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  • Game by Game Team Performance

    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.

    ---

    *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.
    twitter.com/dhackett1565

  • #2
    This is really excellent Dan. I can't see any problems with the methodology, though as you said the data changes every night, and the sample size is still a bit small given that some teams will have spent an inordinate amount of time on the road or at home, against strong or weak opponents, thus altering their baseline expectations. Plus we picked up extra performance against OKC/WAS/MEM due to their injuries (and lost some due to JJ being out). The model will obviously get more and more robust as time goes on.

    Did you back out the teams' performance against us from ORtg/Drtg averages before getting to the expected result? Or does that not make much of a difference?

    Anyways, nice job!

    Comment


    • #3
      Have you tried this for the other top teams so far, like DAL, POR, HOU, SAS etc? 5+ wins over GSW is cool! I'm surprised MEM only gets 48 given how well they've performed thus far. What gives? Does the data suggest they have over-performed to this point?

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      • #4
        a win is a win, thus it is gold.

        Comment


        • #5
          I'd love to see this tracked throughout the season. Making the win projection based on the relative ORAT/DRAT is simple yet really effective. Solid work.

          DanH...the RR's Hollinger.lol

          Comment


          • #6
            Scraptor wrote: View Post
            This is really excellent Dan. I can't see any problems with the methodology, though as you said the data changes every night, and the sample size is still a bit small given that some teams will have spent an inordinate amount of time on the road or at home, against strong or weak opponents, thus altering their baseline expectations. Plus we picked up extra performance against OKC/WAS/MEM due to their injuries (and lost some due to JJ being out). The model will obviously get more and more robust as time goes on.
            Well, in theory, the model should be correcting for early road or home heavy schedules, and for early easy schedules/hard schedules. But you are right - discrepancies like injuries, etc, will not be accounted for (although OKC will be, as they've been hurt all year so far). And yes, the sample is still small, but we are 1/6th of the away through the season now, so it is not a ridiculously small sample.

            Did you back out the teams' performance against us from ORtg/Drtg averages before getting to the expected result? Or does that not make much of a difference?

            Anyways, nice job!
            Thanks! I did not back out the games against the Raptors - given each team has played over 10 games, and only one or two against the Raps, so it shouldn't make a huge difference, and it would be a significant extra step in the calculation (which is already a little cumbersome, as you can see). As the season goes on, this effect will be damped out entirely, but I doubt we'll really see the impact in any obvious way.

            In any case, with the Raptors pretty consistently winning, including their results as I have will make the opposition seem weaker - meaning the Raptors' performance against them will be less impressive, leading to a slightly conservative win prediction.
            twitter.com/dhackett1565

            Comment


            • #7
              JawsGT wrote: View Post
              Have you tried this for the other top teams so far, like DAL, POR, HOU, SAS etc? 5+ wins over GSW is cool! I'm surprised MEM only gets 48 given how well they've performed thus far. What gives? Does the data suggest they have over-performed to this point?
              Takes a little time to input the data, so I grabbed a small sample of teams. I'll take a look at those 5 when I get a chance tomorrow.

              Keep in mind that a) the standard deviation drives a lot of the result, so if a team is particularly erratic in their performances (such as Memphis is) the results are less reliable. And b) Western Conference teams have a very difficult future SOS, as there are loads of winning teams out there. I expect the top Western teams to outperform their prediction just because someone has to win those games between the Western heavyweights.

              But yes, both teams have a fairly weak schedule so far, and have not been as dominant point spread wise as the Raptors have. Both teams are also more prone to significant swings in performance than the Raptors have been, opening themselves up to losses they shouldn't take (in theory).
              twitter.com/dhackett1565

              Comment


              • #8
                OldSkoolCool wrote: View Post
                I'd love to see this tracked throughout the season. Making the win projection based on the relative ORAT/DRAT is simple yet really effective. Solid work.

                DanH...the RR's Hollinger.lol
                Glad you liked it. Yeah, I'll make sure to update consistently.
                twitter.com/dhackett1565

                Comment


                • #9
                  Being the RR's Hollinger

                  Your not ditching us for Memphis too are you?

                  Comment


                  • #10
                    Wow great read. I'm taking a stats course at ryerson right now so its cool to see some of the concepts applied to something I'm interested in. Tried to a find holes in it too but came up empty, again great job DanH!
                    "you can't be playing checkers, on no chess board yoo!" - D'angelo

                    Comment


                    • #11
                      DanH, would you just start submitting it the RR Main Page already?! C'mon, we appreciate you including us, but we're just holding you back. Hahaha This is too good man. You spoil us with your analysis.

                      And for the record, I say your name not like Dan.H., but like Stewey pronounces the H in Cool Whip...

                      Last edited by Joey; Tue Nov 25, 2014, 09:15 PM.

                      Comment


                      • #12
                        I must admit Dan, that when I am rushed and just want to catch up on the latest and most notable posts to the forum, I quickly scan down the list of new posts to see who started them, and the most recent replies, to see who wrote them. Seeing your name automatically means I stop and read. You are right at the top of a very short list of RR members who get this treatment. Joey is right...you need to appear on the front page.

                        Thanks for an awesome bit of work.

                        Comment


                        • #13
                          This is why the forums are better than the main page. Labour of love.
                          Heir, Prince of Cambridge

                          If you see KeonClark in the wasteland, please share your food and water with him.

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                          • #14
                            This is really cool, and verifies that the Raptors have indeed been playing the best in the league to this point. I'm very skeptical of their ability to keep it up and finish with 59 wins, but they have been the best team.
                            That is a normal collar. Move on, find a new slant.

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                            • #15
                              whoah this is great! once i re-read this a few more times to fully understand whats going on, i'm sure it'll be even greater!

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