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)

-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%

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

(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