RealGM

Mike G wrote:SRS = MoV + SoS

SoS does not include HCA.

SideshowBob wrote:Would there be any advantage of using efficiency differential in place of MOV?

I’m going to use football as a starting point. Imagine we want to know the strength (power rating) of every NFL team. The reason we want to know such a thing is so that we can predict the result when two teams face each other. To do this, we first assume that each team can be described by a single rating. This sounds obvious, but what it means is that regardless of the matchup, we can always use the same rating for each team. This is the assumption of linearity. An alternative non-linear assumption would be that teams have different ratings versus different teams. It’s not that the latter assumption is technically wrong; however, given the limited amount of data (i.e. games) in a single season, it is not a practical solution. Therefore, we stick with the linear assumption and assume that each team has a single rating. Given our assumption, let’s say that San Francisco is hosting Arizona and we want to predict the outcome:

MOV = HFA + SF - ARI = 3.0 + 5.0 - 3.5 = 4.5

This equation says the margin of victory (MOV) is equal to the home field advantage (usually around 3 pts) + San Francisco’s rating (which is close to roughly 5 at the time I’m writing this) minus Arizona’s current rating (roughly -3.5). In this case, the equation tells us that the predicted outcome is SF winning by 4.5 points.

But how do we get those ratings? Basically, we reverse the process mathematically and use the actual results from previous games. For example, in the recent “Harbowl”, Baltimore beat SF 16-6:

10 = HFA + BAL - SF

See, now we know the MOV from that game, but we don’t know any of the three values. We can set up an equation like this for every game that has been played. Once we’ve done that, we then use linear regression to calculate for us what the ratings were that most closely replicate the data for each game. Of course, there is a lot of error involved. It’s obvious that for each game, the results are not going to go exactly according to the ratings. Sometimes, the higher rated team loses, after all. However, on average, the weights/ratings determined from the regression give us the lowest error out of all the possible linear weights we could imagine. This is often called BLUE (best linear unbiased estimate).

mysticbb wrote:No. The point differential gives a better prediction. Which is completely understandble, because a team plays usually as their usual pace. The efficiency differential would be just adjusting that to a pace of 100. Well, it is more likely that a team with pace 92 plays the next game at that pace than playing now the upcoming games at a pace 100.

And I think you have the SOS backwards. The average SRS of the opponents for the last 6 games was -1.54. The Heat had a MOV of 17.67, that makes a SRS of 16.13 without the adjustment for HCA during those 6 games. Now, the HCA would push that to 18.26, given the fact that they played 5 on the road and only one at home. Very impressive stretch.