1500 players, using
seasons spent with a single team. I have broken them down by career
length, from single-season careers to a 17+ year group.
The 2nd and 3rd columns are the minutes played as rookie, and in
final season.

career avg. minutes
length season annual decline
----- ----------- ----- --------------
yrs. # first last net min. pct.
1 326 (500) (500)
2 156 685 561 -123 123 .180
3 129 873 626 -247 124 .142
4 93 916 688 -229 76 .083
5 76 1032 678 -354 88 .086
6 65 1150 784 -367 73 .064
7 86 1368 660 -709 118 .086
8 78 1415 734 -681 97 .069
9 96 1266 953 -313 39 .031
10 106 1448 912 -537 60 .041
11 92 1393 983 -410 41 .029
12 70 1534 1020 -513 47 .030
13 57 1779 1101 -678 57 .032
14 42 1734 1030 -704 54 .031
15 24 1436 1053 -383 27 .019
16 19 1881 1037 -844 56 .030
17+ 16 1997 480 -1516 89 .044
__________________________________________
7.7 1531 1240 805 -435 65 .052

This thing has sat on my desktop long enough; I am not ashamed to
say I don't know what to make of it.
One thing is clear: "weak" players (those with brief careers) have
a steeper decline, both in minutes and pct. of minutes, than do
stronger (longer) players. Is it possible to produce a "natural
decline" factor, as distinguished from a "talent concentration"
factor, by comparing the decline rates of stronger and weaker players?
Something about guys who go past 16 years and hanging on to the
bitter end? I don't know how much these 16 players can skew the
overall group, but it does illustrate how a bias can result when
talented young players come in at 2000 minutes and leave at 500.

--- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:
I don't think it matters where
> in your career you peak (early, middle, late), in terms of league-
> wide averages. Rather, it matters how many minutes you played as a
> rookie, and how many you play in your last season, and that is all.
> While a good many players hang on to the bitter end, perhaps
> winding up their career with a 100-minute season, there are very
few
> who get 100 minutes as a rookie, and build up to major minutes
> later. Most good, long-career players are good as rookies.
> So, regardless of the intervening years, only one's first and
last
> seasons really add up to anything in the league totals. If you get
> 2000 minutes as a rookie, you may peak at 3000 or 2500, or
whatever;
> if you play 10 years and end up with a 500 minute season, you lost
> 1500 minutes over 10 years. When you are looking at large numbers
of
> players, the curve smooths out everyone's peaks and valleys, and it
> looks as though every year it is tougher to get minutes; but at
least
> part of this measurement is bogus.
> Now we come to another sticking-point; we could figure
everyone's
> rookie minutes, final-season minutes, and career length, to get an
> average annual minutes-lost number. But this would not distinguish
> between an aging factor and a competition factor.
> So these numbers may mean nothing. Or they may mean something.
> Anyone?
• ... using ... Mike -- I think all this work with minutes is very interesting. Not precisely sure what to make of it either, but it _seems_ relevant and
Message 1 of 14 , Jun 22, 2001
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--- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:
> Responding to one of my own posts, again.
> I went ahead and tabulated the careers of some 1500 players,
using
> seasons spent with a single team. I have broken them down by career
> length, from single-season careers to a 17+ year group.
> The 2nd and 3rd columns are the minutes played as rookie, and in
> final season.
>
> career avg. minutes
> length season annual decline
> ----- ----------- ----- --------------
> yrs. # first last net min. pct.
> 1 326 (500) (500)
> 2 156 685 561 -123 123 .180
> 3 129 873 626 -247 124 .142
> 4 93 916 688 -229 76 .083
> 5 76 1032 678 -354 88 .086
> 6 65 1150 784 -367 73 .064
> 7 86 1368 660 -709 118 .086
> 8 78 1415 734 -681 97 .069
> 9 96 1266 953 -313 39 .031
> 10 106 1448 912 -537 60 .041
> 11 92 1393 983 -410 41 .029
> 12 70 1534 1020 -513 47 .030
> 13 57 1779 1101 -678 57 .032
> 14 42 1734 1030 -704 54 .031
> 15 24 1436 1053 -383 27 .019
> 16 19 1881 1037 -844 56 .030
> 17+ 16 1997 480 -1516 89 .044
> __________________________________________
> 7.7 1531 1240 805 -435 65 .052

Mike --

I think all this work with minutes is very interesting. Not precisely
sure what to make of it either, but it _seems_ relevant and
informative. (Maybe for doing something like James' career projection
stuff...)

For instance, it's interesting that players with longer careers never
fall to the level of 2 year players -- in terms of minutes. That
probably means that they are still better than the 2 year players even
after 16 years in the game.

Another way to look at the data would be to calculate the minutes for
players in their peak year and what year that typically was.
Calculate a decline rate in minutes per year from the year of peak.
I'm guessing that the peak minute year flatterns out at about 5 years,
based on the typical assumption that players' careers peak at age
27-28.

Dean Oliver
Journal of Basketball Studies
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