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Scott S

PostPosted: Sun Aug 10, 2008 9:34 pm Post subject: It's all about winning (championships) Reply with quote

Many advanced statistics come up with an approximation of points created, points above average and points above replacement. When I first saw these statistics converted to wins, I was intrigued. But just as teams should consider winning games rather than just picking up points, I wouldn’t expect many teams to set their long term goals being “pretty good” without considering titles. Now, this is not an attempt in anyway to undermine the careers of all time greats such as Karl Malone, John Stockton, Charles Barkley, Elgin Baylor, Patrick Ewing, etc. and I do realize that there are many other factors such as making money (for many, this is probably the true goal), fame, respectability, as well as being relevant for the long term in the fan base; but winning the title is the driving force and the culmination of the sport.

I had long intended to create a formula for championships created or added, but I was never satisfied with my formula for any points-added value. Over the last few days I just decided to give it a try, despite not being completely satisfied with my points-added method. I initially planned on using existing data, but the number of teams in the league changed frequently and I figured I would try to use distributions to come up with my probabilities of winning a title given each number of possible wins.

I found that the best fit of the distribution of team winning percentage was a beta distribution with alpha and beta of approximately 5. A normal distribution with mean 0.5 and standard deviation of 0.15 also works decently. I didn’t think the variance changed significantly enough based on the number of teams and through the years for me to apply this to my distribution. From there, I determined the probability of a team taking one of 8 spots available for the playoffs in a 15 team conference. I adjusted the upper limit of the cumulative beta distribution to exclude the win variable being analyzed. The probabilities of making the playoffs seem reasonable when comparing to a moving average of the actual results. The actual percentages are slightly higher, as expected due my assumptions including a larger number of teams than the average observed. Also, due to the discrete nature of the binomial distribution, I my average playoff teams were 15.8 instead of 16.

The next step was to determine the probability of winning the

championship given a playoff birth. For now, I have ignored home court expectations and different expected strengths of schedule. I plan on looking into this later, but there were just too many permutations for the time being. This will likely have a noticeable, but perhaps not significant, impact on the results. I started by taking the probability of beating an average playoff team in a 7 game series to the 4th power. However, as expected, this produced a higher probability of winning a

championship then actuality. This is almost certainly due to the weighed average playoff team being higher than the average playoff team. Using a 69% average playoff opponent winning percentage (adjusted up from 65%), the total odds of winning a

championship come to 1 in 30. These odds seem to be higher in the beginning and progress at a higher rate. This, again, is likely due to there being fewer teams in the actual than the expected.

See the following rates:

Code:

Exp Wins Exp

Champs Actual

Champs Freq

42 0.0% 0.0% 3.0%

43 0.1% 0.0% 3.0%

44 0.1% 2.8% 3.0%

45 0.2% 0.0% 2.9%

46 0.2% 0.0% 2.9%

47 0.3% 3.2% 2.8%

48 0.5% 0.0% 2.7%

49 0.7% 5.3% 2.6%

50 1.0% 0.0% 2.5%

51 1.3% 0.0% 2.4%

52 1.8% 10.0% 2.3%

53 2.4% 0.0% 2.2%

54 3.2% 5.9% 2.0%

55 4.2% 0.0% 1.9%

56 5.4% 7.7% 1.8%

57 6.9% 10.0% 1.6%

58 8.8% 23.1% 1.5%

59 11.1% 18.2% 1.3%

60 13.8% 25.0% 1.2%

61 17.0% 20.0% 1.1%

62 20.7% 45.5% 0.9%

63 25.0% 14.3% 0.8%

64 29.8% 0.0% 0.7%

65 35.1% 100.0% 0.6%

66 40.8% 0.5%

67 47.0% 75.0% 0.4%

68 53.4% 0.3%

69 59.9% 100.0% 0.3%

70 66.4% 0.2%

71 72.7% 0.2%

72 78.6% 100.0% 0.1%

73 83.9% 0.1%

74 88.5% 0.1%

75 92.3% 0.0%

Actual data is from 1977-2007 as in most of my tests. Remember that these totals assume 30 teams and 82 games every year.

I then needed to come up with some measure of points and wins added. I didn’t feel like coming up with my own formula, so I used the most accepted and widely available statistic that can be fairly easily converted to apply replacement level and usage (at least to my level of understood). To do this, I used Offensive and Defensive Ratings and adjusted them for replacement.

I assumed a starter had his minutes replaced by the average 2nd string player and the 2nd string player’s minutes were then replaced by the average 3rd stringer and the 3rd stringer’s minutes were replaced by an estimated borderline NBA player. For starters you add all 3 numbers, for 2nd string players you add the last 2 and for 3rd stringers you just use the last figure. The idea is that every player is selected because he is expected to add value that his team would not have if he was not on the team, assuming he is used properly and performs to expectation. Otherwise you should cut him. Starter and bench minutes were determined by assuming the highest 150 players (in a 30 team season) were starters and the next 150 were bench players. I used some regression to estimate increased usage and minutes on a poorer team, where the same player is more valuable on a points basis. This model is better than nothing, but I definitely want to improve on it. Because I didn’t feel my model was appropriate on the extremes, I assumed no player decreased a team’s win, although it could certainly happen. I assumed a rating would not change from team to team, on average. (I would imagine it could.) I took each expected margin (converting everything to a 200 points per game scale) given each number of possible wins and determined the new margin given that player played on the team that season by applying the aforementioned method. Then, I converted it to expected wins using a Pythagorean factor of 14 and then converted wins to expected championships for each of the 83 wins scenarios. I used linear approximation for partial wins expected. After this, I applied the frequency probability to each of the scenarios and subtracted out the probability of winning a

championship before adding the player. This gives us the mean championships added.

Here are 3 sample players I tested:

Code:

Games MCA Wins Added Points Added

Snow 880 16% 47.8 1,483

Paul 222 22% 32.8 1,032

Jordan 1072 201% 209.9 6,737

My results for average points added seem to be lower than observed adjusted plus minus for the higher observations, by about 20% or so. I don’t know if this has something to do with the game flow or something else to do with tendencies involving adjusted plus minus or if my model is just understating their value. I could see either, but lean towards the latter, especially since adjusted plus minus is centered around 0, whereas almost all of my players exceed 0. (I would guess the average would be about 1 point added or maybe even 2.) To make a quick adjustment, I applied a load of 20% to points added. This dramatically changes the results:

Code:

Games ACA Wins Added Points Added

Snow 880 21% 57.4 1,779

Paul 222 32% 39.0 1,238

Jordan 1072 302% 246.2 8,085

Notice that championships are weighed in favor of superstars. This can help add perspective when considering obtaining a young mid-level prospect for an older star. Obviously, finances are typically the primary considerations for the team obtaining a prospect. It would be more applicable to use expected championships added based on the team specific projection. For example, Jordan is estimated to bring his team from about 52 expected wins in 1996 to about 70 expected wins (based on the 20% load method). This means he increased the probability of his team winning the

championship from 2% to 66%. (Incredible!) Without the 20% load, the wins and championships odds of his team would be around 58 wins and about 9%, respectively. His expected championships added might have actually exceeded 60% that year! (This was the best year for Jordan.)

As you can probably imagine, these calculations were somewhat tedious and I am sure I may have missed something that I probably should have considered. And, despite my checks, there may still be calculation errors. I did all of these calculations in excel and there are a number of lookups and a few lengthy formulas. I hope to try to figure out some summation techniques in order to make these calculations more doable in bulk. For this, I might also need to use some programming system. Let me know if you want me to explain something in more detail or provide more information and let me know what you think about the results, if you thing they are reasonable and/or informative.

As always, I appreciate any feedback and criticisms.

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Mountain

PostPosted: Mon Aug 11, 2008 7:39 pm Post subject: Reply with quote

I am taking the method pretty much on faith at this point but it sounds like a good start. As you say home court expectations and different expected strengths of schedule would be enhancements with more time.

I find the expected vs actual table interesting. Unless a team gets up near 65 wins regular season they are on average still a longshot. 60 wins +/- 1 about a 20% actual title win rate and close to 15% expected.

You have identified a good conceptual extension on wins created.

Championship impact is a good argument in favor of the high salaries of stars.

Given this interest in going beyond just regular season wins, if you haven't seen it before you might have interest in this thread

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Mountain

PostPosted: Fri Sep 26, 2008 5:51 am Post subject: Reply with quote

Bump for use in recent discussion.

Scott, could you provide any updates on your method?

Or a larger sample of Adjusted Championships Added values for top player seasons?

And / or

Championship Probability Added on specific teams

(or a link to a longer table?)

Typical 58-60 win team with around 22% chance of winning title (based on actuals above) composed of maybe 3 players adding 16% chance of winning title and the support cast the rest? So you might have players worth 8%, 5%, 3% and maybe a 2%, 1%, 1% and a couple fractions? These would be simple player rating values.. he is a 6, that guy is a 10, 4, etc. But this framework also shows that value is relative to context as shown in the Jordan example.

Last edited by Mountain on Sat Sep 27, 2008 11:49

Neil Paine

PostPosted: Fri Sep 26, 2008 8:53 am Post subject: Reply with quote

Thanks for the bump, Mountain, somehow I missed this the first time around. I'll have to take some time to read the whole post, but it seems like what I was talking about yesterday, when I referenced a "

championship probability added" method.

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Mountain

PostPosted: Fri Sep 26, 2008 9:25 am Post subject: Reply with quote

Sure. You probably jogged my memory.

Continuing a train of thought started above did Ainge help organize the win of the title mostly because Garnett was an exceptionally powerful "wildcard" for making his hand or because he outperformed nearly all other teams with his "big 3" or because his supporting cast had more support players who were "1-2's" (1-2%

championship probability added) than others or did he succeed at all three levels of the game? I think he did a good job at all 3 levels but his performance with the supporting cast may not not get enough attention. What values do you have for the Celtics and other leading challengers last season Scott?

supersub15

Joined: 21 Sep 2006

Posts: 273

PostPosted: Fri Sep 26, 2008 10:05 am Post subject: Reply with quote

Not sure if this will add anything to the conversation, but what the heck.

A while back, I went back to the 1979-1980 season and reviewed all the conference finalists until 2007-2008 (29 seaons). I think a conference finalist is the closest definition of a "contender".

What I discovered was this:

- The average regular season Win% for a conference finalist is .703

- The best Eastern Conference team in the regular season has reached the conference finals every year since 1979-1980.

- The best Western Conference team in the regular season has reached the conference finals 24 times out of 29 since 1979-1980.

- Of the 116 conference finalists during this time period, 53 had the best regular season record in either conference, 36 had the 2nd best, 16 had the 3rd best, 2 had the 4th best, 4 had the 5th best, 3 had the 6th best, 1 had the 7th best, 1 had the 8th best.

- Of the 29 champions since 1979-1980, 27 were ranked 1st or 2nd in their conference, and only San Antonio (3d in 2006-2007) and Houston (6th in 1994-1995) were ranked lower.

So, out of the 116 "contenders", only 9 came from the lower rungs. Mind you, the combined winning% of those 9 teams was .585. Not too shabby.

Basically, you have to be really good in the regular season to have a shot in hell at winning a title. There are virtually no Cinderella stories in the NBA.

Last edited by supersub15 on Fri Sep 26, 2008 11:00 am; edited 1 time in total

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Mountain

PostPosted: Fri Sep 26, 2008 10:33 am Post subject: Reply with quote

Yeah, based on Scott's data, the 4 conference finalists last season had a 110-135% chance of winning the title based on their regular season performance (depending if you counted the Celtics at 75% or 100%).

Regular season excellence is a good indicator of being a playoff contender. But takes unusual excellence to be a true odds-on favorite. Most use some edge in match-up desirability or heightened playoff performance to beat the other 3 contenders and the stray Cinderella.

I try to keep my focus on the top 8 because the top 4 emerge out of that, But who will emerge this time? Celtics & Lakers make 2 but I'd guess 2 new.

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Ryan J. Parker

PostPosted: Fri Sep 26, 2008 11:33 am Post subject: Reply with quote

Quote:

the 4 conference finalists last season had a 110-135% chance of winning the title based on their regular season performance

This lost me. Do you mean 10-35% chance?

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Mountain

PostPosted: Fri Sep 26, 2008 12:05 pm Post subject: Reply with quote

Nope, using the team wins of the 4 conference finalists and Scott's middle column for actual frequency of winning the title of prior teams with similar regular season win totals for his study period I get 110-135% as the sum of the frequencies to be used as a gauge for last season's finalists. Obviously the probability of an event (before it actually happened) can't go that high and would have to be pro-rated based on total probability of all.

Last edited by Mountain on Sat Sep 27, 2008 1:57 pm; edited 2 times in total

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Ryan J. Parker

PostPosted: Sat Sep 27, 2008 12:54 pm Post subject: Reply with quote

I guess I'm just confused with what 110-135% is supposed to mean. Clearly you can't have a chance higher than 100%, so I'm just wondering what that represents.

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Mountain

PostPosted: Sat Sep 27, 2008 1:30 pm Post subject: Reply with quote

I shouldn't have casually said "110-135% chance of winning the title" (around here). As I tried to say in my last post this data would have to be pro-rated to get to a more proper probability estimate given the scores of all teams by this crude method. I used the actual column on my first pass because it it was notably higher and it is the real experience but let me take a second pass using simply the expected values:

4 conference finalists (from first column based on regular wins, rounding)

Boston 41%, Detroit 11%, Lakers 7%, New Orleans 5%

Rest of playoff teams 20% total

Total 84% for all playoff teams

Boston's share of the total about 48%, maybe higher given the actual data. That seems in the right ballpark for their chance to win the title last season based on regular season wins. Detroit next at around 13%, Lakers near 8%, etc.

4 teams with 54+ wins but not in top 4, the most this decade, gave a somewhat greater chance of a Cinderella title winner but it did not happen.

Last edited by Mountain on Sat Sep 27, 2008 1:53 pm; edited 1 time in total

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Ryan J. Parker

PostPosted: Sat Sep 27, 2008 1:45 pm Post subject: Reply with quote

Thanks for the clarification. Very Happy

You're certainly right about this:

Quote:

I shouldn't have casually said "110-135% chance of winning the title" (around here).

Laughing

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Scott S

PostPosted: Sat Sep 27, 2008 5:45 pm Post subject: Reply with quote

Thanks for the interest on this topic. I will try to expand a little on my method. To address a few suggestions/questions:

Mountain wrote:

As you say home court expectations and different expected strengths of schedule would be enhancements with more time.

I factored in home court advantage and the dynamic aspect of playoff matchups. I also used Ed Kuper's expectation for basketball winning percentage, 1/(1+EXP(-(0.59+4.4*Home%-4.3*Away%))). The new results seem much of the same as the old results. 0-63 wins are all within 1%. After that we see the old model is increasingly larger than the new model.

Code:

Wins New Old

64 28% 30%

65 32% 35%

66 35% 41%

67 39% 47%

68 43% 53%

69 47% 60%

70 50% 66%

71 54% 73%

72 57% 79%

73 61% 84%

74 64% 89%

75 67% 92%

76 70% 95%

77 73% 97%

78 75% 99%

79 78% 100%

80 80% 100%

81 82% 100%

82 84% 100%

Obviously, the new results are not binomially based, so if a team can truly be expected to win 82 games, their actual odds of winning a

championship would be 100%. However, the new figures include more aspects than the old and Ed's model seems to be better for predicting, perhaps including some level of credibility of the sample. So I will use this one for now. This doesn't impact many teams anyway. Obviously, it would include Jordan's '96 season, however. A level of credibility being "hidden" in Ed's method could account for the decrease in odds when adding home court would typically increase the better team's championships odds. By this I mean, Ed's method might take a team that is 72-8 and say they have a 80% chance of winning the next game, whereas the binomial distribution would say they have 90% chance. The formula indicates that those 80 games were not enough to fully create expectations for the future/present.

Mountain wrote:

Scott, could you provide any updates on your method?

Or a larger sample of Adjusted Championships Added values for top player seasons?

And / or

Championship Probability Added on specific teams

(or a link to a longer table?)

Typical 58-60 win team with around 22% chance of winning title (based on actuals above) composed of maybe 3 players adding 16% chance of winning title and the support cast the rest? So you might have players worth 8%, 5%, 3% and maybe a 2%, 1%, 1% and a couple fractions? Or are the end of bench players negative factors, pushing the positive higher? These would be simple player rating values.. he is a 6, that guy is a 10, 4, etc. But this framework also shows that value is relative to context as shown in the Jordan example.

I will work on creating a template for comparing everyone last season (or other seasons. I might try to compile expected championships added, which would be team specific, whereas average expected championships added is the average if a player played on all theoretical teams (ignoring fit among others)). I think using statistical plus-minus for the points added portion of the results would provide the best combination of available data, reasonable results, time effectiveness, etc. Any suggestions?

It is apparent that superstars are more valuable than wins added would indicate based on my prior comparisons (Snow versus Paul would be virtually the same and converting to points to wins to championships doesn't change who is better on a snapshot, just who is more valuable over a period of time, if that makes sense.) Obviously, these players also have a greater cost from salary cap and draft picks, etc. and value true worth must consider this. However, there has been a prevailing theory that you need superstars to win in the NBA, not just a good team and most popular beliefs either have some basis in truth or tendency to blur perception of reality, so it is plausible to me.

Good observations supersub15 and Mountain. Note that some of the higher actual

championship odds only have 1 or 2 samples, so they aren't too reliable. And my projected

championship odds are based on a regularly distributed NBA season over the past 30 years, not including last season. A number of variables can influence this, but I did not notice any discernible patterns over this period.

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Mountain

The new lower progression of

championship probability as you move up the regular season win scale makes sense to me.

Statistical plus-minus would be an acceptable tool, especially if adjusted to team results. Perhaps daviswylie will publish his database.

Look forward to possibly seeing more later.

"It is apparent that superstars are more valuable than wins added would indicate based on my prior comparisons"

In a somewhat related observation I was about to pass on that I browsed the salary lists and found that Phoenix had the fewest players making over $2 million (6). probably a consequence of high salaries of the guys on top and relying on them for wins. And their ability to get players capable of playing support roles on a

championship team. Boston, San Antonio, Philly and Denver had 7.

On the other end of things I see Portland and OKC with 12 over $2 million and are probably the leaders (though I didn't resurvey fully, New York "only" had 11). An indication more of their team life-cycle phase and / or philosophy? Lakers and Cavs with 10 are at least tied for the most of a top contender. The depth could be useful. Depends on salary mix, total budget and returns on investments.

There are other ways to describe salary structure or measure concentration and it would be good to look at return by segment before drawing conclusions of course. Bargains and boondoggles in every segment. Market circumstances and team needs will make the story more complicated than a simple count.

Last edited by Mountain on Sat Sep 27, 2008 11:57 pm; edited 1 time in total

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Scott S

PostPosted: Sat Sep 27, 2008 10:13 pm Post subject: Reply with quote

Here are the results of the Boston Celtic's team stats.

Code:

GP Mins SPM PtAd TmWi TmWo WPWo WA ChWo ChW ECA Name

80 2,874 4.6 576 884 309 53.0 69.6 2% 49% 47% Pierce, Paul

73 2,622 2.7 422 884 462 58.3 69.6 11% 49% 38% Allen, Ray

71 2,331 6.5 573 884 311 53.1 69.6 2% 49% 47% Garnett, Kevin

144 4,953 4.5 995 884 (111) 36.6 69.6 0% 49% 49% Garnett Allen

77 2,309 2.5 393 884 491 59.3 69.6 13% 49% 35% Rondo, Rajon

74 1,818 2.6 341 884 543 60.9 69.6 18% 49% 31% Posey, James

78 1,914 0.5 276 884 608 62.8 69.6 24% 49% 24% Perkins, Kendrick

78 1,481 0.5 235 884 649 64.0 69.6 28% 49% 20% House, Eddie

75 1,378 (1.8) 156 884 728 66.1 69.6 36% 49% 13% Allen, Tony

56 808 2.9 182 884 702 65.4 69.6 33% 49% 15% Powe, Leon

69 942 (1.2) 132 884 752 66.6 69.6 38% 49% 11% Davis, Glen

48 512 (4.5) 37 884 847 68.8 69.6 46% 49% 3% Scalabrine, Brian

22 173 (0.1) 28 884 856 69.0 69.6 47% 49% 2% Pollard, Scot

18 208 (1.0) 30 884 854 69.0 69.6 47% 49% 2% Brown, P.J.

15 95 (3.7) 8 884 876 69.4 69.6 48% 49% 1% Pruitt, Gabe

17 296 (3.6) 24 884 860 69.1 69.6 47% 49% 2% Cassell, Sam

SPM- stat +/-

PtAd- pts added in a season

TmWi- team margin with player

TmWo- team margin without player

WPWo- wins in 82 game season without player

WA- wins in 82 game season with player

ChWo- championships expected without player

ChW- championships expected with player

ECA- expected championships added in the given circumstance

Garnett Allen is the combination of Garnett and Allen.

First thing to note is that this is not a statistic that adds up to a total like win shares does. The points add up to the total and the expected championships add up to one per year on average. In this instance, in order to get the totals to add up, we would have to arbitrarily assign credit to something that no one could have done without the other players on the team. Expected championships added basically takes the difference of a rough expectation of wins, and therefore championships, of a team and subtracts what it would have been if that player had been injured and had his minutes replaced by a bench player whose minutes were replaced by a NBDL player, etc. Notice how even the role players can greatly add to the teams chances. Most Celtics had a higher expected wins added than Lebron James and Chris Paul combined. In a sense they are "more valuable" because of their given situation. Obviously this doesn't mean they are better, just that they are in a higher leverage situation. Obviously it makes sense to do all you can when you are competitive.

Many players add 0.00 championships on average since the team is not in reasonable contention. I came up with only a few players who subtracted expected championships from the team due to situational under-performance of the player (none of these players played more than 300 minutes.)

As opposed to these results, the average expected championships added samples from Snow, Paul and Jordan were based on individual results in all expected situations and the top players would look identical to the top players in wins added for the same minutes and games played. The top 5 in expected championships added in 2007 were all Celtics and the next 5 were all Pistons. I can come up with an average expected championships added table too, but it would take a little more time since it accounts for all combinations of wins and their respective frequencies.

(Is there a better way to line up the columns?)

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Mountain

I am not recallling the best way to post tables

but this old post

viewtopic.php?t=423had info on posting charts.

Maybe you can do something similar?

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Ed Küpfer

PostPosted: Sat Sep 27, 2008 11:59 pm Post subject: Reply with quote

Scott S wrote:

(Is there a better way to line up the columns?)

There is no magic bullet. The most reliable way I've found is to convert the tabs into spaces using this peice of freeware. It will left align the columns. It does have a problem when the contents of a cell is longer than the others in the column. For example:

Code:

ATL HELLO

Atlanta HELLO

Atlanta Hawks HELLO

But that is easy enough to fix manually, and totally worth it to make the tables look good. The other way is to take a screen cap of the table, upload it as a pic, and link the image.

More complicated, but guaranteed to look like how you want it.

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Mountain

Still need to digest some of the explanation:

"the expected championships add up to one per year on average"

for teams?

"I can come up with an average expected championships added table too, but it would take a little more time since it accounts for all combinations of wins and their respective frequencies. "

I can sense this would be more time consuming but still desirable.

In the case of the Celtics since they won can the sum of the ECAs be scaled to 1

championship won last season?

Just adding quickly I think the Celtics ECAs add to about 260% so the adjustment would be 1/2.6? So Garnett and Pierce worth about 20% each of this particular

championship and so on?

And maybe runner-ups to their average expected probability of a

championship (unfulfilled) or some such value for scaling in a similar fashion?

Does this conflict with the big 3 / Pareto principle talk in that the big 3 don't reach near 75%? Are these ECAs smaller than conventional wisdom? Is context and rest of team more important than linear metric and previous winshare type evaluation suggests? Change out 6th man Eddie House and Celtics title probability would fall 20%? That is a pretty dramatic argument in favor of importance of depth and chemistry to me.

Maybe too much so? Of course this is just one case, of a team advanced greatly by its shared defense given your use of "defensive rating" as a significant part of the points added method and also implicitly in team margin. It wouldn't be as true for a team that won primarily on offensive strength. Or if defensive credit weren't divided equally among all on the court at same time.

If Garnett got a more realistic larger share and the others were adjusted to a "fairer" level (by adjusted defensive +/- or whatever) the ECAs could shift a good deal. By minutes weighted adjusted defensive +/- you could perhaps argue that Garnett deserves up to about 3/4ths the credit for the team defensive performance/value. Maybe that is excessive but equal credit to all on the court at same time is a simplification that hinders this value calculation. Where is the right mark?

How much- by your current method- is each player's ECA due to a share of team defense? A breakout might be illuminating about the size of this issue in this case.

Maybe after adjustment the share of credit for the big 3 goes back up into the 3/4ths range or more.

If I am off-track in spots or if I am starting to get at the next points and you or anyone can take it further I'd appreciate more explanation.

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Scott S

PostPosted: Sun Sep 28, 2008 2:44 pm Post subject: Reply with quote

Mountain wrote:

"the expected championships add up to one per year on average"

for teams?

Yes, based on expected frequencies of each win total, the sum of each probability of winning a

championship times the probability of a team having that win total adds up to 100%.

I am still coming up with a table for AECA, it is programmed, I just have to plug in the names and years of all of the players. I don't expect these player average totals to add up to anything, either. It should be fairly consistent from year to year, varying only based on the variability of the league strength.

Mountain wrote:

In the case of the Celtics since they won can the sum of the ECAs be scaled to 1

championship won last season?

...

And maybe runner-ups to their average expected probability of a

championship (unfulfilled) or some such value for scaling in a similar fashion?

These numbers shouldn't really be added. For one, Rondo plays on a better team than Garnett does since Garnett doesn't have the benefit of playing with Garnett on his team, if that makes sense. ECA should be viewed independently for each circumstance. As an example, let's replace ECA with expected playoff appearances added and use the Hawks for our example. The Hawks beat out the Pacers by 1 game for the last spot of the playoffs. To simplify, since we know both teams performances (and let's assume for the sake of this example, we know exactly how many wins above replacement each player was worth - I am basing this off of Win Shares), we will assume these numbers are "facts" and not expectations. The Hawks won 37 games and I subtracted off 5 wins that I subjectively guessed a replacement team is worth. The Win Shares above Replacement are as follows:

Code:

Player Name WSAR

Childress 7

J Johnson 6

Smith 5

M Williams 5

Horford 5

A Johnson 1

Bibby 1

Pachulia 1

Lue 1

West 0

S Williams 0

Stoudamire 0

Wright 0

Jones 0

Law 0

Richardson 0

If these numbers are fact and not estimation, then the team would have missed the playoffs if Childress was replaced by a replacement player. Thus, in this situation, he is worth 1 of a playoff appearance added. However, since Joe Johnson, Smith, Williams and Horford are all worth enough wins added, they are also worth 100% of a playoff appearance added in their team. Depending on the tie breaker criteria, Anthony Johnson, Bibby, Pachulia and Lue might be worth either 100% or 0% of a playoff appearance. The team's total could potentially "add" up to 900% because the team would not have made the playoffs if any one of these 9 players had been replaced by a replacement player. This is how expected championships added works, except that it does not assume we know the exact criteria to make the playoffs/win the

championship. In the above situation, we can know if the Hawks would have made the playoffs without Mike Bibby (theoretically of course), but using expected playoffs added, we can only say that the Hawks would have a 15% chance of making the playoffs with 36 wins (without Bibby) and a 21% chance of making the playoffs with 37 wins (with Bibby). Thus Bibby would be worth 6% of an expected playoff appearance added. An average expected playoff appearance added would attempt to remove team situation by applying the player's expected impact for all likely scenarios. ECA is the same thing as expected playoff appearances added and AECA is the same thing as average expected playoff appearances added except that ECA and AECA are based on championships added instead of playoff appearances added. Note that ECA and AECA are based on only REGULAR SEASON positioning and expectations for final playoff results only. Let me know if this clears things up at all or is more confusing.

Remember that ECA is just one small piece of AECA.

Mountain wrote:

Does this conflict with the big 3 / Pareto principle talk in that the big 3 don't reach near 75%? Are these ECAs smaller than conventional wisdom?

Is context and rest of team more important than linear metric and previous winshare type evaluation suggests? Change out 6th man Eddie House and Celtics title probability would fall 20%? That is a pretty dramatic argument in favor of importance of depth and chemistry to me.

Maybe too much so? Of course this is just one case, of a team advanced greatly by its shared defense given your use of "defensive rating" as a significant part of the points added method and also implicitly in team margin. It wouldn't be as true for a team that won primarily on offensive strength. Or if defensive credit weren't divided equally among all on the court at same time.

If Garnett got a more realistic larger share and the others were adjusted to a "fairer" level (by adjusted defensive +/- or whatever) the ECAs could shift a good deal. By minutes weighted adjusted defensive +/- you could perhaps argue that Garnett deserves up to about 3/4ths the credit for the team defensive performance/value. Maybe that is excessive but equal credit to all on the court at same time is a simplification that hinders this value calculation. Where is the right mark?

How much- by your current method- is each player's ECA due to a share of team defense? A breakout might be illuminating about the size of this issue in this case.

Maybe after adjustment the share of credit for the big 3 goes back up into the 3/4ths range or more.

If I am off-track in spots or if I am starting to get at the next points and you or anyone can take it further I'd appreciate more explanation.

ECA and AECA does not have a linear relationship to wins added. This is clear when you look at my comparisons of Snow, Paul and Jordan. I purposely picked Snow and Paul because they had a similar wins and points added. However, a more significant a player is, his championships added accelerates on average. The Celtics results may be deceiving since, as I said, House plays on a different team than Garnett, etc. If Garnett joined a 64 win team (as House did) and we guess he would bring them to expect to win 75 wins, the ECA for Garnett is now 92%-28%=64%. Thus the initial illustration doesn't really compare apples to apples.

Notice that without Garnett and Allen, the Celtics would only be expected to win about half as many games. 75% for the big 3 sounds reasonable to me based on this. As far as defensive rating, I used this for my AECA calcs for Snow Paul and Jordan, but I used Statistical +/- for the Celtics example. You say you would expect Garnett to have a higher value than Pierce? This is possible, but mainly because his apm figures tend to be higher than his spm figures and his minutes might be more high leverage minutes than Pierce since there were some minutes that the game was out of hand for the Celtics this year. These are just guesses though. Obviously, both are elite players, to say the least.

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Mountain

PostPosted: Mon Sep 29, 2008 2:43 am Post subject: Reply with quote

I understand what you are saying about ECAs and so adding them was a wrong impatient move. I was pushing for what the name sounds like but ECA is really expected

championship value lost if a player is replaced at replacement level. I'll wait on AECA.

You use statistical +/- but how do you use points added from team margin in calculating ECA now as opposed to the original description? I am not sure I understand how they fit together.

My defense concerns still seem relevant even if "defensive ratings" per se are not involved since you are using team defense when on the court equally for all.

Is it correct you not actually using adjusted +/- at all?

You said you applied an additional load of 20% to points added to match up with it. Why use raw team margin for points added instead of pure adjusted?

Don't mean to rush you but am trying to understand the method better.

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Mike G

PostPosted: Mon Sep 29, 2008 6:14 am Post subject: Reply with quote

Here's my contribution to the thread (for now):

Code:

GP Mins SPM PtAd TmWi TmWo WPWo WA ChWo ChW ECA Name

80 2,874 4.6 576 884 309 53.0 69.6 2% 49% 47% Pierce, Paul

73 2,622 2.7 422 884 462 58.3 69.6 11% 49% 38% Allen, Ray

71 2,331 6.5 573 884 311 53.1 69.6 2% 49% 47% Garnett, Kevin

144 4,953 4.5 995 884 (111) 36.6 69.6 0% 49% 49% Garnett Allen

77 2,309 2.5 393 884 491 59.3 69.6 13% 49% 35% Rondo, Rajon

74 1,818 2.6 341 884 543 60.9 69.6 18% 49% 31% Posey, James

78 1,914 0.5 276 884 608 62.8 69.6 24% 49% 24% Perkins, Kend.

78 1,481 0.5 235 884 649 64.0 69.6 28% 49% 20% House, Eddie

75 1,378 (1.8) 156 884 728 66.1 69.6 36% 49% 13% Allen, Tony

56 808 2.9 182 884 702 65.4 69.6 33% 49% 15% Powe, Leon

69 942 (1.2) 132 884 752 66.6 69.6 38% 49% 11% Davis, Glen

48 512 (4.5) 37 884 847 68.8 69.6 46% 49% 3% Scalabrine, B.

22 173 (0.1) 28 884 856 69.0 69.6 47% 49% 2% Pollard, Scot

18 208 (1.0) 30 884 854 69.0 69.6 47% 49% 2% Brown, P.J.

15 95 (3.7) 8 884 876 69.4 69.6 48% 49% 1% Pruitt, Gabe

17 296 (3.6) 24 884 860 69.1 69.6 47% 49% 2% Cassell, Sam

SPM- stat +/-

PtAd- pts added in a season

TmWi- team margin with player

TmWo- team margin without player

WPWo- wins in 82 game season without player

WA- wins in 82 game season with player

ChWo- championships expected without player

ChW- championships expected with player

ECA- expected championships added in the given circumstance

Garnett Allen is the combination of Garnett and Allen.

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Mike G