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Hi all.
With so much talk of how the Raptors' easy schedule is driving their success, and questions about whether they can sustain this, or whether it is fool's gold, I wanted to take a look at how exactly the team has performed, correcting for their opponents and home games, and extrapolating that over the entire season, game by game, and predicting a final record.
There are lots of different sites that do this to one degree or another, but most are black boxes for the most part, or do some but not all of what I am trying to do here. Hopefully this post can shed some light on the approaches commonly taken to adjust for strength of schedule, as well as lend some clarity to how much the record so far really means.
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*The following is a fairly wordy explanation of the approach. I'll put a more straightforward breakdown in the next section if this is too long for your tastes.
So, first, the methodology. The basic concept is to look at each game, take the opposition's average ORTG and DRTG, compare the Raptors' ORTG and DRTG in that game to those numbers, and determine an offensive and defensive performance for that game. For example, if the opposition has a 100 ORTG and 100 DRTG, and in the game against them the Raptors post a 110 ORTG and a 105 DRTG, they would have a +10 offensive performance and a -5 defensive performance, meaning a +5 overall performance.
Then you look at the average of all the games so far to determine a season-to-date performance (offensive and defensive). You can take that average performance, add it to the league average ORTG and DRTG, and you get an opposition-adjusted ORTG and DRTG, which can be used via a simple pythagorean win projection to predict the final record.
So that takes care of the opposition correction. Now what about home and away? League wide last year the home team on average performed 1.4 points per 100 possessions better on both offence and defence. So, to correct for a home-heavy schedule, all we do is give either the Raptors or the opposition a 1.4 point boost in ORTG and DRTG when calculating the game performance. So, to use the same example as before, say the 100 ORTG and 100 DRTG team is hosting the Raptors. In that case, the Raptors' expected performance is not 100 ORTG and 100 DRTG, it is 98.6 ORTG and 101.4 DRTG. So when they post an ORTG of 110 and a DRTG of 105, they are earning a +11.4 and +3.6 offensive and defensive performance for the game.
Now, the one other thing that bothers me about win projections with the pythagorean approach is that it assumes every team has a similar strength of schedule over the entire year. To correct for this (and to allow us a look at the upcoming schedule and which teams were are more or less likely to beat), we'll use a standard deviation approach.
If you look at the team's 14 games so far, you can extract an average value for offensive and defensive performance from the 14 data points. From the same data set, you can calculate the standard deviation for offensive and defensive performance as well. Assuming a normal distribution of performance throughout the year (a bell curve), you can find the probability of the team achieving a particular performance or better in a game.
So, then looking at any game, you take the expected performance of the Raptors based on the opponent (in our example, it was 98.6 ORTG, 101.4 DRTG, or a 2.8 point loss), apply the Raptor's average performance thus far in the year, and you get a predicted result for that game. If the Raptors' overall average performance is +5, then the predicted result would be a 2.2 point win (-2.8 expected performance + 5 average performance).
Then you determine how poorly or well the Raptors would need to play to get to a predicted tie game. So in this case, the Raptors would need to be 2.2 points below their average. Then all you need to do is divide that by the standard deviation of their performance to date, and use the normal distribution to determine the chances of exceeding that mark.
That yields the chances that the Raptors win that game. That translates directly to number of expected wins - a true toss up game would predict that the Raptors have a 50% chance to win, and would be worth 0.5 wins. An expected huge win (say against Philly) would show that the Raptors have a 90% chance to win (for example), and that would be worth 0.9 wins. Then you just add up the predicted number of wins for the entire season, or for any stretch, to get a predicted record in that time frame, with strength of schedule, home game, and opponent all accounted for.
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Here's a quick order of events to summarize:
Past games:
Opponent ORTG and DRTG for the season -> Expected opponent performance
Expected opponent performance +/- home court advantage -> Expected opponent performance adjusted
In-game Raptors ORTG and DRTG - Expected opponent performance adjusted (ORTG and DRTG) -> Raptors Game Performance for that game
Using all Raptors Game Performances gives a season-to-date average and standard deviation Raptors performance.
Future games:
Expected Opponent Performance Adjusted + Average Raptors Performance -> Expected Result
Expected Result - Tie Game Result -> Minimum Raptors performance required to win
Minimum Raptors Performance Required / Standard Deviation performance -> Chances to exceed minimum performance (i.e. chances of winning)
Chance to win = number of expected wins from that game
The sum of the expected wins gives the predicted record.
---
Anyway, that's the strategy.
Here are the Raptors' game by game performances so far.
Game | Offensive Performance | Defensive Performance | Overall Performance
vs ATL | +3.6 | -1.9 | +1.7
@ ORL | +6.8 | +2.4 | +9.2
@ MIA | +2.2 | -8.1 | -5.9
vs OKC | +3.3 | -3.4 | -0.1
@ BOS | +6.6 | -4.0 | +2.6
vs WAS | +6.7 | +12.3 | +19.0
vs PHI | +6.8 | +4.0 | +10.8
vs ORL | +0.9 | -3.0 | -2.1
vs CHI | -9.5 | +1.2 | -8.3
vs UTA | +15.1 | -0.1 | +15.0
vs MEM | +7.7 | +1.7 | +9.4
vs MIL | +25.0 | +9.0 | +34.0
@ CLE | +8.0 | +16.1 | +24.1
vs PHX | +0.4 | +1.6 | +2.0
And here's a detailed look at the PHX game, for reference.
PHX season ratings: 102.1 DRTG, 105.2 ORTG
PHX expected result due to road game: 103.5 DRTG, 103.8 ORTG
Ratings in game vs PHX: 103.9 ORTG, 102.2 DRTG
Performance: +0.4 ORTG, +1.6 DRTG, +2.0 Overall
Average season performance from all 14 games: +5.8 ORTG, +2.2 DRTG, +8.0 Overall
---
So, with those average season performances, we can simply add to the league average ORTG and DRTG (103.7 right now) to get a predicted end of season net rating, from which you can get a pythagorean win expectation. It would peg us at 61 wins at the end of the year.
But as I noted, I don't want to use pythagorean predictions, since a) it does not account for schedule and b) it gives you no idea where the losses are likely to come from.
Instead we'll use the standard deviation approach described above.
First, let's see what the model would predict for the 14 games already played, based entirely on the season ORTG and DRTG for each opponent and the average performance by the Raptors so far. The model predicts a 10.5-3.5 record, so we've picked up a win and a half that we shouldn't have already (great news). The lowest 3 games in terms of expected wins were MIA, MEM and CHI - of which we lost two and edged out the other. So that seems to hold up to the smell test.
Now we can look at predictions. Here are the next 10 games as predicted by the model.
Game | Expected win margin | Odds to win
@ ATL | +5.6 | 65%
vs DAL | -1.0 | 47%
@ LAL | +15.8 | 86%
@ SAC | +3.4 | 59%
@ UTA | +8.9 | 73%
vs CLE | +10.6 | 76%
vs DEN | +11.9 | 79%
@ CLE | +5.1 | 64%
vs IND | +14.2 | 84%
@ NYK | +9.9 | 75%
Total W-L: 7.1-2.9
And the entire season is predicted to be a 59-23 affair.
---
As a quick reference, I quickly ran some top East and West teams to get an idea where that 59 win projection stands.
CHI: 44 wins
WAS: 47 wins
MIA: 39 wins
MEM: 48 wins
GSW: 54 wins
---
So I hope this was interesting to some of you, and that at least a couple people read to the end...
Apologies for the length, but I wanted to go in-depth with this one.
It should be noted that the data to be input to this changes every night, as teams' performances impact their season ORTG and DRTG, and doubly so on game nights, when everyone who played is updated, plus the Raptors' average season performance changes.
Any questions, comments, criticisms and concerns are always welcome.
With so much talk of how the Raptors' easy schedule is driving their success, and questions about whether they can sustain this, or whether it is fool's gold, I wanted to take a look at how exactly the team has performed, correcting for their opponents and home games, and extrapolating that over the entire season, game by game, and predicting a final record.
There are lots of different sites that do this to one degree or another, but most are black boxes for the most part, or do some but not all of what I am trying to do here. Hopefully this post can shed some light on the approaches commonly taken to adjust for strength of schedule, as well as lend some clarity to how much the record so far really means.
---
*The following is a fairly wordy explanation of the approach. I'll put a more straightforward breakdown in the next section if this is too long for your tastes.
So, first, the methodology. The basic concept is to look at each game, take the opposition's average ORTG and DRTG, compare the Raptors' ORTG and DRTG in that game to those numbers, and determine an offensive and defensive performance for that game. For example, if the opposition has a 100 ORTG and 100 DRTG, and in the game against them the Raptors post a 110 ORTG and a 105 DRTG, they would have a +10 offensive performance and a -5 defensive performance, meaning a +5 overall performance.
Then you look at the average of all the games so far to determine a season-to-date performance (offensive and defensive). You can take that average performance, add it to the league average ORTG and DRTG, and you get an opposition-adjusted ORTG and DRTG, which can be used via a simple pythagorean win projection to predict the final record.
So that takes care of the opposition correction. Now what about home and away? League wide last year the home team on average performed 1.4 points per 100 possessions better on both offence and defence. So, to correct for a home-heavy schedule, all we do is give either the Raptors or the opposition a 1.4 point boost in ORTG and DRTG when calculating the game performance. So, to use the same example as before, say the 100 ORTG and 100 DRTG team is hosting the Raptors. In that case, the Raptors' expected performance is not 100 ORTG and 100 DRTG, it is 98.6 ORTG and 101.4 DRTG. So when they post an ORTG of 110 and a DRTG of 105, they are earning a +11.4 and +3.6 offensive and defensive performance for the game.
Now, the one other thing that bothers me about win projections with the pythagorean approach is that it assumes every team has a similar strength of schedule over the entire year. To correct for this (and to allow us a look at the upcoming schedule and which teams were are more or less likely to beat), we'll use a standard deviation approach.
If you look at the team's 14 games so far, you can extract an average value for offensive and defensive performance from the 14 data points. From the same data set, you can calculate the standard deviation for offensive and defensive performance as well. Assuming a normal distribution of performance throughout the year (a bell curve), you can find the probability of the team achieving a particular performance or better in a game.
So, then looking at any game, you take the expected performance of the Raptors based on the opponent (in our example, it was 98.6 ORTG, 101.4 DRTG, or a 2.8 point loss), apply the Raptor's average performance thus far in the year, and you get a predicted result for that game. If the Raptors' overall average performance is +5, then the predicted result would be a 2.2 point win (-2.8 expected performance + 5 average performance).
Then you determine how poorly or well the Raptors would need to play to get to a predicted tie game. So in this case, the Raptors would need to be 2.2 points below their average. Then all you need to do is divide that by the standard deviation of their performance to date, and use the normal distribution to determine the chances of exceeding that mark.
That yields the chances that the Raptors win that game. That translates directly to number of expected wins - a true toss up game would predict that the Raptors have a 50% chance to win, and would be worth 0.5 wins. An expected huge win (say against Philly) would show that the Raptors have a 90% chance to win (for example), and that would be worth 0.9 wins. Then you just add up the predicted number of wins for the entire season, or for any stretch, to get a predicted record in that time frame, with strength of schedule, home game, and opponent all accounted for.
---
Here's a quick order of events to summarize:
Past games:
Opponent ORTG and DRTG for the season -> Expected opponent performance
Expected opponent performance +/- home court advantage -> Expected opponent performance adjusted
In-game Raptors ORTG and DRTG - Expected opponent performance adjusted (ORTG and DRTG) -> Raptors Game Performance for that game
Using all Raptors Game Performances gives a season-to-date average and standard deviation Raptors performance.
Future games:
Expected Opponent Performance Adjusted + Average Raptors Performance -> Expected Result
Expected Result - Tie Game Result -> Minimum Raptors performance required to win
Minimum Raptors Performance Required / Standard Deviation performance -> Chances to exceed minimum performance (i.e. chances of winning)
Chance to win = number of expected wins from that game
The sum of the expected wins gives the predicted record.
---
Anyway, that's the strategy.
Here are the Raptors' game by game performances so far.
Game | Offensive Performance | Defensive Performance | Overall Performance
vs ATL | +3.6 | -1.9 | +1.7
@ ORL | +6.8 | +2.4 | +9.2
@ MIA | +2.2 | -8.1 | -5.9
vs OKC | +3.3 | -3.4 | -0.1
@ BOS | +6.6 | -4.0 | +2.6
vs WAS | +6.7 | +12.3 | +19.0
vs PHI | +6.8 | +4.0 | +10.8
vs ORL | +0.9 | -3.0 | -2.1
vs CHI | -9.5 | +1.2 | -8.3
vs UTA | +15.1 | -0.1 | +15.0
vs MEM | +7.7 | +1.7 | +9.4
vs MIL | +25.0 | +9.0 | +34.0
@ CLE | +8.0 | +16.1 | +24.1
vs PHX | +0.4 | +1.6 | +2.0
And here's a detailed look at the PHX game, for reference.
PHX season ratings: 102.1 DRTG, 105.2 ORTG
PHX expected result due to road game: 103.5 DRTG, 103.8 ORTG
Ratings in game vs PHX: 103.9 ORTG, 102.2 DRTG
Performance: +0.4 ORTG, +1.6 DRTG, +2.0 Overall
Average season performance from all 14 games: +5.8 ORTG, +2.2 DRTG, +8.0 Overall
---
So, with those average season performances, we can simply add to the league average ORTG and DRTG (103.7 right now) to get a predicted end of season net rating, from which you can get a pythagorean win expectation. It would peg us at 61 wins at the end of the year.
But as I noted, I don't want to use pythagorean predictions, since a) it does not account for schedule and b) it gives you no idea where the losses are likely to come from.
Instead we'll use the standard deviation approach described above.
First, let's see what the model would predict for the 14 games already played, based entirely on the season ORTG and DRTG for each opponent and the average performance by the Raptors so far. The model predicts a 10.5-3.5 record, so we've picked up a win and a half that we shouldn't have already (great news). The lowest 3 games in terms of expected wins were MIA, MEM and CHI - of which we lost two and edged out the other. So that seems to hold up to the smell test.
Now we can look at predictions. Here are the next 10 games as predicted by the model.
Game | Expected win margin | Odds to win
@ ATL | +5.6 | 65%
vs DAL | -1.0 | 47%
@ LAL | +15.8 | 86%
@ SAC | +3.4 | 59%
@ UTA | +8.9 | 73%
vs CLE | +10.6 | 76%
vs DEN | +11.9 | 79%
@ CLE | +5.1 | 64%
vs IND | +14.2 | 84%
@ NYK | +9.9 | 75%
Total W-L: 7.1-2.9
And the entire season is predicted to be a 59-23 affair.
---
As a quick reference, I quickly ran some top East and West teams to get an idea where that 59 win projection stands.
CHI: 44 wins
WAS: 47 wins
MIA: 39 wins
MEM: 48 wins
GSW: 54 wins
---
So I hope this was interesting to some of you, and that at least a couple people read to the end...
Apologies for the length, but I wanted to go in-depth with this one.
It should be noted that the data to be input to this changes every night, as teams' performances impact their season ORTG and DRTG, and doubly so on game nights, when everyone who played is updated, plus the Raptors' average season performance changes.
Any questions, comments, criticisms and concerns are always welcome.
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