# Updating My Beliefs About Neon Jesus

US Presswire

Last week I did some analysis and created a visualization of the correlation between rookie preseason and rookie regular season performance on a number of stats. Before the sell by date of the analysis passed, basically as soon as the regular season starts and the preseason is expunged from our collective memory, I wanted use that data to update my expectations of this year’s rookies.

At this point one could run a couple linear multiple regressions with college stats and preseason stats, or maybe use one of the single number metrics. But, there is a huge amount of colinearity between the college stats and preseason. Guys who rebound well in college, for example, tend to do so in preseason, meaning many of the variables end up getting confounded, especially dealing with relatively small sample sizes.

In any case, Bayesian analysis actually lends it’s self much better to updating our expectations using sequential data, small data sets than multiple regression, and it’s analytically ‘on trend.’

A key to Bayesian analysis is to establish a prior belief, or starting point. To do that I used a combination of general rookie averages and the incoming draft class’s college stats and ranks. Â As an example Celtics number thirteen pick Kelly Olynyk had an effective field goal percentage of 63.1% last year using data from Draft Express. I don’t start my expectations that he will be able to do that in the pros. On the other hand, the fact that he was significantly above the 54% eFG% college average of his fellow rookies (2.075 standard deviations above) in that category is important information.

In the last three years rookies with over 200 minutes of playing time in the regular season had an eFG% of 45.8%, four percent below the NBA average via data from RealGM. So, taking that information, my Prior Expectation for Olynyk’s eFG% was formed as below:

Rookie Average + (Standard Deviations from Class * Standard Deviation) = Prior Expectation

In this case: 0.458 + (2.075 .0506) = 56.3%

One could argue for tempering the adjustment away from the Rookie average, particularly for shooting. However, given that I am going to update these expectations with preseason observations, I think it forms a good informative starting point.

In eight games over the preseason Olynyk had an eFG% of 55.1%. Unfortunately, for demonstration purposes that means the Updated Expectations won’t move too much. Â To update my expectations I had to weight my prior expectation and Olynyk’s preseason performance using a Bayesian weighting formula (shown below) coming out as 56.11%.

So, to look at one stat where Olynyk did move the expectations meter in the preseason, we can look at personal fouls. On personal fouls Olynyk already committed more fouls than average for his class, putting his expected fouls per 48 minutes above the rookie average of 4.9, at 5.63. But the big young Canadian well-surpassed expectations in the preseason getting called for fouls at a rate of 8.01 per 48 minutes. Weighing the two together Olynyk’s Updated Expectations come to 6.81 fouls per 48 minutes (meaning they don’t let you play 48 minutes in one game).

I applied the same methodology to all the 2013 rookies with college experience and significant playing time this preseason. Below are the preseason numbers, my ‘Prior’ belief and the Updated Belief for eFG%, Rebounds per 48 minutes, and Assists per 48.

 Player Team Pos Pre eFG% Prior eFG% Updated eFG% Pre REB Prior Reb Updated Reb Pre ASTS Prior Asts Updated Asts Anthony Bennett CLE PF 0.413 49.7% 48.31% 12.05 11.68 11.87 1.96 1.7 1.83 Victor Oladipo ORL PG 0.447 57.7% 55.5% 10.27 8.88 9.58 8.45 3.3 5.87 Cody Zeller CHA PF 0.443 48.5% 47.8% 12.87 10.88 11.88 3.41 2.2 2.81 Ben McLemore SAC SG 0.546 51.4% 51.96% 7.84 6.38 7.11 2.32 2.9 2.61 Kentavious Caldwell-Pope DET SG 0.375 45.6% 44.25% 8.92 8.28 8.6 1.96 2.5 2.23 Michael Carter-Williams PHI PG 0.388 35.9% 36.35% 8.07 5.48 6.78 7.58 8.7 8.14 Steven Adams OKC C 0.622 49.1% 51.27% 16.39 10.78 13.59 1.46 1.5 1.48 Kelly Olynyk BOS PF 0.551 56.3% 56.11% 9.3 10.98 10.14 3.87 2.9 3.39 Tony Snell CHI SG 0.362 42.9% 41.79% 5.85 3.38 4.62 5.85 4.1 4.98 Mason Plumlee BRK PF 0.409 52.3% 50.39% 14.63 11.48 13.06 2.72 2.6 2.66 Solomon Hill IND SF 0.24 46.3% 42.58% 5.09 6.48 5.79 3.52 3.7 3.61 Tim Hardaway Jr. NYK SG 0.482 42.8% 43.72% 5.13 5.18 5.16 1.56 3.2 2.38 Andre Roberson OKC SG 0.273 43.5% 40.83% 12 13.38 12.69 0.92 2.1 1.51 Archie Goodwin PHX SG 0.415 37.7% 38.33% 4.82 5.78 5.3 1.75 3.8 2.78 Tony Mitchell DET PF 0.733 40.1% 45.63% 12.62 10.38 11.5 1.1 1.3 1.2 Jamaal Franklin MEM SG 0.468 37% 38.66% 8.69 11.28 9.99 4.97 4.4 4.69 Peyton Siva DET PG 0.404 37.6% 38.03% 2.53 2.98 2.76 9.49 7.7 8.6 Erik Murphy CHI PF 0.293 54.8% 50.56% 9.69 8.38 9.04 1.79 2.5 2.15

The positive movers are in yellow and the negative in red in terms of changes in expectations. Â Effective field goal percentage didn’t move much for anyone, primarily because the high variability of scoring and high standard deviation of eFG% in preseason. Â Though Steven Adams moved up in eFG% somewhat, while Erik Murphy moved down. Â On rebounds, Steven Adams looked like a beast on the boards all preseason, enough to significantly move his Updated Rebounds expectations, and Victor Oladipo playing a facilitating role with Orlando moved his Updated Assists up as well.

In addition I ran the numbers for free throws, turnovers and personal fouls, all per 48 minutes.

 Player Team Pre FT% Prior FT% Updated FT% Pre TOV Prior TOV Updated TOV Pre PF Prior PF Updated PF Anthony Bennett CLE 0.692 66.4% 67.8% 6.17 2.83 4.5 10.37 5.53 7.95 Victor Oladipo ORL 0.839 71.4% 77.7% 5.94 3.33 4.63 4.11 5.63 4.87 Cody Zeller CHA 0.548 72.5% 63.7% 3.68 3.13 3.4 4.73 5.13 4.93 Ben McLemore SAC 0.692 83.8% 76.5% 3.19 2.73 2.96 3.77 4.43 4.1 Kentavious Caldwell-Pope DET 0.7 76.5% 73.3% 2.18 2.53 2.35 5.44 4.63 5.03 Michael Carter-Williams PHI 0.647 66.2% 65.5% 2.44 4.03 3.23 5.38 4.73 5.05 Steven Adams OKC 0.529 41.1% 47% 4.39 2.03 3.21 7.9 4.93 6.41 Kelly Olynyk BOS 0.7 74.8% 72.4% 3.62 3.83 3.72 8.01 5.63 6.82 Tony Snell CHI 0.714 81.1% 76.3% 1.72 2.73 2.22 2.75 3.83 3.29 Mason Plumlee BRK 0.593 64.9% 62.1% 4.76 3.43 4.09 3.74 5.03 4.38 Solomon Hill IND 0.75 73.4% 74.2% 1.96 2.83 2.39 3.52 4.73 4.12 Tim Hardaway Jr. NYK 0.615 66.3% 63.9% 1.56 2.23 1.89 2.9 4.33 3.62 Andre Roberson OKC 0 51.9% 26% 4.62 3.03 3.82 8.31 5.13 6.72 Archie Goodwin PHX 0.588 60.5% 59.7% 4.82 4.03 4.42 3.07 5.83 4.45 Tony Mitchell DET 0.5 63.7% 56.9% 1.1 3.23 2.16 7.68 5.73 6.7 Jamaal Franklin MEM 0.8 75.8% 77.9% 3.73 4.23 3.98 4.55 5.33 4.94 Peyton Siva DET 0.833 83.5% 83.4% 6.64 3.53 5.08 5.38 5.43 5.4 Erik Murphy CHI 0.5 75.2% 62.6% 1.08 2.23 1.65 9.69 6.33 8.01

Again the most significant negative Updated Expectations are in red and positive in yellow. Â It looks like I might let my parochial New England interests bury the lead as Anthony Bennett struggled enough with turnovers and personal fouls to worsen his Updated Expectations. That said, coming off an injury and by all accounts not being in game shape, I could probably temper my expectations adjustment somewhat. And I am not a ‘Bash the Number One Pick Because He isn’t the Best Guy in his Draft Class’ kind of guy, I wouldn’t have taken him there, but that’s on Chris Grant not Anthony Bennett.

I also tracked blocks and steals, but neither showed much impact on expectations.

As promised above, here’s the expectations updating formula I used. It is designed to diminish the impact of measures with high variability as measured by standard deviation. When trying to formulate a Bayesian continuous update formula this weekend, I ran across this one via Daniel Myers.

Updated Expectation= (Prior Expectation / Prior StDev^2 + New Observation/ New Observation StDev^2) / (1/Prior StDev^2 + 1/New Observation StDev^2).