# Enhanced PORPAG

Submitted by MaizeAndBlueWahoo on February 18th, 2011 at 9:27 PM

Alright, so.  If you clicked, you probably remember and liked the PORPAG metric for evaluating basketball players espoused by The Only Colors.  I don't wanna totally rehash it so here is the overview.

I like PORPAG.  A lot.  It's elegant.  It's the only time something created by Spartys will ever be called elegant.  I'm a sucker for a number that's simple to understand, simple to calculate, and remarkably informative.  As you might remember, though, PORPAG ignores defense.  It's strictly an offensive metric.  I was thinking that I wished it did, so I set out to figure out if there were a good way to incorporate defense.  The result is Enhanced PORPAG.

The new number I wanted had to also reflect "points above replacement" in the same way PORPAG does, because this was to be an add-on.  No need to recreate the wheel: my goal was to stand on the shoulders of geniuses, to borrow a phrase.  The problem, of course, is that there's no defensive rating the same way there's an offensive rating; if there were, someone would already have done this.  You can't have a defensive rating the same as an offensive rating, though, because not every defensive possession is ended by the actions of a defensive player.

But some are.  I'll spare you the list of discarded ideas and jump right into the equation, with explanations to follow:

### EPORPAG = PORPAG * ( ( ( Block% / 2 ) + Steal% ) - 2.45 )

If PORPAG is negative, divide rather than multiply.

Explanation (if this is likely to bore you, just skip to the bottom where the CHART is):

A block or a steal are the two tools a defensive player has at his disposal to actively end a defensive possession.  Rebounds are excluded because those aren't under direct control of the defender.  That's just grabbing a loose ball - the fact that the shooter missed is almost never the result of the rebounder's actions.  There's also the side effect that including rebounds would skew the stat inexorably towards big men.  But blocks and steals are about even between the two, and again, that's how the defense can end a possession.

It's reasonable to assume that a steal denies the opposition two points, because the average possession that results in points, results in two.  One point and three are about equally common.  And a steal always ends a possession, whereas a block ends a possession roughly half the time.

So, add a player's steal percentage to half his block percentage to get the percentage of possessions he ends while he's on the floor.  PORPAG multiplies O-rating to account for the amount of time a player is playing; block% and steal% already do that.  It's built in.  2.45 is the "replacement level", obtained by:

1) Taking the D-I team average for each; 2) dividing each by five to represent one player; 3) multiplying by 0.87, because that's the proportion of replacement-level O-rating to the national average.

Example calculation: Zack Novak's PORPAG is 2.34.

2.34 * (((0.5 / 2) + 1.0) - 2.45) = 1.19.  Novak's defensive numbers are well below replacement-level.

I already did this for the ACC on my own UVA blog, and it sanity-checked very well.  There are a couple caveats, of course:

- It's kinda fishy the closer you get to zero PORPAG.  A replacement-level offensive player could block literally every shot and still be replacement-level.

- It still doesn't account for unaccountable things like off-ball defense or chemistry.

I'm sure people can think of other things.  But enough babbling.  IT'S TIME FOR THE CHART.

 Year Player Team PORPAG Block % Steal % EPORPAG So. JaJuan Johnson Purdue 3.73 6.5 1.6 7.38 Jr. Draymond Green MSU 2.71 4.4 3.5 6.29 Sr. Jeff Brooks PSU 3.31 6.1 1.6 6.28 Sr. Jon Leuer Wisc. 4.57 3.8 1.3 5.96 Fr. Jared Sullinger OSU 4.67 1.9 2.0 5.62 Jr. John Shurna NW 3.39 3.0 2.5 5.53 Sr. Keaton Nankivil Wisc. 2.81 5.7 1.7 5.22 Jr. Trevor Mbakwe Minn. 2.41 6.3 1.9 4.97 Sr. David Lighty OSU 2.84 1.8 3.2 4.76 Jr. Jordan Taylor Wisc. 6.33 0.5 1.5 4.52 Sr. E'Twaun Moore Purdue 3.32 1.8 2.4 4.48 Jr. Ralph Sampson III Minn. 1.73 8.5 1.2 3.84 Sr. Michael Thompson NW 2.74 0.0 2.7 3.02 Sr. Jon Diebler OSU 3.40 0.3 2.0 2.99 Sr. Mike Tisdale Ill. 1.54 7.2 1.1 2.96 So. Christian Watford IU 2.65 1.9 1.7 2.87 So. Darius Morris UM 3.46 0.0 2.0 2.83 Sr. Talor Battle PSU 4.19 0.1 1.6 2.82 Sr. Demetri McCamey Ill. 2.95 0.5 2.0 2.71 Fr. Melsahn Basabe Iowa 1.39 6.8 1.1 2.55

Some interesting, names, yes?  Again, though, I think it passes the sanity test.  The better teams are also generally the better-represented teams.  Guys that contribute mostly only on offense get a bump in favor of more well-rounded players.  I know, for example, that I looked at the PORPAG list and knew I'd rather have Draymond Green on my team than most of the bottom half.  This quantifies that.

I know you'll want to find out about Michigan's guys, so here you go.  Only players included are those with over 30% of minutes played, so guys like Horford and Christian don't make the cut.

 Year Player Team PORPAG Block% Steal% EPORPAG So. Darius Morris UM 3.46 0.0 2.0 2.83 Fr. Tim Hardaway, Jr. UM 1.93 0.7 2.1 1.93 Fr. Jordan Morgan UM 1.42 2.4 1.5 1.57 Jr. Zack Novak UM 2.34 0.5 1.0 1.19 Jr. Stu Douglass UM 0.88 1.0 1.2 0.61 Fr. Evan Smotrycz UM 0.59 1.8 1.3 0.53 So. Matt Vogrich UM 0.46 0.7 1.5 0.35

That's actually kind of worse than a lot of the Big Ten, but UM tends to roll flatter but deeper.  Novak is better than at least half of other teams' 4th-best guys.  I would put up the rest of the league, but this is getting long.  Enough people take interest, I will.  There you have the data; enjoy.

Edit: One point that needs clarifying - I was challenged on this by an FOV reader.  The average team offensive rating is about 101 - therefore the average possession is one point.  So if a steal takes away a possession, shouldn't steals take away one point, not two?  No, because for the average possession to be worth a point, the successful possession must be worth two.  A steal denies a successful possession, not an average possession.  It's only appropriate to speak of taking one point off the board by denying a possession if that possession never begins in the first place.  Once it's begun, the outcome can be assumed to be binary - either zero or two points.  (One or three is possible, but they average each other out to two.)  Therefore a steal prevents two points.  And a block is half a steal because the offense is assumed to recover the ball half the time.

Not a successful possession. I think the metric needs to account for the fact that a player can just shoot and miss. You can make it complicated by throwing in the opponent's eFG, but I think you have it to make it simpler -- change the blocks denominator to 4 and add a steals denominator of 2 (or to make it fancier, take the blocks denominator and multiply it by 1/eFG).

Also, on your replacement level, when you say "The Division 1 averages of each", which "each"? Just steals and blocks? If so, that's OK. But if PORPAG's in there, too, then there's a bit of trouble because the product of two averages is not always the same as the average of the products of individual level scores (example: take 1, 2, 3, 4 and 1, 2, 3, 4). Avg of 1*1 + 2*2 + 3*3 + 4*4 = 30/4, or 7.5. Product of the averages is 2.5 * 2.5, or 6.25.

Also, on your replacement level, when you say "The Division 1 averages of each", which "each"? Just steals and blocks?

Yes.

I suppose I could get really fancy and work further on it to refine the effect of a steal into how many points it really takes off the board by using eFG% for the shots not taken. But if I changed the blocks denominator to 4 and the steals denominator to 2, I would also have to change the replacement-level value by an equal factor (i.e. divide it by two.) Why? Because I can't handicap the effect the actual player has but not the fictitious replacement player. So I'd have to halve the replacement value, and the multiplier would end up being exactly the same.

is skewed to the big guy especially those who can block shots.

Steals is not really a good measure of how good of a defender they are.  Allen Iverson is one of the best in steals but is he a good defender? No.  It does have an effect on defense to some degree but shouldn't be relied upon as a stat.

It's much harder to measure defense than it is on offense because you can see points and assist output as well as FG% plus shots taken.

I think that it'd be interesting to see if there sabermetricians can figure out how to measure defense.  Maybe they can do points allowed, FG% allowed when they have to guard players who is shooting in their area.  Kind of like CB metrics where they used yards allowed, YPA, number of completions, completion % allowed.

Of course it's skewed to guys who can block shots.  That's like saying offensive rating is skewed to guys who can score.  It's a component of the rating.

Snark aside, I don't think the prevalence of big guys at the top of the list is evidence of a bias in the formula toward bigs.  I think it's just an indication of how valuable a shot-blocking, scoring big guy is.  That, and the overall prevalence of scoring bigs in the Big Ten.

A replacement-level guy on offense who is ridiculously good on defense (or vice versa) is worth a lot more than a guy who's replacement level on both ends. I think what you want is additive, maybe something like:

DPORPAG = (avg pace) * %Min * (%Blk/2 + %Stl - 2.45%)

as an estimate of the number of points saved on defense per game played at some average pace (every block, on average, saves half a point since the offense gets half of them back and averages one point on those possessions; steals save a full point since they by definition don't get it back). Then add this to the offensive number.

The other problem, of course, is that there is much more to defense than just blocks and steals; forcing difficult shots, taking charges, rebounding (though that would have to be adjusted on account of position), avoiding fouls are all components of defending well and aren't really accounted for. I don't know a good way to do so, though, so we may be stuck with the simpler version above for now.

I agree that something additive would be ideal, instead of multiplicative.  But I actually did consider something similar to what you have, and discarded it, because min% is already a component of steal% and block%.  So that'd be including min% twice, which I don't think you can do.

The other finalist idea besides this one was:

(Min% / (On-court minus / team points allowed) ) * PORPAG

In other words if you're on the court for more than your fair share of points allowed, it theoretically reflects badly on your defense.  Problematic for several reasons, though, not least because almost all of the multipliers ended up being in a fairly useless .95-1.05 range.  And it really only compares you to your own teammates.  But at least the idea dealt directly with points, which is preferable.

Individual defense, naturally, doesn't lend itself well to statistics.  Fouls could be included, just have something like:

fouls * min% * (whatever factor accounts for the average number of points scored via free throws)

Again, though, I think it'd be too small of a factor to matter.  Rebounds, again - they don't really factor into points denied, because by the time the rebound happens the points are already off the board, and the rebounder probably didn't have anything to do with it.

I'm surprised nobody's hit on what I think might be the Achilles heel of the whole thing, which I thought of about a day after I posted this: a player with a slightly negative PORPAG for his offensive contributions but ridiculously good defensive numbers would still be negative.  I suppose a real statistician would discard the stat right then and there since it can't apply correctly to all players, but maybe I can just lampshade that away by saying offense matters more?  Yes?  Maybe?

Haven't had a chance to look at this in detail, but there actually is a stat called defensive rating.  It looks at the available individual defensive statistics (defensive rebounding %, block%, steal%--the first probably being the most important) and then basically divvies up the rest of defensive team performance (the portion of field goal defense not captured in block%, in particular) into equal chunks based on minutes played (if I'm recalling things correctly).

You'd have to read "Basketball on Paper" for all the details (review linked below).  Unfortunately, I don't think anyone calculates and publishes individual defensive ratings at the college level.

Short of having those ratings available--which would still be a much less reliable indicator than the offensive ratings in terms of pinpointing individual performance--i'd be very hesistant to try to create a comprehensive individual defensive metric.

Finally, if you're trying to value a steal in terms of points prevented, I'd say the correct number is opponents' effective points per possession--i.e. points scored per possession on which the opponent doesn't turn the ball over.  That's usually a number around 1.2-1.3.  But to make the value comparable to a replacement-level player, you'd need a measure of how many steals a replacement-level player produces.

It's quite a mess.  The beauty of PORPAG is that it takes statistics other people have done the heavy lifting on and turns it into a single, more easily interpretable number.