Calculating Championship Odds Based on SRS

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Calculating Championship Odds Based on SRS 

Post#1 » by ElGee » Sun Jul 22, 2012 7:11 am

4/15/13 Update: More data, incorporation of PS data

The goal:
Spoiler:
Figure out how much a player impacts winning a championship on a random team based on his impact on their SRS.


The Method:

Spoiler:
-Calculate the win probabilities in a given game based on SRS differentials of the two teams (using 2008-2012 RS data and 2001-2012 PS data)
-Given this, Calculate the win probabilities in a 7-game series based on SRS differentials
-Calculate the odds of of a given team's opponent quality in each round of the playoffs based on their SRS (using 1986-2012 data)
-Calculate the odds of a player being on a given team from -8 SRS to +8 SRS (using 1986-2012 data)

Defining SRS Impact:
SIO is the simple SRS impact on a true theoretical 0 SRS team. A +8 "SIO" player, by this working definition, improves a 0 SRS team to 8. A +3 SIO Player to 3. And so on.

Before we can compare the differences in performance with a player on vs. off a team, we have to use an "SIO curve," or some kind of simple adjustment for diminishing returns in basketball. A +8 player does not improve a +8 SRS team to 16 (diminishing returns). As a result of this, we will use the following formula with 3 variations:

(a) High Portability* Players -- (SIO * 1.5 ^ (1- e^(SRS/15)))
(b) Normal Portability* Players -- (SIO * 1.5 ^ (1- e^(SRS/10)))
(c) Low Portability* Players -- (SIO * 1.5 ^ (1- e^(SRS/7)))*

*Normal portability formula used for SRS below 0

---
Portability is how well a player's skill translate, or travel to, different team situations and still maintain impact.

The three different kinds of portability players will impact teams like this, for eg:

High Portability +5
--Makes 0 SRS --> 5 SRS
--Makes 3 SRS --> 7.6 SRS
--Makes 6 SRS --> 10.1 SRS

Normal Portability +5
--Makes 0 SRS --> 5 SRS
--Makes 3 SRS --> 7.3 SRS
--Makes 6 SRS --> 9.6 SRS

Low Portability +5
--Makes 0 SRS --> 5 SRS
--Makes 3 SRS --> 7.0 SRS
--Makes 6 SRS --> 8.9 SRS
----

-We can now calculate the impact on SRS based on the "SIO" -- their simple SRS impact on a true theoretical 0 SRS team -- based on 3 kinds of players: High, normal and low portability.
-We can also calculate the impact on team SRS based on health (Games played) of such a player

All told, we can now input the following information and be given the odds of winning a championship:
(1) A Player's SIO (His SRS impact on a neutral team)
(2) A Player's Portability (The degree to which his impact diminishes on good teams)
(3) A Player's Health (No. of games played in the RS)


The Results
Spoiler:
For the purpose of space, the full results will not be attached here (see imaginary Fig 1). Instead, below are the results for player's who have perfect health (95% RS games or more, full PS health):

Odds of Winning Title based on SIO Impact
Normal Portability Player

10 63.2%
9.5 59.4%
9 54.1%
8.5 49.3%
8 44.8%
7.5 41.1%
7 35.7%
6.5 32.0%
6 27.2%
5.5 24.8%
5 21.4%
4.5 18.4%
4 15.3%
3.5 14.0%
3 11.1%
2.5 9.7%
2 8.4%
1.5 6.1%
1 6.1%
0.5 3.8%
0 3.7%
-0.5 3.7%
-1 2.2%
-1.5 2.2%
-2 1.6%
-2.5 1.2%
-3 1.1%



Discussion
Spoiler:
So, what's this all mean?

(1) The majority of all player's only have a relevant impact on good teams.

Only the elite of the elite (8 SIO+ players) will be turning below average teams into title contenders. This means that the ability to turn a 15-win team into a 45-win playoff team is useless. What matters is how well the same player would impact a 45-win team, and even more importantly, how well he'd impact a 50-win team.

This is precisely why portability is so important. The way a player's game scales to better and better teams -- think of the opposite of redundancy -- matters most.

(2) As a result of No. 1, fantastic "second options" (or even "third options") are more important than players who can be first options on decent teams but will see strong diminishing returns on good teams.

(3) Regular Season Player Health matters less than you think.

In the RS, for a normal portability 5 SIO player, playing the whole year results in a 21.4% chance to win the title. Playing half the year? An 20.2% chance. Playing even 10% of the year still results in an 18.0% chance to win the title, assuming the player is playing at a +5 SIO level in the RS and in the PS.

Why? Because the SRS differential the player created in the playoffs is more important than the HCA advantage lost. The majority of below average teams will never see the PS with such a player missing most of the year, but almost every time a player is on an above average team (51% of teams since 1986) his teammates will have qualified for the playoffs. Think Wilt Chamberlain in 1970 or Michael Jordan in 1986 and 1995.

The better the player, the more missing time will hurt him (because of the likelihood of losing HCA in the later rounds against better teams). An 8 SRS player added to a random team gives them a 45% chance of winning title if he's healthy all year. If he plays 10% of the RS and then the playoffs, a 32% chance of winning a title.

(4) No One can guarantee a title

Perhaps most obviously, even we assume a god-like +10 SIO for the best peaks in NBA history, they still will be holding a trophy at the end of the year about 2 in 3 times. This is fantastic...but it's also far from a sure thing. It's easy to see how a player with a 5-year, MVP-level peak of +6 SIO -- the difference between a 41-win and 57-win team -- could play 100% of his games at such a level and not win a championship. In fact, it will happen to about one in every five such players. (Especially if there are many spread across the league at once - -there simply aren't many titles to go around.)

(5) A way to balance longevity and peak

Assume we have two healthy, normal portability players.

Johnny Peak plays 1 year at +8 SIO.
Jimmy Longevity plays 5 years at +5 SIO.

After 5 years, their Expected Value of Championships is:

Peak 0.54
Longevity: 1.12

OK. But +5 SIO is near MVP stuff in some cases. Let's make Jimmy slightly weaker and Johnny even better and stretch out the peak/longevity comparison:

Johnny Peak plays 2 years at +9 SIO.
Jimmy Longevity plays 10 years at +3.5 SIO.

After 10 years, their Expected Value of Championships is:

Peak: 1.25
Longevity: 1.48

Finally, we have some basis with which to balance different situations with high peaks versus steady longevity careers. Yes, peaks matter...but longevity matters a great deal, especially the better the player. And yes, longevity matters even for lower impact players.

Included below are the team championship odds based on SRS using this method:

14 95.2%
13 92.0%
12 87.4%
11 82.2%
10 72.1%
9 62.7%
8 52.4%
7 35.3%
6 22.3%
5 16.3%
4 9.9%
3 3.7%
2 0.8%
1 0.4%
< 0 0.0%


EDIT: Using -2 (1.8% odds) as replacement player level
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Re: Calculating Championship Odds Based on SRS 

Post#2 » by mysticbb » Sun Jul 22, 2012 9:30 am

Couple of notes:

1. The formula for the portabilities is mixed up. You need to switch the one for high and low players.
2. Choosing the point of orgin as 0 SRS on your scale gives you two pretty weird things. First, that means a low, normal and high portability player will have the same effect on an average SRS team. You can use that as a some sort of definition, but I don't think that is a good definition. Players show dimishing returns based on the skillset even with cast based on average players. Second, when you go to a negative SRS team, you will end up saying that a high portability player is actually a worse choice than the low portability player with the same SIO. I doubt that this is something you agree on.
I suggest using a different point of origin here. During the 3pt era the 34 worst teams had an average of -9.7 SRS, and the 34 best teams in average +8.2 SRS. Well, even though that means we don't really have a linear scale, we can still use one. Put the starting point 0 at -9.7 SRS and then raise it to 17.9 for the 8.2 SRS team. Well, you would need a new base (something like 1.1 instead of 1.5) to make it work.
In that way you get a different overall impact for different portability players on average teams while not having the problem with the below average teams.
3. The Bulls in 1986 were an outlier, a 30 win team making the playoffs due to circumstances. Also, without Jordan that team would have missed the playoffs.
4. Longevity vs. Peak. Does your conclusion mean that you agree with my assessment that 12 years of Nowitzki are worth more than 8 years of James? ;)
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Re: Calculating Championship Odds Based on SRS 

Post#3 » by ElGee » Sun Jul 22, 2012 3:24 pm

1. Thanks

2. Totally fair point.

First, let me say that I'm aware of the negatives and thought of having all players use the standard portability on negative teams to avoid this problem (although I could even see the argument that good and bad should flip). In general though, the impact on negative had such little bearing on championships it seemed borderline irrelevant. Which leads to your other point about point of origin -- it's a good idea, although I'm not sure your concern is as common as you think.

Using 0 SRS is easy to conceptualize, and it's also right near the median for team distributions. If you play around with, it seems pretty fair -- especially concerning teams that are above average.

3. I suppose using the 86 Bulls and "average" in the same sentence was a misstep. ;)

4. Yes. If we exclude 2012, I'd take Dirk now.
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Re: Calculating Championship Odds Based on SRS 

Post#4 » by Doctor MJ » Sun Jul 22, 2012 7:54 pm

Great stuff. As we do the Peaks project, I'll be assembling my subjective ratings, and look forward to see how they come out when sent through this process.
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Re: Calculating Championship Odds Based on SRS 

Post#5 » by mopper8 » Sun Jul 22, 2012 8:21 pm

mysticbb wrote:4. Longevity vs. Peak. Does your conclusion mean that you agree with my assessment that 12 years of Nowitzki are worth more than 8 years of James? ;)


I think his conclusion has to be, roughly speaking, that any top 10 player all-time for say 5 years is a worse bet than players, say, 15-25 for 10 years. No?
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Re: Calculating Championship Odds Based on SRS 

Post#6 » by mysticbb » Mon Jul 23, 2012 7:03 am

ElGee wrote:(although I could even see the argument that good and bad should flip).


That would depend on the definition of "portability". For me a player which has his main strength in skills which are rather often avaiable (like a small player who can handle the ball and can shoot, there are tons of those players), is not very portable. But then again, it also depends on how SIO is defined. In such a case level over replacement sounds a more reasonable choice. That's also how I calculate PW48, when I make the fit, I come up with -2.9 as replacement level, which would equate to a -14.5 per 100 possession team. Looking at the team results, -2.2 might be a better "choice", well ...
That might be a good starting point for your SIO here. If you have that defined as level over average, adding something between 2.2 and 2.9 might be reasonable when you start putting the 0 at the -10 team level.

ElGee wrote:In general though, the impact on negative had such little bearing on championships it seemed borderline irrelevant.


That was my first thought as well, but it is relevant, because you get the same values for each of the different portability players, if you put them on an average team. I just don't see that this is true.

ElGee wrote:Which leads to your other point about point of origin -- it's a good idea, although I'm not sure your concern is as common as you think.


From 2001 to 2012 the average championship team was -2.3 with the "best" player off, while being +10.7 with the "best" player on. I think it is really common. Because when we transport your method into the reality we see that a low portability player is in average more valuable for winning a championship than a high portability player. I don't think that this is true.

ElGee wrote:Using 0 SRS is easy to conceptualize, and it's also right near the median for team distributions.


Completely agree. It is easy to apply, that's why it is pretty common to set things to the league average. It is just in conflict with the used power law in your method in order to determine impact on different strong teams.

ElGee wrote:4. Yes. If we exclude 2012, I'd take Dirk now.


Why would you exclude 2012? 2005 to 2012 for James vs. 2001 to 2012 for Nowitzki makes 8 seasons for James vs. 12 seasons for Nowitzki, which equates overall to a higher amount of "championship odds" for Nowitzki. The difference in performance level between those two is just too small in average in order to come up with a different conclusion.
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Re: Calculating Championship Odds Based on SRS 

Post#7 » by mysticbb » Mon Jul 23, 2012 7:14 am

mopper8 wrote:I think his conclusion has to be, roughly speaking, that any top 10 player all-time for say 5 years is a worse bet than players, say, 15-25 for 10 years. No?


Yes, that's how it looks like. But well, I would put those "Top 15-25" player ahead of the "Top 10" player in such a case.
It might also be not as easy to see the longevity for different players, when longevity is not just the amount of years those players were in the league, but rather some sort of "All-NBA-like" seasons, a season in which the player can be the cornerstone (clearly best player) of a contending team. And when I look at a player like Moses Malone, for example, I have a hard time following the notion that he had such great longevity. Well, which has also something to do with the problem of converting raw per game numbers into real impact ...
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Re: Calculating Championship Odds Based on SRS 

Post#8 » by ElGee » Mon Jul 23, 2012 4:53 pm

mysticbb wrote:
ElGee wrote:(although I could even see the argument that good and bad should flip).


That would depend on the definition of "portability". For me a player which has his main strength in skills which are rather often avaiable (like a small player who can handle the ball and can shoot, there are tons of those players), is not very portable. But then again, it also depends on how SIO is defined. In such a case level over replacement sounds a more reasonable choice. That's also how I calculate PW48, when I make the fit, I come up with -2.9 as replacement level, which would equate to a -14.5 per 100 possession team. Looking at the team results, -2.2 might be a better "choice", well ...
That might be a good starting point for your SIO here. If you have that defined as level over average, adding something between 2.2 and 2.9 might be reasonable when you start putting the 0 at the -10 team level.


Very good points. As you know, value over replacement is a grand question in basketball statistics and not easily handled. Something closer to -2 might be a better "base" point for a future iteration.

ElGee wrote:In general though, the impact on negative had such little bearing on championships it seemed borderline irrelevant.


That was my first thought as well, but it is relevant, because you get the same values for each of the different portability players, if you put them on an average team. I just don't see that this is true.


I see I did use "normal" portability below 0 for bad port players -- wasn't sure last time. For some perspective, the good portability players have their title odds changed by a few tenths of a percent at the high end, and once we get to a +5 SIO player there is no difference.

ElGee wrote:Which leads to your other point about point of origin -- it's a good idea, although I'm not sure your concern is as common as you think.


From 2001 to 2012 the average championship team was -2.3 with the "best" player off, while being +10.7 with the "best" player on. I think it is really common. Because when we transport your method into the reality we see that a low portability player is in average more valuable for winning a championship than a high portability player. I don't think that this is true.


I don't using raw on/off for all the reasons that confound the stat. Good teams will have good players playing together. They will then rest together, especially during blowouts. This alone will stretch the net number.

Consider that a title team plays in about 4 more blowouts per year than the average team in the league, and they often rest players for another game or two at the end of the season. That alone can create maybe ~100 of the 800 minutes the "best" player will be off the court. In those 100 "garbage time" minutes the title team would need it's scrubs to be outscored by 38 points to actually be 0 for the rest of the year...and that still doesn't include lineup combinations. So I don't think that's a very accurate indicator.
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Re: Calculating Championship Odds Based on SRS 

Post#9 » by Doctor MJ » Wed Jul 25, 2012 12:35 am

fwiw, I like the idea of using essentially the worst imaginable actual team as a baseline for replacement players. So that's about -15 SRS and thus -3 per player.
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Re: Calculating Championship Odds Based on SRS 

Post#10 » by mysticbb » Wed Jul 25, 2012 6:15 am

ElGee wrote:So I don't think that's a very accurate indicator.


But your extreme example is? And also, if your idea would be true, the NET for the starters would be essentially the same for those teams, but it is not the case. It is obious that the difference is not just created in garbage time. It also could very well end up the other way around, and thus lowering the NET, both things can be rationalized.

Matter of fact is that the championship teams showed a big difference between the time with and without their respective best player. And given the structure of your method you will run into a problem, if you use league average as the starting point.
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Re: Calculating Championship Odds Based on SRS 

Post#11 » by ElGee » Sat Jul 28, 2012 1:26 am

Doctor MJ wrote:fwiw, I like the idea of using essentially the worst imaginable actual team as a baseline for replacement players. So that's about -15 SRS and thus -3 per player.


For my calculations, I'm using -2. I don't know the "right" answer here, but given that the majority of the work was calculating teams between -8 and +8 SRS (most teams fall within this range), and that there have been nine -11 teams in NBA history, and even this year's Bobcats didn't reach the -15 mark, I'm not too worried about looking at VORP at -2 instead of -3. Using Normal Portability (which assumes a slightly smaller dent the better the team), which seems reasonable to me, the different between -2 and -3 is 0.65% (1.85% down to 1.20%) championship odds. At that point, it's barely shifting players more than a spot or two on my own list.
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Re: Calculating Championship Odds Based on SRS 

Post#12 » by SideshowBob » Thu May 16, 2013 6:26 am

What happened to the odds for Low/High players?

EDIT: I was able to find them through the Internet Archive, but I assume that you've updated your research on those as well.
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Re: Calculating Championship Odds Based on SRS 

Post#13 » by SideshowBob » Tue Jun 4, 2013 6:26 pm

Also, what would be the odds for a normal +10.5 and +11.0 player? I'd guess about +4-4.5% for each 0.5 increment, but I figure the jump may be even steeper at that level
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Re: Calculating Championship Odds Based on SRS 

Post#14 » by ElGee » Wed Apr 23, 2014 2:34 am

Updated Tables for Portability and Health:

Image
Image
Image
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Re: Calculating Championship Odds Based on SRS 

Post#15 » by ElGee » Wed Apr 23, 2014 2:38 am

Hmm -- I think it cut the 100% healthy line. :/

Normal Port:
1.1%
1.2%
1.6%
2.2%
2.2%
3.7%
3.7%
3.8%
6.1%
6.1%
8.4%
9.7%
11.1%
14.0%
15.3%
18.4%
21.4%
24.8%
27.2%
32.0%
35.7%
41.1%
44.8%
49.3%
54.1%
59.4%
63.2%

High Port:
0.9%
1.2%
1.2%
2.2%
2.2%
3.7%
3.7%
3.8%
6.1%
6.1%
9.4%
9.7%
12.8%
14.2%
17.2%
19.6%
22.6%
25.8%
28.8%
33.0%
36.9%
41.3%
44.8%
50.0%
51.8%
57.1%
60.0%

Low Port
1.4%
1.6%
2.1%
2.2%
2.5%
3.7%
3.7%
3.8%
5.7%
6.1%
7.3%
8.7%
10.4%
12.5%
14.2%
17.2%
19.5%
22.6%
26.0%
30.4%
34.9%
39.2%
43.5%
48.3%
52.8%
59.5%
64.5%

All of those are -3 to +10 with 1/2 point increments.
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Re: Calculating Championship Odds Based on SRS 

Post#16 » by ElGee » Wed Oct 8, 2014 5:18 am

So I've finally incorporated what I always considered to be the elephant in the room with this model, which is essentially salary. (Although ego plays a part.)

In the previous model, every player had the same odds of being on the same team. In other words, it assumed that the likelihood that a superstar landed on a +8 team was the same likelihood that a +1 player would land on such a team. (This was done for simplicity.) In reality, this is not the case...I think. I did not have the time to use any real salary data, and perhaps won't be too confident until I do so, but I changed the model to examine what would happen if the odds became increasingly less likely that the better a player become, the lower his odds of a playing on a good team would become.

To put in perspective the adjustment I basically "made up" without having the official salary data, the odds of being on a positive SRS team are about 50%. I shifted those all the way up to 65% for weak players and all the way down to 35% for elite players; ultimately, at the edges, I made it 2x less likely than the average and over 3x less likely than a mediocre player to land on a great team.

The actual use-cases for this kind of adjustment are as follows: Imagine a player who thinks he THE MAN and also clearly commands a max salary on the open market. The odds of this player landing on an elite team in free agency are very small, and in fact, only Wilt (69), Moses (83) and LeBron (11) exist as counterexamples. Players can be traded, but rarely are trades so lopsided (and involving a max-contract player!) that the team landing the superstar would be a title contender without him. Finally, teams can land players through the draft, and while occasionally a super-elite young player might develop on a great team (e.g. 98 Duncan), there are still forces that prevent this happening (namely the lottery).

All told, whether I have the distribution odds correct, here are the results for a "normal portability" player with full health:

9 44.0%
8.5 38.7%
8 33.8%
7.5 29.5%
7 25.6%
6.5 22.1%
6 19.1%
5.5 16.6%
5 14.6%
4.5 13.0%
4 11.9%
3.5 11.2%
3 11.0%
2.5 10.1%
2 8.7%
1.5 7.5%
1 6.3%
0.5 5.3%
0 4.4%
-0.5 3.6%
-1 2.9%
-1.5 2.3%
-2 1.8%
-2.5 1.5%
-3 1.2%

Portability
Adjusting for portability can be thought of as a +/- 1% adjustment up to about +1 players, +/- 2% up to about +4 players, and up to +/- 3% as players approach +9.

Health
Adjusting for health can be though of as ~50% value lost if a player plays ~10% of the season and still plays in the playoffs. This drops to ~30% value loss at 40% of a full season played, and over 50% loses no more than 20% value typically. 80% of the season played carries ~90% of a players value.

Comparing Lists
So now I have a career odds calculator that takes into things that might cause on uneven distribution of odds to land on certain teams, and another that assumes all players have the same odds of just randomly plopping down on a team, no matter how good. What does that do to career value?

The "salary" list now becomes incredibly longevity heavy. The following players moved up the most in my top 50:
Allen (+12 spots)
Parish (+11)
Havlicek (+11)
Hayes (+10)
Kidd (+8)
Stockton (+8)
Miller (+7)

These are longevity-driven players, all without elite peaks (I'm not sure any of those peaks are in my top-50.) On the other hand, all the high-peak, low-longevity players dropped:
Paul (-16)
Frazier (-15)
Mourning (-11)
McGrady (-11)
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Re: Calculating Championship Odds Based on SRS 

Post#17 » by colts18 » Fri Oct 10, 2014 4:56 am

Elgee, do you have a career top 50 list that you can post?
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Re: Calculating Championship Odds Based on SRS 

Post#18 » by ElGee » Fri Oct 10, 2014 12:52 pm

colts18 wrote:Elgee, do you have a career top 50 list that you can post?


Using which model?
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Re: Calculating Championship Odds Based on SRS 

Post#19 » by colts18 » Fri Oct 10, 2014 3:26 pm

ElGee wrote:
colts18 wrote:Elgee, do you have a career top 50 list that you can post?


Using which model?

The new one. Or the old one if you still have it
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Re: Calculating Championship Odds Based on SRS 

Post#20 » by RSCD3_ » Fri Oct 10, 2014 8:26 pm

colts18 wrote:
ElGee wrote:
colts18 wrote:Elgee, do you have a career top 50 list that you can post?


Using which model?

The new one. Or the old one if you still have it


Also would like to see it


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