The Raptors Probably Need To Outshoot The Warriors From Downtown To Take The Title

The NBA Finals are almost here and we are finally, mercifully, treated to a matchup which is not Warriors vs. Cavaliers.  The Raptors, in their first NBA Finals appearance, will get a chance to dethrone the champs and I, like most fans, am really excited to see how this turns out.

To get a feel for how a series might shake out, I like to start by looking at the regular season point differentials of both competitors.  By this measure, this Finals looks pretty even.  The Warriors and the Raptors were 2nd and 3rd in the NBA, respectively, at +6.5 and +6.1.  My simple point differential only model pegs the Raptors as slight favorites (55% chance to win the series) by virtue of having home-court advantage.  Plus, the Warriors look to be without Kevin Durant for at least the first few games in the series, which hurts their odds.

However, Las Vegas really likes the Warrior’s chances to defend their crown.  As of Sunday afternoon, the Westgate Super Book had Golden State at -300 and Toronto at +240, which implies a roughly 27% chance that the Raptors win the series.  This does not seem crazy given the playoff Warrior’s tendency to take their game to another level.

With all this in mind, I decided to do a little research into one source of variability in an NBA playoff series: 3-point shooting.  The vagaries of playoff 3-point shooting caught my eye during the extremely tight Raptors vs. Sixers series in the Eastern Conference Semifinals.  Toronto eked out a series win in 7 games despite really struggling to shoot the ball from the outside.  The Raptors made just 29.8% of their 3-pointers in the series, despite being a 36.3% 3-point shooting team in the regular season, per basketball-reference.  They were probably saved in that series by the fact that Philadelphia also shot poorly on 3’s, making just 32.9%.

In the next round, the Raptors were the ones to benefit from opponent bricks.  Their Eastern Conference Finals opponent, the Bucks, made just 31% of their 3’s while Toronto shot 37.4% for the series.  This outside shooting edge was crucial considering that Toronto won a number of close games in the series and only outscored Milwaukee by 1 point per game.

So how big a deal are 3-pointers in the playoffs?  To answer this, I considered all playoff series from 2012 to 2018.  I decided not to go back earlier because I wanted to capture a representative sample of series played in the 3-point shooting heavy league of today.

Unsurprisingly, 71% of the time the team which outshot their opponent on 3-pointers ended up winning the series.  But what I was really interested in was the following: given the difference in strength between two teams and the final 3-point shooting margin of the series, what is the likelihood that each team wins the series?

To this end, I defined Series 3-Point Margin (S3-PM) as the following:

S3-PM = (Home Team Series 3-PT% – Away Team Series 3-PT%) – (Home Team Regular Season 3-PT% – Away Team Regular Season 3-PT%)

In the above equation, the “Home Team” is the team in the playoff series with home court advantage (I will use home team in this manner from now on).  Basically, S3-PM is telling us how much better the home court team shot on 3’s relative to their opponent in the series, relative to our expectation from the regular season.

As an example, take the recently completed Raptors vs. Bucks Eastern Conference Finals.  The Raptors outshot the Bucks 37.4% to 31% on 3-pointers.  In the regular season, the Raptors were also a better 3-point shooting team, 36.6% to 35.3%.  So the S3-PM of the series (calculated from the home Buck’s perspective) is (0.31 – 0.374) – (0.353 – 0.366) = -0.051.  In other words, the Bucks were outshot by about 5 percentage points more than might be expected.

I took a look at the distribution of  S3-PM and found that it is roughly normally distributed around a mean of 0 and standard deviation of 0.06.  What this means is that if two teams with identical regular season 3-point percentages are facing each other in a playoff series, our rough 95% confidence bound for the final 3-point percentage difference in the series is +/- 0.12.  Anything in this +/- 0.12 range is not really surprising.

Using S3-PM, I ran a simple logistic regression which predicted the winner of each playoff series from 2012 to 2018.  I used only S3-PM and the difference in net rating between the home team and road team in the series (I call this net rating difference).  This model is not truly “predictive” because we are using information from an already played series in our projection.  Still, it gets at the heart of quantifying the impact of 3-point shooting on a series.

As one might expect, knowing how the 3-point battle turned out in a series is helpful in determining the outcome.  Both net rating difference and S3-PM were significant predictors of the series winner, at the 0.01 significance level.

To get a feel for how much 3-point shooting affects a typical playoff series, suppose two teams with the same regular season net rating and 3-point percentage are facing off in the postseason.  The chart below gives the predicted win probability of the home team, based on S3-PM.

Screen Shot 2019-05-28 at 9.08.09 PM

What we see makes sense.  If both teams wind up shooting the exact same percentage on 3-pointers in the series, then we are not really sure who will win because the two teams have equal ability.  The home team is a slight favorite with a 59% chance of winning the series in this scenario.  But if the home team outshoots their opponent by 6 points from beyond the arc, then we know they will probably be victorious.  They have a 78% chance of winning.  The visitors do make up the 3-point deficit in the other areas of the game 22% of the time in this scenario, but it’s an uphill battle.

So what does all this mean for the Raptors and Warriors in this NBA finals? Well, let’s take it at face value that the Warriors have a 72% chance of winning this series, as betting markets imply.  A typical home court team (as the Raptors are in this series) which is this big an underdog is 5 points of net rating worse than their opponent.  Using this 5 point net rating difference, we can project the Raptor’s chances of winning the series based on the difference in the teams’ 3-point percentage in the series.  This is shown below.

Screen Shot 2019-05-28 at 9.34.35 PM

To interpret the above plot, first note that the “fat” part of the distribution is centered around -0.02.  The Warriors shot roughly 2 percentage points better on 3’s in the regular season than the Raptors, 38.5% to 36.7%,  so outcomes around -0.02 (from the Raptor’s perspective) are relatively more likely than more lopsided 3-point differentials.  Centered around a mean of -0.02, the Raptor’s 3-point percentage advantage is normally distributed with a standard deviation of 0.06.

If we move to the left of -0.02, we are in a scenario where the Warriors have shot even better than expected and/or the Raptors have shot worse.  Toronto is unlikely to win if this happens, as shown by the diminishing size of the red bars.

What about if the two teams shoot the same 3-point percentage?  This would actually be a small win for the Raptors because they have been the worse shooting team this year, but they would still be underdogs in this scenario.  Their win probability would be 33%, up a little from the baseline of 27%.

So how much do the Raptors have to outshoot the Warriors on 3’s to actually be the favorites?  From my model, the answer is by roughly 5 percentage points.  We should keep in mind, however, that even in this rosy scenario Toronto is still just a little over a coin flip to beat Golden State.

In this Finals clash, keep an eye on the 3-point shooting battle.  If Fred VanVleet and company are not lighting it from the outside or the Warriors are not a little colder than usual, it will be an uphill battle for the challengers from north of the border.

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