Following up on yesterday’s attempt to invent a statistic, here are the current Points Over Replacement Per Adjusted Game (PORPAG) numbers for the MSU players listed at Kenpom:

Player |
Min% |
OffRtg |
%Poss |
PORPAG |

Lucas | 76.0 | 121.3 | 23.0 | 3.90 |

Morgan | 67.3 | 112.7 | 25.6 | 2.88 |

Allen | 49.8 | 108.9 | 24.0 | 1.70 |

Suton | 35.5 | 123.6 | 17.4 | 1.47 |

Summers | 50.2 | 104.6 | 20.0 | 1.15 |

Walton | 68.8 | 98.1 | 15.3 | 0.76 |

Roe | 41.7 | 99.3 | 20.0 | 0.67 |

Green | 21.7 | 110.6 | 15.2 | 0.51 |

Gray | 33.0 | 99.5 | 18.6 | 0.50 |

Thornton | 10.8 | 109.9 | 17.6 | 0.28 |

Lucious | 20.7 | 91.0 | 24.8 | 0.13 |

Ibok | 16.8 | 78.1 | 8.8 | -0.09 |

TOTAL |
13.86 |

Michigan State’s current (raw) offensive efficiency figure is 112.0. So in a 65-possession game, they’d be expected to score 72.8 points. A team of replacement level players (offensive efficiency=88.0), meanwhile, would be expected to score 57.2 points. That’s a gap of 15.6 points–which is 1.7 points higher than the total PORPAG shown above. That difference must be some function of:

1) Contributions by the guys at the end of the bench (who are actually shooting a combined 7-12 from the field). I think this is probably not too significant.

2) A potential advantage MSU might have in terms of team rebounds on offense, which would be the only offensive stat that doesn’t show up in the individual offensive ratings. This might be significant, but probably doesn’t account for 1.7 points/game.

3) Some missing mathematical piece in the formula I don’t have a grasp of.

Anyway, I think the formula gets pretty darn close to divvying up team offensive performance among individual players–as far as that’s possible, given that basketball is inherently a team sport.

Other notes:

- Together, Kalin Lucas and Raymar Morgan account for almost exactly half of MSU’s performance above replacement level.
- Goran Suton, despite only having played a little over a third of available minutes this season, still ranks 4th in his absolute contributions to the offense.
- Travis Walton, despite ranking second on the team in minutes played, ranks only sixth in PORPAG. The question is whether his defense and leadership makes up for that. My intuitive judgment is that it does, given how well he’s hounded opposing guards this season. (On my to-do list: Compile a game log of offensive performances by opposing team’s top perimeter scoring threats.)

on January 21, 2009 at 1:31 amSpartanDanInteresting. The effect of offensive rebounds has to be figured into the ratings somewhere (I don’t have Basketball on Paper and don’t know the formula, but my guess is that a missed shot probably counts as a fraction of a possession used rather than a full possession like a turnover would to account for the possibility that the shot does not actually end the possession). If this is calculated based on “average” offensive rebounding, then it seems likely that a team with great offensive rebounding will have a better team efficiency than PORPAG suggests and a team with poor offensive rebounding will have a worse team efficiency.

A possible test of this hypothesis would be to do a similar analysis for teams all over the offensive rebounding spectrum and see if there’s a correlation. However, I just did a quick test with Northwestern (who’s about as far from us on the offensive glass as you can get) and came out with a similar-size gap – actually slightly larger (though MSU’s page lists a higher percentage of total minutes than Northwestern’s does – if you add up all the %Min on MSU’s page you get 483.6, while Northwestern’s is 477.2).

Maybe the effect of a potential offensive rebound isn’t factored in at all (which would lead to everyone’s offense being underestimated by this formula to varying degrees). But that doesn’t seem likely, because Indiana’s actually overestimated by nearly a full point (although there are enough possessions and minutes among the players not listed to account for the difference if their rating is really terrible, in the 40-50 range).

on January 21, 2009 at 8:22 amkjOffensive Rating incorporates all the offensive stats: FG/FT shooting, assists, offensive rebounds, turnovers. I don’t fully understand the math, but my intuitive sense is that it does a very good job of capturing the costs/benefits of each stat with the goal of replicating team efficiency at the individual level.

I’ll have to think this through some more.

on January 21, 2009 at 10:42 ambigtengeekKJ,

I like the idea of this stat (especially the replacement-level thinking), but there’s one area in which it needs to be modified – though I’m not sure how. When a guy takes 27% of the available shots, for instance, he isn’t just racking up more PORPAG on those 7%, he’s making things easier for his teammates, who are being asked to shoot less (and thus, they shoot better). Conversely, the guy who takes 13% of the available shots isn’t just missing out on 7% of PORPAG, he’s making things tougher on his teammates, forcing them to shoot because he won’t.

I’m not sure how to account for this, but I like this start. Well done.

on January 21, 2009 at 4:32 pmSpartanDanThat effect is really difficult to quantify (how much does a player’s contribution improve because someone else is taking the hard shots?), and I’m not sure it can be done without sacrificing the intuitive value behind the formula’s simplicity (which is basically an estimate of how many points you gain by having that player on offense instead of a random 9th or 10th man).

I think you’ll find that effect in the numbers anyway, to an extent. You may be lowering your ORtg by taking the “hard” possessions, but the boost to your usage rate (unless you’re extremely inefficient in those extra possessions) will outweigh that and PORPAG goes up. You’re boosting your teammates’ ORtgs by taking the hard shots yourself so they don’t have to, but at the same time that drops their usage rates and (unless they would be replacement-level or worse on those marginal possessions) the net effect is to reduce their PORPAG.

You could make the case that “replacement level” on those marginal possessions is lower. There might be some truth to that, but at the same time it’s not always the high-usage players that get the toughest possessions. Last year, for instance, Neitzel was only fifth on the team in usage rate – and he probably took more of the hard shots than anyone.

One possible tweak is in determining what the best “replacement level” is. A lower level sets a higher emphasis on usage (at 88, 101/27% and 115/13% are equivalent, at 1.825 for 80% minutes; bump replacement level down to 75, and 101/27% is now equal to 129/13% at 3.65 for 80% minutes). I’m a little leery of formula tweaks that involve messing around with the usage rate component, though – an offset like with ORtg runs into the issue that an extremely low-rating, low-usage player could actually get a large positive rating (from the product of two negatives), and putting an exponent on the usage factor loses the simplicity behind the interpretation of the number.