I've dug a little into an effect that Matthew Goldman and Justin M. Rao first discovered and talked about in a presentation at SSAC'13. You can watch the video of the presentation here
(the for this analysis relevant part starts at ~minute 16, but since it's an awesome presentation there's no harm in watching all of it) and you can find the full paper here
The part I dug further into is, specifically
We also find a strong motivating effect of losing—the trailing teams displays an overall boost in efficiency[..]
If the above quote holds true then we should see, e.g., higher PPP of an attacking unit that's down 10, compared to when the game is tied (assuming all players are average).
To try to quantify how large the effect is I put in additional binary variables into my RAPM framework, one variable for being up a certain amount of points before each possession started. Those variables run from 'down 57' to 'up 57'.
Thanks to the RAPM framework we're controlling for player quality and can then take a look at how much the offense (or opponent defense) is being influenced by being up X (down -X)
I find the same effect as Matthew Goldman and Justin M. Rao did, and, according my results, it's huge and most likely linear. The following chart displays the results
According to this, an away team that is down 10 points is expected to score ~3.5 points more PPP than if it were tied. Inversely, if they were up
10 they would be expected to score ~3.5 points less
than if they were tied. Down 20 you're expected to score ~6.2 PPP more than 'normal' - that's like replacing an average offensive player with LeBron
- With adjustment built in, a 5 man unit that's down 10 is required to score more than average points to get an average rating in RAPM. This leads to another side effect: Assuming you have two teams A and B playing a third team C. Both Team A and Team B win by 15 against Team C. Team A jumps out to an early 15 point lead and holds it the entire game, while Team B is tied until the last quarter and outscores Team C by 15 in the last 5 minutes. With the adjustment Team A will get more 'credit' for their 15-point win
- It's probably a good idea to check whether giving less weight to those 'garbage time' possessions is also a good idea. That's something Mark Cuban is a fan of
- This analysis can't tell us whether a) defenses start to clamp down when down (1) and loosen up when up (2), or b) offenses start to fool around (become less efficient) when up (3) and give more effort when down (4). We don't know because the variables for (1)+(3) and (2)+(4) are identical in the regression
- You should really watch the above video as Matt provides some interesting hypotheses on why we observe this effect