FanPost

The "Retired Janitor's Law", The 3p shot's Variability, and their Importance for the ECF.

Fact no.1: Bucks do not lose when they have a positive 3p% differential.

Fact no.2: Bucks lose half the times when they have a negative 3p% differential.

Although we don't understand WHY 3p% relates in such a way with W/L for our team (several hypotheses have been thrown around in discussions during the regular season) the sheer predictive power of this simple stat is astonishing. The question is simple enough: "will we have a positive 3p% differential in the upcoming series?" If we do (even 2-3 games will do it) then we advance. If we don't, then it's a coin toss...

One could simply go and look at the two teams' 3p% averages and take a guess based on that. However there's two problems. First TOR and MIL have shot very similarily (in terms of %), and second averages do not convey variability info. 3p shots are notoriously variable so just looking at the means won't cut it. I decided to dive a little deeper into the abyss that 3p shooting is...

DISCLAIMERS

This might seem technical to some and simplistic to others.

This is long. Very long. This might actually be too long. You have been warned!

This has a lot of graphs.

METHOD

I got all the data used for my analyses from NBA.com. I used three main dependent variables (i.e. things that were measured): 3p takes, 3p makes and 3p%. Usually we look only at 3p% (which is fine) but I felt we're missing something if we don't include makes and takes also. More about that in the discussion below.

I used three grouping variables (or indepedent variables): Teams (MIL, TOR), Season (Regular, Playoffs) and Round (1st and 2nd).

All the analyses and graphs presented here were perfomed with JAMOVI (a brilliant open access statistics package).

DESCRIPTIVE STATISTICS

Just looking at averages to describe 3p shooting misses out on the variability measures of the shot. Two teams might have the same 3p% average but one might shoot consistently around 35%, while the other might shoot anywhere from 10% - 60%. When we're looking to predict which team will do better in a short game series, we would prefer to bet our money on the consistent shooter. So the first thing I set out to see was how the two teams shot from 3 during the regular and the post season combined.

Toronto shot 36% while Bucks shot at 35.3%. Toronto's shooting was a bit more variable than Bucks' (standard deviations at 8.61 vs 7.54). Here's our first graph. It shows the boxplot for 3p % for the two teams. The longer the whiskers the more variable the shot. The thick black line in the middle of the boxes is the median. The dots that can be seen are considered "outlier cases".

GRAPH 1. 3P% FOR REGULAR AND POST SEASON COMBINDED.

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As you can see the shooting for the two teams looks quite similar. Note that MIL has 4 outlier measuments. 3 below and 1 above what would be expected based on the distributions.

Now let's see the same graph but for number of makes. Here's the boxplot.

GRAPH 2. MAKES FOR REGULAR AND POST SEASON COMBINED.

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As we can see MIL makes more shots than TOR per game. No outliers here and MIL's "floor" is higher than TOR's (which is a good thing).

What about takes? Surely since MIL and TOR are shooting almost the same %, and MIL has more makes than TOR, MIL must shoot more threes than TOR. Here's the boxplot:

GRAPH 3. TAKES FOR REGULAR AND POST SEASON COMBINED.

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MIL shoots 4.6 more 3pointers than TOR per game. No outliers here and both ceiling and floor are higher for MIL.

So here's the first set of conclusions from the data.

1. TOR shoots slightly better from 3p range than MIL

2. MIL makes more 3s than TOR

3. MIL takes more 3s than TOR

At this point someone might think that it's all a wash. Surely if you take more shots you'll make more, but this might lower your percentage. So I set out to look at correlations between Makes, Takes and Percentages. Below you can see a scatterplot with the correlations indicated for the three variables:

GRAPH 4. CORRELATION SCATTER PLOT FOR MAKES, TAKES AND 3P%.

Makes,Takes and Percentages

Of course makes and percentages correlate positively (lower left plot), as do takes and makes (top left plot). Look at the bottom right plot though. Takes and percentages do not correlate! So the assumption that if you shoot high volume 3s will hurt your percentages, doesn't seem to be supported by the data! This means that the team that takes more, will make more, without dropping it's percentage! Let'em fly boys!

The next question I asked was: is the same picture obtained if one splits the data by regular vs post season? Apart from reasons having to do with playing more difficult oponnents, game slowing down, etc., looking at the post season data vs the regular season, gives us an idea about consistency and current performance levels. So let's dive in.

Here's the boxplot for both teams measuring 3p% for the regular and the post season:

GRAPH 5. BOXPLOT OF 3P% BASED ON TEAM AND SEASON.

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Bucks are extremely consistent with their 3p shooting going from regular to post season. However TOR's % has dropped during the post season. They are shooting at 32.6% vs 36.5% they shot during the regular. This is good news. Another thing that you should note is that the Bucks have already had a "low outlier" performace during the POs, which makes it less probable to observe another one of those.

If we look the same type of graph for made shots the picture gets even clearer as to which team has the advantage.

GRAPH 6. BOXPLOT OF MADE SHOTS BASED ON TEAM AND SEASON.

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From 1 more make during regular, we went to 2.8 more makes during POs! Also note that TOR has already two "high outlier performances" in the POs.

I was a bit puzzled about why TOR is making less 3s in the post season. I decided to look at the difference between playoff rounds. After all Philly took the series to 7 games, part of their success might have been the fact they kept TOR below their average for 3p makes. The data were very clear. Both TOR and MIL have a lower 3p% during the second round compared to the first round, but TOR's numbers really got a hit. Here's the boxplot for 3p%.

GRAPH 7. BOXPLOT OF 3P% BASED ON TEAM AND ROUND.

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While our % dropped from 37.4 to 34, theirs plummeted from 37 to 29.5! And here's where the "let'em fly" mandra pays dividents. Although our % went down, our makes went up! Yeah... we just shot more. Take a look at the two boxplots that follow for makes and takes.

GRAPH 8. BOXPLOT OF MADE SHOTS BASED ON TEAM AND ROUND.

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GRAPH 9. BOXPLOT OF ATTEMPTED SHOTS BASED ON TEAM AND ROUND.

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Second set of conclusions:

1. During the post season, MIL is better than TOR in 3p shooting whether one looks at %, makes, or takes.

2. While MIL elected to fight the drop in % from Rnd1 to Rnd2 with increased 3p attempts, TOR stayed par. Their terrible drop in 3p% almost cost them the series...

So are we a better 3p shooting team going into the ECF compared to the Raps? Descriptive data seem to suggest so, but the differences might not be "real" but "random". We need more "advanced" statistics to answer that question. The next section describes two ANOVA's that'll help us answer the next question: is the superiority of the Bucks in 3p%, and makes significant or not?

The first graph is from looking at 3p% based on TEAM and PO round.

GRAPH 10. MARGINAL MEANS OF 3P% BASED ON TEAM AND ROUND.

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The effect of round was marginally significant, meaning that the difference in 3p% from Rnd1 to Rnd2 is not random.

The next two graphs are the same analysis for Makes and Takes.

GRAPH 11. MARGINAL MEANS OF MADE SHOTS BASED ON TEAM AND ROUND.

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GRAPH 12. MARGINAL MEANS OF ATTEMPTED SHOTS BASED ON TEAM AND ROUND.

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In both of those analyses the effect of TEAM was significant, meaning that the difference in makes and takes between the two teams is not random.

2 more graphs follow for makes and takes for TEAMS vs SEASON (reg or post).

GRAPH 13. MARGINAL MEANS OF MADE SHOTS BASED ON TEAM AND SEASON.

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GRAPH 14. MARGINAL MEANS OF ATTEMPTED SHOTS BASED ON TEAM AND SEASON.

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In both analyses the Bucks are significantly better at makes and takes than the Raptors.

Final set of conclusions.

1. Bucks are a better 3p shooting team than the Raptors.

2. This effect is more pronounced during the POs.

3. Bucks really let'em fly. As they should. The hard math are behind them...

4. From these data it's difficult to see how TOR will have a chance of beating the Bucks in a series if "Retired Janitor's Law" keeps delivering.

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