8 SECONDS LEFT: The ball bounces off the rim, and Bosh grabs it, surrounded by Kawhi Leonard, Manu Ginobili, and Danny Green. To measure a player's impact based on rebounds, I look at the percentage of contested rebounds they get per game, where contested rebound opportunities are defined by the amount of times a player and an opponent are within 3.5 feet of the ball. I do not look at uncontested because if there is no opponent they're battling than it's not really a measure of their rebounding skill. In this case, let us assume that Leonard, Ginobili, and Green are all within 3.5 feet (luckily they have computers and tracking stuff to figure out exactly where they are). An average player grabs only 26.88% percent of contested rebounds, and using the simple theory that a rebound is worth an extra possession, and that teams score roughly one point per possession, we can conclude that an average player, when presented with a contested rebound opportunity, provides about 0.2688 points per his team. Because Bosh grabbed that rebound, he contributed 1- 0.2688, or 0.7312, points above what an average player would get. Since the three Spurs failed to grab a rebound, they contributed 0.2688 each below what an average player would have gotten. Therefor, the PAA allocations for this play are: Chris Bosh: +0.7312 PAA; Danny Green, Manu Ginobili, and Kawhi Leonard: -0.2688 PAA.
5 SECONDS LEFT: Bosh passes the rebound to a wide open Ray Allen, who drains a catch and shoot three. Using the same logic as in the first paragraph, Bosh is credited with +0.277 PAA, and Ray Allen with 3-0.934, or +2.066 PAA.
So that's essentially PAA in a nutshell. As you can see, it is not nearly as complex as EPV. It doesn't track the value continuously, it doesn't account for other options available to player, and it doesn't account for the quality of the shot (guarded vs unguarded) or how good the pass was.
At the same time though, it does have several benefits over EPV. For one, it is fairly easy to calculate - I didn't need a supercomputer, all I used was Excel. Also, it allows me to view player's contributions in different categories, while EPV is (for the moment) only total. As far as the different categories go, PAA incorporates more aspects. For example, in both their Sloan presentation and their final paper, the team behind EPV never mentions rebounding, so I am unsure if/how they incorporate that. Also, while in their Sloan paper it seemed like they counted passes, I'm not sure that they do in their most recent paper. If you look closely, you'll see that the jumps in EPV by passing are not shaded to belong to any player's contributions. Although I may be mistaken, I think this is the case as you'll notice that in the Sloan paper Chris Paul was ranked by far and away the best player by EPV, while in the new one Kevin Durant and Dirk Nowitzki are the leaders of the pack by a good margin, and most of the top ten are shooters (Calderon, Lillard and Love round out the top five, Chris Paul isn't in the top ten). Again, I don't know exactly how they did it, so passes may be included in both and there might just be some small sample bias in the first paper. But if they're not counting for passes then that's a serious mistake in my opinion. Also, they have done nothing on the defensive side of the ball. PAA incorporates rim defense, and I have tried to ease in stat for steals which uses a linear combination of playing time and time with the ball to try to predict how often they're guarding opposing players. While the rim defense stat is fairly sturdy, I am less sure about the steals one.
In conclusion, EPV is definitely far better than PAA, although PAA is easier to handle and may present a more well rounded view of a player.