Neal’s 3rd rounder: deconstructing a beautiful condition

Last week I analyzed James Neal’s projected goal totals for 2019-20, concluding that his average goal expectation was around 18.5 goals over an 82 game schedule. An astute observer noted that it was unlikely he would play the entire schedule, making that prediction a bit optimistic.

I’ve also been a bit fascinated by the Lucic/Neal trade’s conditional 3rd round pick in 2020, which is conditional on both of these 2 outcomes:

1. Neal has to score 21 or more goals in 2019-20
2. Neal has to score 10 or more goals than Lucic

In this post, I’ll be exploring multiple things in order to find the probability of the Oilers losing their 3rd round pick to the above conditions.

Estimating Neal’s games played

The first thing I’ll have to address is the shortcoming of my previous analysis — I’d estimated that Neal’s average expectation was going to be about 0.225 goals per game next year, which translates to about 18.5 goals over 82 games. But I need to estimate his games played as well in order to really get a sense of how many goals he will score.

My initial thought was to build a similar linear regression as last time to estimate the % of a season played — basically, taking each players’ age 27-31 season played percentage (so if 82 out of 82 games this is 100%) and seeing if these variables can predict the age 32 season’s games played percentage. It turns out this was a very poor model — only 5% of the variability in my response variable was described by this model. The age 31 season did seem to be quite relevant, but in the end it seemed that injuries and missing games seems quite hard to predict based on a player’s own recent history of missing games.

Because of this dead-end I’ll change tact — I’ll instead simply use the empirical distribution of age 32 games completed percentage of my original 249 observations (forwards that scored at least 0.08 goals per game between the ages of 27 and 31).

In effect, I’ll just be assuming that Neal has the same chance of any player in the last 20 or so years to miss games at age 32. Looking at the histogram above, you can see that fully one-third of my observations played between 80 and 82 games at age 32. So, I’m going to give Neal that same chance, along with every other proportion you see above.

Estimating Mr. Lucic

In order to figure out the probability of losing the 3rd rounder, I have to estimate Lucic’s expected distribution of goal scoring for 2019-20. I won’t bore you all with the details, other than to say that I used a very similar methodology as I did for Neal, except that I just used 4 seasons of history to estimate his goals per game instead of 5 (Lucic is one year younger using the standard hockey-reference birthday cutoff). It turns out all ages between 27-30 were somewhat relevant in predicting age 31 goals per game with a heavy, heavy emphasis on the previous year’s scoring at age 30. I formulated a similar variable to account for bad shooting luck at age 30, which will help players who shot below their recent career average (such as Lucic). This model described about 51% of the variability in age 32 scoring, which is quite good and comparable to Neal’s model.

It turns out that this model for Lucic predicts he will score 0.152 goals per game next year, or about 12.5 goals per 82 games. The model is 95% confident he’ll score between 0 and 25 goals and about 68% confident he’d score between 6 and 19 (again, over 82 games).

I also created an empirical distribution for age 31 players that I’ll use to estimate Lucic’s games played for next year that looks similar-ish to the one above for Neal.

My approach…

So, how would you try to figure out the probability of the Oilers losing that 3rd round pick next year? My first thought was to just multiply the area under Neal’s curve beyond 21 goals by the area under Lucic’s goal scoring curve 11 goals and under. But of course, that is wrong — the second part of the condition is about a 10 goal gap — this creates a fascinating creeping conditional probability that hurts my brain to think about and I’m quite sure there isn’t a closed-form way to figure that out perfectly via calculus.

For math nerds, I suppose the next best way may be to use Riemann sums — perhaps approximate the area under Neal’s curve that pertains to between 21 & 22 goals and multiply that by Lucic’s area 11 goals and below, then take Neal’s area between 22 & 23 goals and multiply by Lucic’s area 12 goals and below, etc. But this sounds tedious and boring.

My preferred approach today will be to use simulation! It will allow me to handle crashing together my 4 different distributions (games played empirical distributions and goal scoring rate bell curves for both players) and simply let the chips fall where they may. With this many interacting stochastic (or random) variables, I’m going to use 100,000 iterations. Basically, I’m going to let Neal and Lucic play the 2019-20 season 100,000 times over apiece and see what both of their goal scoring curves look like, what their goal-scoring differential curve is, and ultimately what the probability of losing the pick is.

My results…

The above chart shows the results of my 100,000 simulations of Neal’s goal scoring totals in 2019-20. It’s a beautiful normal distribution! It turns out that Neal has about a 23.2% chance of scoring 21 or more goals next year. His expected (or average) goal total is just a shade under 16. We’re about 95% confident that he’ll score between 4 and 28 goals. We’re 68% confident (+/- 1 standard deviation) he’ll score between 10 and 22 goals. He’s got a very small shot of getting 30 or more — about 1.8% — and his maximum goal total out of the 100,000 simulations was 46 goals (which is a great display of a Gaussian’s infinite extent!).

The above chart outlays Lucic’s total goal probabilities for 2019-20. I’ve used the same scale as the previous chart for Neal so that you can compare them easily by eye — just scroll up and down to see the distinct leftward shift of Lucic’s curve towards 0 goals. Like a glacier ramming up against a mountain, Lucic has more scenarios that pile up at zero goals on the left.

Lucic is estimated to average about 10.8 goals for next year. His 95% prediction interval would be something like between 1 and 22 goals.

The above chart shows Neal’s goal lead over Lucic in each of the 100,000 simulations — so, 0 means they had the same amount of goals, +10 means Neal outscored Lucic by 10, etc. You can see that it’s not inconceivable for Lucic to actually outscore Neal — this would be the sum of all bars in the negatives. But Neal still is overwhelmingly likely to outscore or tie Lucic — around 73.2% likely.

But the most pertinent figure in the above chart is the probability that Neal scores 10 or more goals than Lucic. You can see the yellow bars that pertain to these scenarios. Added up, I’d give Neal a 30.3% chance to score at least 10 goals more than Lucic.

So — now what? Can we just multiply the probability of Neal scoring over 21 goals by the probability of Neal scoring 10 or more than Lucic (or 7.0%)? Unfortunately it’s not that simple, as these two concepts are not cleanly separated like that — there are plenty of instances where Neal scores less than 21 and outscores Lucic by 10, for example.

Luckily, I can use the simulation itself quite easily — I just need to setup triggers for the two conditions, and if both are met I log that scenario as ‘1’. Sum up those scenarios and I have a great estimate for the probability of meeting both conditions.

The treemap above outlines how many times either one or both of the trade conditions were met out of the 100,000 simulations. You can see that in ~ 63,000 simulations neither condition was met — so about 63% of the time.

This means that at least one trade condition was met 37% of the time. The key quantity of interest is the number of times both trade conditions were met — this happened 16,813 times, or about 16.8% of the time. This is the probability that the Oilers give up their 3rd rounder.

You can also use this chart to see when one condition happened but the other did not — it was twice as likely for Neal to outscore Lucic by 10 goals but not scoring 21 or more himself than vice versa.

What’s 16.8% of a 3rd Rounder worth?

Referring to some old numbers I’d created, I can get a sense of the likelihood of finding an ‘NHL’ player between picks 63 and 93 of the draft. I’d estimate the average likelihood of finding a player in that range of the draft is about 12.3% — or you have about a one-in-eight chance of finding an NHL player in the third round.

Now we can get a real sense of the value of that conditional 3rd. Let’s take the 16.8% probability that the Oilers give up that pick and multiply it by the 12.3% probability of finding an NHL player in the 3rd round. This is about 2.1%.

So, in other words, the conditional 3rd round pick that the Oilers gave the Flames is worth about 2.1% of a useful NHL player.