Let me elaborate, as I think my point wasn't clear the first time. I'm not trying to argue that the Spurs' playoff strength estimate should be 10.2. My point is that summing xRAPM gives systematically higher values than SRS, at least for playoff teams, and the two cannot be treated as equivalent. The values we are seeing from summing xRAPM come in higher than SRS values should come in, and this isn't explained simply by the change in minutes. To illustrate this, I calculated the sum of xRAPM values using the exact minute weightings we had over this past season, and found that the xRAPM values summed to a couple points higher than the actual SRS of that season, at least for the two teams I checked. If the sum of minute-weighted xRAPM could be treated as an SRS estimate, this should've been equal, or pretty close to it.colts18 wrote:You ran the projection and got +10.2 for the Spurs because though are actual minutes. I'm using playoff strength. The Spurs aren't playing many scrubs in the playoffs so their strength is higher than +10.2. Plus J.E. already said that his xRAPM takes into account the leading by X effect.ryannow wrote: The numbers still just don't add up. I ran the exact same equation, but with the actual total minutes played for this year's Spurs, and I came out with a value of 10.2. Did it for the Warriors and got 7.2. Both of those are more than 2 points higher than the team's actual SRS in that time period. It makes sense why this would happen: if you add one +4 player to a team at 0, you can expect them to go to around +4, but that doesn't mean a second one would lift the team to +8, or a third one to +12. That's what the "effect of being up x" term is attempting to capture; it's harder to take a team that's already very efficient and boost it by n points than it is to take an inefficient team and boost it by n points. As a result, you can take +10 worth of players, and end up with a +8 team, although I'm not sure exactly what the shape of this curve is in J.E.'s model.
I recognize that it takes into account the leading by X effect, and in fact I believe that's the reason why this occurs. The difference between +0 and +1 is less than the difference between +7 and +8, and equivalently the difference between +0 and +8 is more than 8 times the difference between +0 and +1. From my calculations before, it seems it's more like it takes 10 times the amount of improvement to go from 0 to +8 as it does to go from 0 to +1. To the best of my understanding, that means if you have a team at +8, xRAPM will have the sum of your team's parts as about 10 times as far above average as a +1 team.
If we want to convert from sum of xRAPM to SRS, then, we'd need to apply the inverse of that function. We'd need to recognize that when xRAPM says the Spurs are 10 times farther above average than a +1 team is, that doesn't mean they're a +10 SRS team, it means they're +8 SRS. This function scales the values to reasonable proportions.
I don't know the exact shape of this function, and it seems it would have to be empirically determined rather than being inferred from the formula, since it depends to a degree on whether a team built their leads early in the game or late, but some normalization function is necessary. Without doing it, you end up with the Warriors finishing 6th in the conference, losing their starting C who ranks as one of their best players, distributing his minutes to significantly lesser players on their bench, and, due to a few extra minutes for their starters and fewer for their reserves, more than doubling their SRS to the point that they are projected to have a higher SRS in the playoffs than every team in NBA history in any season, yet they're still projected to only rank third in their conference. GSW's starters and one-big lineups have been good enough that I could buy a +7 or +8 estimate if I knew xRAPM was high on their players, but there's no way forecasting a Bogut-less GSW at +11.9 SRS passes the laugh test, playoff rotations or not.
Gotcha. That makes sense.I used the pythagorean win% from DSmok1's posts for both teams. Then I used the log 5 method to generate an expected win%. Log 5 formula:
(home win%/Home loss%)/(home win%/home loss%+road win%/road loss%)