Thursday, February 17, 2011

basketball mathitude

One of the neat things about basketball is that, after baseball, it's the sport that best lends itself to cold, hard statistical breakdowns and the creation of fancy sabermetric stats - in hoops, they're called "APBRmetrics," which hasn't caught on like "sabermetrics" because it needs either more vowels or friendlier consonants to be reasonably pronouncable.

One stat that I like actually comes to you not from the usual suspects like Ken Pomeroy, but from Michigan State blog The Only Colors. (Technically they didn't come up with it, someone else did that lets TOC use it, but I saw it at TOC first and you can follow the credit chain all the way back to the beginning if you like.) They call it PORPAG: Points Over Replacement Per Adjusted Game. Follow the links all the way back for the full explanation; here's the summary (you may already know this stuff if you're a hoops math geek, or maybe not):

- It's like baseball's VORP; it tabulates how many points a player is worth over a "replacement" player - not "average", but "replacement", which is actually below average. Replacement = a guy you can get just about anywhere.

- The equation is thus: (Off.Rtg - 88) * Min% * Poss% * Pace

The stats can be found at KenPom or at StatSheet. Offensive rating is a creation of way smarter people than you or I that tells you how many points a player produces per 100 possessions. 88, because that's what they decided was replacement level. "Min%" is the percentage of available minutes in the season (40 * games) that a player has played. "Poss%" is the percentage of possessions a player ends while on the floor - ends, by either taking a shot or turning the ball over. "Pace", if you followed the links, is .62 because the average Big Ten game has 62 possessions. I used .65, because the ACC moves a little faster.

- The reasoning is that offensive rating is points per 100 possessions, so taking into account only the possessions actually used by the player (poss%), the minutes he's actually on the court (min%), and the number of possessions in a game, you get an approximation of how many points the player is worth per game, over someone you could just pull off the street (well, the recruiting trail, anyway) with no effort. Simple.

- The stat does nothing for defense, nor does it account for the interaction between players, chemistry on the court, etc.

Using .65 for the pace factor, and keeping the replacement-level 88 the same, here are the PORPAGs for all ACC players with over 30% of minutes played, except for those who sustained season-ending injuries early in the year (Mike Scott, Dorenzo Hudson.)

To save you a click, the top 10 are:

Reggie Jackson (BC)
Nolan Smith (Duke)
Malcolm Delaney (VT)
Kyle Singler (Duke)
Malcolm Grant (Miami)
Corey Raji (BC)
Reggie Johnson (Miami)
Jerai Grant (Clemson)
Jordan Williams (Maryland)
Tyler Zeller (UNC)

And UVA's guys:

#21- Mustapha Farrakhan - 2.05
#33 - Joe Harris - 1.59
#39 - KT Harrell - 1.24
#63 - Sammy Zeglinski - 0.53
#68 - Will Sherrill - 0.44
#86 - Assane Sene - 0.07
#87 - Jontel Evans - 0.04
#88 - Akil Mitchell - -0.01

So you see why we lose so much.

The point originally was to apply something useful someone else had done to the ACC. But I wasn't quite satisfied. Must be a way, I figured, to bring defense into the equation somehow, but nobody's ever come up with a defensive rating for individual players. I racked my brain, fiddled with numbers, and came up with this:

PORPAG * ( ( (Block% /2) + Steal %) / 2.45)

That's a lot of parentheses. Here's the thinking:

- Blocks and steals are the player's way of taking points off the board for the other team.

- The average team offensive rating is about 101, so essentially, teams average a point per possession. Possessions are, most of the time, either two or zero points, though. One point is about as common as three. So when you come up with a steal, you took two points off the board. A block would also be two, but roughly half the time the offensive team ends up with the ball again and the possession doesn't end. So I went with the assumption that a block takes one point off the board.

- One problem with defense is that certain stats (rebounds, blocks) lend themselves toward big men; and steals, toward guards. I left off rebounds because they generally have nothing to do with who caused the miss. This, plus the dividing of blocks in two, keeps big men from dominating the stat.

- Block percentage and steal percentage are explained here. I'm not gonna get deep into them, but suffice it to say they're basically the percentage of possessions which a player is on the floor for that he comes up with a block or a steal, respectively.

- "Replacement level" is 2.45. I came up with this by:

- Starting with the national average team block and steal percentage (9.2 and 9.5, respectively.)
- Dividing each by 5, because there are five players on a court (1.84, 1.9.)
- Multiplying again by .87, because that is 88/101 - the replacement level offensive rating divided by the average (1.6, 1.65.)
- Dividing the block percentage by 2, because of the reasons stated above (0.8, 1.65.)
- Add together for 2.45.

Divide a player's (block% + steal%) by 2.45 and you get a multiplier to apply to his PORPAG. This approximates adding his defensive contributions to his offensive ones. This is, for lack of a better phrase, enhanced PORPAG. EPORPAG. Acronyms should probably not have three syllables in them, but screw it. The new chart:

I'm as surprised as you are about the top player, but consider: Grant blocks 10% of opponent's shots that occur while he's on the floor. That's a crazy number. And that's a big steal percentage for a shot-blocker. Is he worth 9, almost 10 extra points to his team? Yeah, maybe.

Despite the presence of a lesser-known (and heretofore referred to as "wicked underrated") player on the top of the chart, I think this passes the sanity test. Look at Chris Singleton, considered one of the top players in the league. DPOY. He goes, from a middling nobody under PORPAG (less valuable than Mu Farrakhan) to one of the league's top players again under EPORPAG. Offensive dynamos - the guys that get the headlines - still get their due credit. Jackson and Smith are still way up there. Delaney, not as much, because he's not too far above average on defense. Iman Shumpert gets his due for being a steals fiend.

The problem is that it's kinda fishy the closer you get to zero PORPAG. A guy like Assane Sene, who blocks a zillion shots, still doesn't quite get his due for it because he's a stiff on offense. Theoretically, a guy could be exactly replacement-level on offense and block 100% of shots on defense and he'd still be replacement-level. And this still says nothing about on-court chemistry, and good off-ball defenders still don't get their due because their guys don't get the ball. Like a cornerback that quarterbacks never throw at. (But this is a stats-based thing, and there will never be a stat for good off-ball defending.)

So there are still limitations, just as there were with the original. But this is why coaches run the show and not statisticians. I think in general, the limitations with this as a new stat are limitations with statistics themselves, and not this one in particular, which is as good as I can hope for. And I think ultimately, I've taken a good thing and made it better.


Anonymous said...

Looking at Akil Mitchell's two negative ratings certainly makes me feel better about leaving James Johnson's redshirt in place.

Dave said...

"The average team offensive rating is about 101, so essentially, teams average a point per possession. Possessions are, most of the time, either two or zero points, though. One point is about as common as three. So when you come up with a steal, you took two points off the board."

I don't follow this logic. A steal takes away a possession; a possession is worth 1 point, on average; therefore a steal takes one point off the board, not two.

True, few possessions end in exactly one point, but we're dealing in averages. So in short, you're over-counting steals (and blocks).

If you want to not recalculate your metric (and I wouldn't blame you), leave it the same but argue that: "Every steal is itself worth ~1 point, but a steal is also strongly correlated with not-directly-measurable strong defensive play (which results in forcing bad shots, etc.). To give credit for that defensive play, I'll just apply a 2x multiplier to steals." Similarly for blocks.

Overall, I do like your improvement on the metric -- I just want it to be better justified...

Brendan said...

Well, look at it this way: If I'm overcounting both steals and blocks, then the replacement-level number of 2.45 is also too high. If I were to cut the value of steals and blocks in half, I'd also have to cut the replacement-level value in half for the same reason, and I'd end up with the same multiplier.

Anyway, maybe this is a better explanation. The average possession is one point because a successful possession is two points. A steal prevents the offense from having a successful possession, not an average possession. Therefore it's worth two points. A block is half a steal because the offense recovers half the time.

The time to apply the logic that taking away a possession results in taking one point off the board is in a situation where you prevent the possession from ever happening in the first place - such as by slowing the pace down. Once the possession has begun, the outcome is assumed to be binary - either zero or two.

Dave said...

A steal ends an average possession, not a successful one. Sometimes when you steal the ball, you've ended a possession that wasn't going to result in points anyway. The other team was going to miss the shot, dribble it off their foot, or throw an errant pass. And sometimes when you steal the ball, you've ended a possession that *was* going to result in points. On average, those two binary outcomes work out to ~1 point per possession ended by steal.

I won't belabor the point further, because after all, we just swept VPI and ruined their NCAA bid, so what else matters, really?