A few weeks ago, I came up with the Championship Equation which set out to establish the necessary (but not sufficient) conditions for building a championship team. The intent was to have an edge in quickly identifying and separating the title favorites, the contenders and the pretenders. I then revised it based on reader feedback. I then revised it again based on some more reader comments (go here for the Basics). The equation now reads as follows.
To win or contend for a championship a team must:
- Win 52 or more games (Houston in 1995 is an aberration that is explained below)
- Have two star points (either >2 Stars, > Star + Superstar or > 2 Superstars) in your Playoff Top 6. A star is >.200 WP48 Player, a Superstar
- Have at least one .140 WP48 player who plays PF or Center in your Playoff Top 6 (credit to some dude and we’ll call it the Suns Corollary)
- A superstar puts you in the conversation if you can make it into the playoffs and surround him with talent (i.e no duds) in the top 6 (credit to Neal Frazier and we’ll call it the Hakeem Factor). There are multiple paths here:
- Houston did this in 1994. They did not quite have a superstar (Hakeem clocked in at .280). However they had 4 other players in their playoff rotation come in between .128 and .159 (Thorpe,Horry,Kenny Smith and Sam Cassell). So it’s possible to win if your superstar is a little off if you have 4 other guys who can step up and you get some ridiculous three point shots and the best player in the league decides to retire in his prime. We’ll call this the Impossible Dream Scenario.
- If a team with 1 superstar on your roster finds a superstar in the draft that can yield immediate results. Just don’t hold your breath for this happening. Well call this the The Magical Legendary Exception.
- Houston in 1995. They only won 47 games in the regular season but they went off and got another star (Drexler) to complement Hakeem at mid-season. So you can trade yourself into contention (but it’s not very likely unless Chris Wallace or Kevin McHale is prominently involved). We’ll call this The Trade exemption.
- Not have Bad players (<-.01WP48) in the playoff rotation(top 6 in minutes played). The rule of thumb here is that you need two star points for every playoff sink hole but it makes you a marginal contender. We’ll call this the Mr. Eva Longoria Rule.
- Players can step it up in the playoffs and they can also step it down. Star/Superstar depth is really important. The last 4 champions have featured at least 4 guys at greater than >.150 WP48 in the regular season and it not always the same people who come thru (Posey for the Celts in 2008 is a good example). The one superstar approach is a much riskier proposition it’s always better to have the depth than to not have it and regret it (see Posey and the Celts in 2009). We’ll call this Posey-Horry’s Law for identifying favorites.
So with this set of conditions in hand and a good projection model for player performance in 2011, we should be able to identify the favorites, contenders and pretenders.
Projecting Stars and Superstars for 2011
Here I’m going to use my rookie model (Boo Boo) and my player performance model to project the worst, nominal and best case for each player based on projected performance and the standard predicted error. For rookies the error is std at .065 WP48 (with one notable exception which I’ll explain). For veterans the error will vary by position and age. Each player will get star points as follows:
- 1.2 if they qualify as a superstar in the nominal scenario.
- .4 if they qualify as a superstar in the high or low scenario
- .6 if they qualify as a star in the nominal scenario.
- .2 if they qualify as a star in the high or low scenario
To explain visually it looks like this:
Good Big men scoring will be done the same as star scoring (if they qualify as a >.140 WP48 big in nominal .6 of a point, .2 if they qualify in high/low).
My justification for the scoring?
Normal Distribution is normal
Position adjustments will be done based on the average for the last three years and the players average position in 2010. The projection looks as follows:
Looks nicer doesn't it?
137 players and only five guaranteed superstars and 22 stars. Only three players put you in contention immediately (Love,Howard and Camby qualifying as superstars and good bigs). Who’s my one notable exception? Demarcus Cousins gets a boost from my Lee/Noah theory (which I’ll explain in a future post).
As for what it means for the individual teams? Stay tuned for part 2 tomorrow.
Bwahahahahaha
Note: I initially posted this at 1:30 am with no proofing (BAD IDEA!!!). I went back and fixed some things and some of the scoring.I think it looks much nicer now
What I did not do last night (image courtesy of xkcd.com)
Arturo's Silly Little Stats v2.0 
EntityAbyss
10/14/2010
Why don’t you believe that Chris Paul will have the best per-minute production? I don’t think he has been slowed, and he’s still young. Also, 2 years ago, he posted the highest wins produced in the league (also higher than anything Lebron has produced (by a little margin though)). I figured he’d be the best player this year. Why not?
arturogalletti
10/14/2010
EA,
Remember it’s not me it’s the model. He’s third and the difference is tiny. The model does penalize him somewhat for his injury and his age and position. I also expect Lebron and Camby’s WP48 numbers to go up (think 96 Bulls, and 08 Celts). The fact that I just typed that about the 2010 Blazers is really,really freaky.
neal frazier
10/14/2010
I think you meant ‘1/3 of a point for each scenario they qualify as a star’ rather than as a superstar.
Curious about what the likelyhood is that the geezers, Kidd, Nash, and Camby, will have their wheels come completely off – their low end projections all seem awfully high.
arturogalletti
10/14/2010
Neal,
Changed the scoring somewhat now to look more like a normal distribution and clarified the explanation (I would have done last night but it was late 🙂 ).
I’m projecting low and high based on the error by position and age. Older players like them did not have their wheels come completely off in the last five years (I wrote about this before search for age model).
todd2
10/14/2010
Off topic, I know. Pierce, Allen and Rondo played upward of 40 minutes last night in a squeaker vs NYK. And the Knicks had 42 fta’s. What gives?
arturogalletti
10/14/2010
The Knicks are better than last year but besides that who knows what Doc is thinking.
Evanz
10/14/2010
I don’t know if it will make a huge difference, but I don’t think the minutes allocation for Wright, Amundson, and Williams are correct. Dorell is a starter and will probably get the 4th most minutes (Biedrins can’t seem to stay out of foul trouble). Williams and Amundson will likely be the first 2 off the bench.
arturogalletti
10/14/2010
It’s the automated version of the Minute allocation. I need to review that in detail prior to final projection.
Mike
10/14/2010
One difficult thing to do with a model like this is to predict the minute allocation and positions. This is most difficult to predict for players who switch teams. I suspect David Lee’s position to be between 4 and 4.5 this year instead of his solid 5 while he was in NY. This makes Lee’s current projections from the model more pessimistic. There are probably very few examples of this happening over the years however. Great job Arturo, can’t wait for the team projections tomorrow.
arturogalletti
10/14/2010
The exact position adjustment is only really important for the individual WP48. The approximate is good enough for estimating total minutes (I hope)
Fred Bush
10/14/2010
Ever since Tony’s been Mr. Longoria he’s been posting positive WP stats.
BTW, all of these conditions are starting to make me very dubious about the equation/overfit. “Your team’s nickname must not be an animal. Exception: The ‘Rodman had a cow’ rule.”
Given how much variance there is in a 7-game series, is it worth distinguishing between championship teams and runners-up? Do all of these rules fit the runners-up as well as the finalists?
arturogalletti
10/14/2010
The conditions mostly relate to things you can do to improve your roster in-season or through the draft. The basic three are star points, 52 wins and a decent big.
I’ll do a full thing on runner ups during the season.
jglanton
10/14/2010
Blake Griffin is not going to stay in that gray zone!
arturogalletti
10/14/2010
Blake will be awesome. I just don’t think he’ll be superstar level immediately. We’ll know fairly quickly though. If the Clippers are even close to .500 after ten games he’s a bonafide superstar.
Fred Bush
10/14/2010
I’ll buy “win 52 games”, since that should get you an objectively easier run through the playoffs. I’ll also buy ‘only the top 6 guys who get playing time are important in the playoffs’, since you’ve presented solid evidence.
But do the rest of these really matter in particular for the playoffs, or are they just artifacts? In order to win 52 games+ you generally need to have these things already. For instance, all 52+ game winners over the last five years had a .140+ big man starter, so it doesn’t seem to be telling us much new.
arturogalletti
10/14/2010
Fred,
The key finding is related to the Top 6 guys. You can have a team with one superstar and a bunch of decent guys that does extremely well in the regular season. Come playoff time you need to have a concentration of win production in your top 6 and you need at least decent production from the 4/5 or you’re out of luck. I probably do need to work the evidence here more thoroughly but there an extremely good case for the top three being necessary conditions. BTW you can have 2 superstars and a decent big and still wash out if the rest of the team is horrible (94 & 95 Spurs come to mind).
Raspu10
10/14/2010
Off topic, Arturo, but there may be a bug in the Playmaker stat when you generalize it to all players. Players who gen more possessions than they spend – rebounders – will show negative points created per possession.
arturogalletti
10/14/2010
I saw this too when I did it for all players.
some dude
10/14/2010
Fred, the purpose of the >.140 big is to eliminate the 52 win teams with a superstar that isn’t a contender (Suns this season, I believe). The Suns will be an abysmal rebounding team and I simply don’t believe they are a contender, but without that addendum the model would say they are. Arturo discovered that without a >.140 big, you’re not a contender so we could eliminate them.
I still think Kobe will land closer to the higher end of the model because I think the injury woes that plagued him will not be an issue (crosses fingers). But I don’t blame the model since he was hurt and the model is using that since it can’t know (and injury probability should be a part of it).
Really wish Pau would end up higher than Lamar. Some day the system will fix this atrocity.
Fred Bush
10/14/2010
looking over the last few years it seems like 1/4 of the 52-win teams of late do it without 2 star points. So that might be a reasonable criterion. The rule about bigs just doesn’t seem to exclude enough teams to be useful. If only 10% of 52-win teams, say, have 2 star points and no quality big man, it could easily be random chance that they’ve failed to win a title.
I guess my basic issue is that you’re using player metrics as well as an overall wins metric, and that’s not very elegant. A lot of the player stats are subsumed in the wins stat. It’s not very obvious to me why 52 wins means anything, except through its fruits, playoff seeding. Is 52 wins really more useful than something like “don’t be seeded worse than 3rd in your conference”?
Fred Bush
10/14/2010
Some dude: the problem is that it appears to me that the vast majority of 52-win teams already have a big man with >=.140 (all of them in the last 5 years do). So we run across a problem that the set of teams that we’re considering is quite small. If it’s small enough, (<=10% or so) then it can be hard to reject it being chance that they're not winning titles.
There's also the factor that teams with 52+ wins and no quality big are also probably winning fewer games in the regular season than other 52+-win teams, and thus getting worse playoff seeding. But then the issue to look at is the playoff seeding, IMO, not the manpower.
some dude
10/14/2010
If 10% of teams over the past 35 years that win 52+ have not won a title or been a contender, then I think that’s a pretty big number considering how many that would be and would yield significant results.
The point in Arturo’s model here is to allocate percentages to win a title. Anything that can rule out a team completely matters. If without this addendum the Suns would be a 20% probability to win the title, then it matters a lot because without it that 20% is allocated among the real contenders.
Furthermore, I highly doubt that it’s just a coincidence those teams haven’t won a title. Oliver has shown what 4 factors matter most and rebounding is a big one. The Suns were a very bad rebounding team last year with the potential to be the worst of all time this year. I like others believe WP48 overrates individual rebounding, but make no mistake, team rebounding % isn’t overrated. And since big men are boosted most by rebounding % in WP48, if they don’t have any .140 bigs, it can be assumed they don’t rebound well as a team.
I would look at team rebounding % moreso than individual WP48. I’m fairly certain that if you looked at defensive rebounding % of all title winners, there’s a threshold that is far more significant than 10% of 52+ win teams. WP48 implies this.
Of course, it is often said the game is played “inside-out” and so maybe Arturo is more accurate by looking at individual WP48 than just rebounding % as a team (projected).
Either way, there has never been a team that has won a title without a significantly above average big man and good defensive rebounding team and for good reason. This can be used to knock out what would otherwise be considered a contender by a lesser model, thus is it very useful.
being as accurate as possible is paramount, even if it means eliminating 1 team every 2 seasons.
Chicago Tim
10/15/2010
Am I missing something? Where is Luol Deng for the Bulls?
arturogalletti
10/15/2010
.194 is his high end projection so he misses the cut.
Chicago Tim
10/15/2010
So Taj Gibson has a higher projection than Luol Deng? Does this have something to do with Deng’s history of injuries? Uninjured, he seems like a better player than Gibson. Or does it have to do with Gibson being a power forward and Deng a small forward? Or both?
arturogalletti
10/15/2010
Taj is Younger so is projected to improve more. Deng has been inconsistent (and last year was off for him). Their projections are almost identical. Wait a bit and i’ll have all the projections up (it’s taking me longer than initially planned, dammed euros and unbalanced rosters)
Shawn Ryan
10/25/2010
-I know, zombie comment, but I was a bit behind on my blogs reading. Reading this made me wonder what you’re models are teaching you specifically about how injury history at a given point affects likelihood of being injured again and how much water the idea of an “injury prone”-ness holds.
I’ve always thought that there was probably a small correlation between past injuries, especially injuries to the knees, feet, ankles hands, elbows and back, but that mostly the idea of injury prone-ness was an artifact of a fooled by randomness effect. It seems like you may have developed evidence that would be pertinent to these assumptions, and it’s something that I’ve wondered about for years. Have you?
arturogalletti
10/25/2010
I haven’t done a definite study but I have found that there is significant correlation in minutes played. I’ve also found that Medicine is stretching a players productive prime. So there’s evidence that structural factors that contribute to injury exist. I think this is a future study, I just have to figure how to build the data set. If you look at something like football (which is higher stress I know) it just adds more credence to that idea. The problem is how to differentiate between common cause and special cause variation (one time injuries and recurring injuries that affect performance). Fascinating topic though and one I would commission a study if I were a gm or owner.