PORPAG
Points Over Replacement Per Adjusted Game
Baseball statistics were my first love, so I thought it would be fun to cook up something as obscure as VORP or BABIP.
But let’s back up:
There was some conversation following my last scatterplot post about how to appropriately interpret the graph in terms of which players have played most effectively on offense. The individual player offensive rating/usage rate scatterplot isn’t as easy to interpret as the team offensive/defensive efficiency scatterplot.
With offensive rating and usage rate, you really need to multiply the two numbers together (as opposed to subtracting defensive efficiency from offensive efficiency to get efficiency margin). Taking this concept a bit further, SpartanDan came up with the following:
I wonder if the best measure might be something like (ORtg – 90) * (%Poss), somewhat analogous to baseball’s VORP (value over replacement player). Not many players below 90 get significant playing time in the major conferences (in the Big Ten, there are eight with 30% or higher minutes and below-90 ORtg, but five play for Indiana), so 90 might be considered “replacement level”. This formula would give the increase in team points per 100 possessions relative to having a player with ORtg 90 taking all of your possessions.
Breaking this down mathematically:
- Offensive rating (OffRtg) is basically points produced per 100 possessions used.
- Usage rate (%Poss) is possessions used per 100 possessions played.
- So multiplying the two gets you points produced per 100 possessions played.
- By using (Offensive rating minus 90), you get points over replacement level per 100 possessions played.
So far, all the credit here goes to SpartanDan.
Here’s my addition: If you want to look at which players have contributed the most marginal offensive value for their teams, you really want an absolute value, not a rate statistic. If Player A can play 35 minutes per game at a given efficiency/usage level, while Player B plays only 25 minutes per game at the same levels, Player A is contributing more to his team’s efforts to win a given game, since Player B’s team has to find another player (presumably a less efficient one) to play the extra 10 minutes.
Here’s the equation for PORPAG:
(OffRtg – 88) * %Poss * Min% *65
Notes:
- I’ve tweaked “replacement level” down to 88. That’s the average of the 9th best offensive rating on each Big Ten roster at the moment. (In some cases, the 9th best rating was really, really low, in which case I subtracted 5 from the 8th best rating.)
- Min% is the percentage of a team’s total minutes a player has played. Games missed due to injury drive that percentage down.
- 65 is the current average adjusted tempo for the 11 Big Ten teams.
If my math is correct, this equation gets you something like “Marginal offensive points contributed per game, accounting for a team’s average pace.”
Caveats:
- Offensive rating accounts for basically all the offensive statistics we have, but can’t cover everything that happens on the court (setting picks, intangibles, etc.).
- The numbers obviously say nothing at all about a player’s defensive contributions.
- The “replacement level” concept works better in baseball–where swapping out one player for another in the batting lineup or pitching rotation is a pretty simple change–than it does in basketball–where swapping one player for another alters the team’s on-court dynamics. But that’s the nature of basketball statistics.
- We’re using data for both nonconference and conference games, so the numbers reflect individual offensive performances against differing levels of opposition. Ideally, we’d do this at the end of the year using conference-only data (at which time we’d want to revisit the replacement-level/average-pace assumptions).
OK, so here’s what this approach gets us. I’ve calculated PORPAG for the top 30 per-game scorers in the league:
| Player | Min% | OffRtg | %Poss | PORPAG |
| Battle (PSU) | 91.6 | 121.5 | 26.6 | 5.46 |
| Harris (MICH) | 81.2 | 113.0 | 32.5 | 4.46 |
| Lucas (MSU) | 76.0 | 121.3 | 23.0 | 3.90 |
| Gatens (IOWA) | 78.2 | 127.2 | 18.9 | 3.86 |
| Pringle (PSU) | 69.6 | 121.3 | 23.0 | 3.57 |
| Sims (MICH) | 76.8 | 115.8 | 24.8 | 3.57 |
| Hummel (PUR) | 63.5 | 125.7 | 20.8 | 3.32 |
| Meachem (ILL) | 75.7 | 128.1 | 16.4 | 3.32 |
| Moore (NW) | 87.7 | 117.2 | 18.5 | 3.18 |
| Hughes (WIS) | 77.1 | 114.9 | 21.6 | 3.02 |
| Turner (OSU) | 84.8 | 106.5 | 27.3 | 2.93 |
| Morgan (MSU) | 67.3 | 112.7 | 25.6 | 2.88 |
| Bohannon (WIS) | 77.2 | 115.7 | 19.5 | 2.81 |
| Johnson (PUR) | 60.5 | 117.6 | 23.3 | 2.80 |
| Coble (NW) | 84.4 | 109.7 | 22.4 | 2.79 |
| Landry (WIS) | 77.1 | 110.1 | 23.1 | 2.67 |
| Davis (ILL) | 70.5 | 111.6 | 20.9 | 2.36 |
| Peterson (IOWA) | 78.5 | 105.5 | 23.3 | 2.20 |
| Diebler (OSU) | 83.9 | 109.3 | 17.7 | 2.15 |
| McCamey (ILL) | 71.4 | 104.9 | 24.6 | 2.04 |
| Westbrook (MIN) | 54.1 | 107.6 | 27.3 | 1.98 |
| Cornley (PSU) | 85.0 | 102.5 | 22.6 | 1.94 |
| Leuer (WIS) | 48.2 | 107.2 | 28.3 | 1.79 |
| Tucker (IOWA) | 39.9 | 115.3 | 23.8 | 1.75 |
| Buford (OSU) | 55.9 | 107.8 | 22.7 | 1.72 |
| Allen (MSU) | 49.8 | 108.9 | 24.0 | 1.70 |
| Tisdale (ILL) | 57.7 | 103.5 | 24.5 | 1.52 |
| Pritchard (IU) | 73.6 | 98.0 | 24.6 | 1.29 |
| Moore (PUR) | 78.5 | 95.7 | 26.3 | 1.17 |
| Dumes (IU) | 70.2 | 89.0 | 26.9 | 0.25 |
I think these results are, for the most part, pretty intuitive. Talor Battle, Manny Harris, and Kalin Lucas would be at the top of almost everyone”s player of the year ballots right now. Remove any of them from their respective teams’ lineups and you’d expect team scoring to go down by 4-5 points per game.
At the other end of the list, removing E’Twaun Moore (the way he’s been playing this season, at least) or Devan Dumes from their team’s lineups would have a pretty negligible impact.
If anything, the system probably overvalues offensive rating relative to usage rate. Matt Gatens, Stanley Pringle, Trent Meachem, and Craig Moore all rank in the top ten on this list largely because they’re good 3-point shooters (although Pringle’s got a healthy usage rate). It’s hard to separate out how much credit should to go the 3-point shooters versus the other guys on the team who set the picks and made the passes to get them the open looks.
Meanwhile, Evan Turner and Raymar Morgan–two players with decent, but not great, offensive ratings and pretty high usage rates–slide down the ladder relative to their per-game scoring averages. The preseason conference player of the year, Robbie Hummel, doesn’t rank in the top five as a result of the minutes he’s missed due to back problems.
Anyway, I’ll be interested to hear if these statistical gymnastics make sense to others. On one hand, one hates to manipulate tempo-free stats too much. I think the main reason that advanced basketball stats have caught on in the mainstream more quickly than advanced baseball or football stats is that they’re more elegant. On the other hand, I think the result of the manipulations we’ve done here is a pretty intuitive one, answering the question “How much is this guy contributing on offense each game?”
Final note: To the extent there’s value here, the bulk of the credit goes to Dan. And, as the academics say, the responsibility for any errors rests solely with the author.
Update: I’d forgotten that Dean Oliver calculates individual win-loss records in “Basketball on Paper” (using a more complex methodology that looks at defense, too). Here’s an explanation of calculating “Win Shares” for the NBA. And here’s an ACC blogger who developed a formula for calculating Wins Over Replacement Player. So others have attempted to cross this river before.
Personally, I like the points-based stat; pushing things to the win-loss level seems a bit too much at the college level, where the quality of your opponents varies so much across the season. And there are, of course, issues with individual defensive ratings; beyond steals and blocks, you’re basically just divvying up team defensive performance.
Seems reasonable. Any concerns about multicollinearity with %poss and %min. One would think that a player playing more minutes would also have the opportunity for more possessions.
Quite interesting. While I understand the concerns about making this more complicated, I wonder if there is a way to incorporate “Assist Rate” into the calculations to make this a true measure of offensive value (rather than just point scoring value).
I really don’t like the sole focus on points in terms of offensive contributions. In many cases the person that drives to the basket, pulling the defense, and then dishing out to the scorer adds more to the team than the person that waits on the three point line for the pass and shoots an unchallenged shot.
This would address your point about how to differentiate the 3-point shooters from the real offensive weapons, because the more complete offensive players will also have high assist rates.
Now, I’ll leave the part about how to incorporate that into the formula (or even if it is possible), to the statistics wizards…
Of course, if you were to follow up on my recommendation, you would have to rename your measure to OORPAG (Offense Over Replacement Per Adjusted Game)
1. See the update at the bottom of the post for information on previous attempts to do something like this.
2. GBBound: The Min% factor just reduces the possessions/game figure to account for how much of the game a player is on the floor. So I don’t think there’s any issue in terms of an interaction with usage rate.
3. Tuxster: I’m 99% sure that Offensive Rating incorporates assist rate (as well as offensive rebounding%), although I have to confess I don’t fully understand the rating–despite reading the appendix to Oliver’s book multiple times. There’s a calculation in terms of figuring out how many points an assist or offensive rebound is equivalent to on a given team.
Using %Min seems to be a useful tweak, though I think in the case of players who sat out for a while with injuries it can be misleading. Pomeroy’s site does list number of games played along with %Min, which can help account for this. (For instance, through January 11th Suton played in 10 of 15 games; we can adjust for this by multiplying his %Min by 15/10 to get the %Min in games played.) This tweak pushes Hummel back up to 3.70, good for 5th place.
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