## Thursday, June 21, 2012

### Homecourt and rest time advantage

In a previous post, I looked at the true impact of homecourt advantage in the NBA, for the league in general and for each individual team. The model was simple, only considering whether the game was at home or away.

The main take-away was that playing at home bumped your probability of winning by almost 20 percentage points, from 40% to 60%. Quite a significant jump, although not every team observed the same jump.

I did however feel that the model was a little over-simplistic in ignoring another phenomenon which could impact a team's performance: rest time between games. Especially over the 2011-2012 condensed season with certain teams playing back-to-back-to-back games, one can definitely wonder how rest days come into play. If a team is playing on the road, can the fact that they have had three days of rest as opposed to their opponents back-to-back games mitigate the opponent's home court advantage?

The data and methodology are almost identical to the post I mentioned earlier: I looked at all 2009-201 and 2010-2011 games, and for each match-up looked at which team played at home and how many days of rest each team had.

Since we are now looking at multiple variables instead of just the homecourt impact, I will only provide the breakdown of results for the league in general, providing them for each team would just take up too much space.

Impact of rest days

The following table provides the victory probability based on where the game is played and the number of rest days for both teams.

Team A at home Rest days (Team A) Rest days (Team B) Win probability
Yes 1 1 59.1%
No 1 1 40.9%
Yes 2 1 65.2%
No 2 1 47.4%
Yes 3+ 1 62.6%
No 3+ 1 44.6%
Yes 1 2 52.6%
No 1 2 34.8%
Yes 2 2 59.1%
No 2 2 40.9%
Yes 3+ 2 56.4%
No 3+ 2 38.3%
Yes 1 3+ 55.4%
No 1 3+ 37.4%
Yes 2 3+ 61.7%
No 2 3+ 43.6%
Yes 3+ 3+ 59.1%
No 3+ 3+ 40.9%

Some interesting highlights are that:
• independently of the number of rest days each team has had the difference homecourt advantage is always around 17-18%
• the homecourt effect is much more predominant than the number of rest days: even in the best case scenario, the win probability on the road is 47.4%, so essentially a +7% percentage uplift due to rest days, as opposed to the +20% we saw in the previous post for the homecourt advantage impact.
• it turns out that resting 2 days improves probability of victory compared to one day only, and three or more days is also more beneficial than one day only, two days is actually preferable to 3 or more days. This is also a debate that comes around often especially during playoff time, where one team comes out of a game 7 to meet a team that finished a sweep over a week before. Is too much rest a bad thing? From this data it does appear that 2 days provides the optimal balance between hitting your stride while you're hot and resting your sore legs.

Team's optimal rest days

What is true for the league isn't necessarily true for individual teams. I wanted to check if all teams preferred to rest 2 days instead of 1 or 3+ days. Were younger teams eager to have back-to-back games? Were older teams dreadful of tight schedules?

Team Significant Optimal rest days
NBA Yes 2
ATL Yes 2
BOS No 3
CHA Yes 2
CHI Yes 2
CLE No 2
DAL No 3
DEN Yes 3
DET Yes 3
GSW Yes 1
HOU No 2
IND Yes 2
LAC Yes 2
LAL Yes 1
MEM Yes 2
MIA No 2
MIL Yes 1
MIN Yes 1
NJN Yes 2
NOH Yes 3
NYK No 3
OKC No 3
ORL No 2
PHI No 2
PHO Yes 3
POR Yes 1
SAC No 1
SAS No 2
TOR Yes 3
UTA No 3
WAS Yes 3

Upon close inspection there does not seem to be any strong correlation between the team's age and the preferred number of rest days. Sure Boston is an old team preferring over three days and Golden State is one of the youngest team performing best on back-to-back games, but the Lakers are an old team also preferring back-to-back teams and the Wizards are a young team with best odds after 3+ days of rest.

To conclude, while rest days do influence performance in different ways for different teams, homecourt advantage remains the most impactful variable for outcome prediction of a game.