The unfair advantage

Some things in this life are just not fair. In my last post I referred to one of those things in the following paragraph:

“Value in basketball terms for a player to me can be easily defined in terms of Wins Produced for the team and we know those are highly correlated to point differential. By that logic, in the simplest terms the MVP must be the player that has generated the most Wins or point differential for his team. Now there are some additional factors to consider. Where you play your homegames is important (i.e. the Jazz and Nuggets players are teeing off from the kiddie tee and I’ll probably expand on this in the future) .”

Now before you get all outraged at me for hating on the Jazz and Nuggets, let me explain.

Baby Patton Oswalt demands satisfaction

This all goes back to my previous post on Homecourt advantage in the NBA (which you can read here). The basic equation goes something like this:

Probability of Home team winning a game (Win %)

= (Projected Wins Home Team-Projected Wins Road Team)/82 +.606

=Win %: (Proj. Home Team Win% – Proj. Road Team Win%) +HCA(.606)

This is the simple equation I came up with for the home team winning  a single game (see here for detail). The base assumption being that based on the data set (all regular season games from 1999 thru 2008  ) the home team wins 60.6% of time) and  this was good and worked fairly well. As I got older and wiser (or at least more creaky), I then decided to add some more factors in:

  • Add in the effect of rest days and back to backs.
  • Add in the effect of altitude
  • Use a more recent data set.

I downloaded every game for the last five years ( see here ). And I went about adding the rest days and altitude. I did that as follows:

  • For rest days, I chose three levels:
    • 0 for back to backs
    • 1 for day of rest between games
    • 2 for >2 days of rest
  • For Altitude, I also chose three levels:
    • Zero to low elevation (430′ or below): Boston, LA, Memphis, Miami, New Orleans, Sacramento,New York City,Orlando,Dallas,New Jersey,Toronto,Houston,Seattle(gone but not forgotten),Portland,Golden State and Washington (hi Ted!)
    • Some elevation (430′-1117′): Charlotte (Jordan with just some elevation seems wrong somehow), Milwaukee, Chicago, Cleveland, Atlanta, Indiana, Detroit, San Antonio, Phoenix, Minnesota
    • Nosebleed Country (5300-9400′): Denver and Utah

I did some maths (which if you want to read just follow the link already) and figured the homecourt advantage in each scenario over playing at a neutral site. I then put that in a pretty table like so:

In summary, both, altitude and rest days affect the Homecourt advantage (HCA) and they interact with one another. Average HCA is at 59.9%.  Altitude is directly proportional to HCA . Rest days are a little stranger.  Altitude directly interacts with rest. Denver and Utah kill teams at home if they have a rest edge but they get killed themselves if the other team is coming in with at least a two day rest edge.

So how does all this lead to me claiming that Utah and Denver players are playing with nine foot rims? Let’s illustrate. If I:

  • Grab last year’s NBA schedule
  • Work out scenarios for each game
  • Assume all teams are equal in talent (i.e send in the clones)
  • And Simulate it!

I get:

So if I assume all teams are equal,  Utah and Denver both get a 10% boost in winning percentage when they play at home. This is good for four extra wins a season versus the average (and about 6.2 Wins against poor Golden State last year). It’s really not a level playing field.

Unfair advantage is Unfair!

But there is a dark side to this advantage. It’s effect in amplified during the regular season and a Lot of it goes away once the playoffs begin. So if you’re looking at a playoff series between two 55 win teams and one of them is Utah or Denver and the other is the Lakers? It’s a very likely that the Jazz and Nuggets are significantly overrated and the Lakers are about to crush their hopes (yet again).

Overrated is Overrated

Oh and a new podcast is up.


  1. emceef
    December 29

    This doesn’t actually help explain any DEN/UT/ATL playoff problems.

    In a playoff game, both teams are coming off the same amount of rest (They just played each other in the last game of the series), and that’s almost always 2 days or more.

    So it seems that the relevant stat for the playoffs would be the difference between the teams when they both have two or more days rest. And according to your chart, the high elevation teams would have an above-average advantage in home games under that scenario, winning 77.8% of the games, when coastal teams should win just 59.7% of home games.

  2. Shawn Ryan
    December 29

    Hmm.. so would you say that for a high minute/usage players on these teams (e.g. Melo or D Will) that they may be getting a Wins Produced bump from this affect? For Melo:

    36.4MP(career) / 240 team min * 4.0 = 0.61 extra wins

  3. Shawn Ryan
    December 29

    Actually, the above calculation fails to account for missed games, so Melo’s share of the 4 wins would be exaggerated a bit. Knock off another 10% and we should be there.

    • December 29

      Exactly. By nature, the Utah and Denver players are overrated (same as their team about 5%). Conversely other players are underrated.

  4. December 29

    Prefacing this with small sample size and injury. Boozer and Jefferson look to be having a hit in the AdjP48 close to what you are saying. Of course two players over 30 games is not proof. Just cool for it to line up :)

    • December 29

      Are you saying two players is not enough evidence to speak conclusively?

  5. Guy
    December 29

    Interesting analysis. Two thoughts:

    1) your current method is slightly understating the high altitude HFA by using the team’s season stats to predict the outcome of each game. Half of UT’s and DEN’s statistics were accumulated at home, and are thus inflated by the very HFA you are trying to measure. So if you had a stadium-neutral measure of each team’s talent (which would be a bit lower), the estimate of HFA would be even larger.

    2) This doesn’t necessarily confer an advantage on these teams. It’s possible that descending from high altitude takes a toll on them when they go on the road. So maybe this exaggerates their HFA, but has little overall effect on their record. There is some evidence that the CO Rockies in baseball, who tend to have a high HFA, struggle on the road (not sure how strong the evidence is). You might want to look at how UT and DEN perform in their first couple of games of each road trip, especially with few days of rest, to see if they underperform expectations.

    • December 29

      Good point. It is a bigger advantage than stated. I’ll very probably redo this before the playoffs.

      As for the second one, that’s kind of implied. The team is really not as good as they show at home.

    • EvanZ
      December 29

      As someone who has taken physiology twice and climbed Mt. Kiliminjaro once, I would be very surprised to learn there are any ill effects of descending from altitude. But I suppose any change could affect a shot that is adapted to a particular condition, even if the “change” is that you gain a bit of strength or quickness coming down off the mountain, so to speak.

      • Guy
        December 30

        I think EvanZ is probably right. The high-altitude players should not be hurt at low altitude, and may even have a slight edge there as well (like runners who train at high altitudes). The baseball example I mention is not analogous, because altitude changes the game of baseball — curveballs don’t curve, much for example. So in that sport, adapting to different conditions on the road could plausibly put CO players at a disadvantage. But it’s hard to see why that would be true in basketball.

        The fact that high altitude teams have the biggest edge following days of rest, and when opponent has few days of rest and thus must have arrived at altitude only a short time before game time, seems to confirm this is mainly a function of adapting to altitude. I bet if you look at high-altitude team wins over the course of a homestand, you will find they do better after the first couple of games (even if you control for days of rest).

        What this means for visiting teams headed for CO or DEN is that you should arrange to fly there immediately after your preceding game, and get your players to altitude as many days/hours prior to game time as you possibly can. I wonder if any teams do that?

  6. Fred Bush
    December 29

    Guy: it looks like the jazz and the nuggets are basically right on the league average for road wins. Manipulating days of rest creates sample size issues and is inconclusive. It seems almost impossible to tell whether they’re average teams that are very good at home, or good teams that are better at home and worse on the road.

  7. guy
    December 29

    Fred: I agree it would be very hard to disentangle. Only thing I can think of is looking at players who also played on other teams, and see if their productivity in DEN/UT is higher than when playing elsewhere.

  8. Tom
    December 30

    Maybe you could look at players who use those high altitude tents when they sleep and see how their WP correlates with the UTA/DEN players. I’m guessing the theory is that the UTA/DEN players are more used to the lower pressure environment (maybe you have a different causation in mind). I read about Arenas doing it, not sure who else does:

  9. August 9

    What NBA teams would suffer the most from back-to-back-to-back games?…

    After the season ended the answer to this was surprising – Utah and Denver! Utah and Denver are at a much higher altitude than other NBA teams. The offset of this is that teams with a back to back heading into Denver and Utah get crushed…usually. In …

  10. […] Well because of its isolation Denver. Denver is often the last game on road trips. And usually the nuggets are in Denver waiting for teams. Not to mention the west coast back to backs. The Airport being 30 minutes away, time changes, opposing teams getting to the hotel at 4 in the morning. Its not rocket science. Since 03-04 the Nuggets are winning 75% of their home games and 45% of their road games. The gap alone should tell you all you need to know. Getting used to the altitude is key. That's why having off days in Denver is so important. And opposing teams rarely have off days in Denver but the Nuggets often have off days in Denver. Altitude is a factor. There's a number of articles that dive deeper into the stats. But I don't feel like looking for all of them. So I will just share this one with you The unfair advantage | Arturo's Silly Little Stats […]

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