Player Effectiveness Formula

[cspan37421]

Back in the good old days (that is, when Barry Jacobs published his Fans' Guide to ACC Basketball), each player was evaluated according to a formula that took into account shooting percentages (from the field and the line), turnovers, steals, assists, etc., per minute played - thus putting starters and subs on a level playing field, statistically. IIRC, he credited the formula (or an earlier version of it) to a Georgia Tech assistant coach (prob. under Cremins). Unfortunately my Fans' guides are gone.

If anyone remembers what the formula is, please post in a reply.

Thanks,

cspan

[The Gordog]

Back in the good old days (that is, when Barry Jacobs published his Fans' Guide to ACC Basketball), each player was evaluated according to a formula that took into account shooting percentages (from the field and the line), turnovers, steals, assists, etc., per minute played - thus putting starters and subs on a level playing field, statistically. IIRC, he credited the formula (or an earlier version of it) to a Georgia Tech assistant coach (prob. under Cremins). Unfortunately my Fans' guides are gone.

If anyone remembers what the formula is, please post in a reply.

Thanks,

cspan

This is from memory, but here goes.

(points scored + rebounds + assists + steals + blocks + charges taken(if the stat is available) - turnovers - fouls)/minutes played per game. That's it!

[ACCBBallFan]

That formula would be decent for comparing players at the same position. However it skews things in favor of bigs and should not be used to compare a post player to a perimeter player.

Here’s how Duke players would score per 40minue game using this formula:

NAME Formula(40min) MIN PTS REB AST TO STL BLK PF

Josh McRoberts
26.28895184 35.3 13.0 7.9 3.5 2 1.2 2.5 3
Demarcus Nelson
23.19749216 31.9 14.1 5.4 2.0 3 1.3 0.5 2
Brian Zoubek
19.17808219 7.3 3.1 2.2 0.2 1 0.1 0.3 1
Gerald Henderson
18.44559585 19.3 6.8 2.9 1.1 1 0.5 0.3 1
Jon Scheyer
18.27893175 33.7 12.2 3.3 1.8 2 1.2 0.2 2
Greg Paulus
16.2962963 32.4 11.8 2.2 3.8 3 1.2 0.1 3
David McClure
15.11520737 21.7 4.2 4.9 0.5 1 1.2 0.7 2
Lance Thomas
8.053691275 14.9 4.0 2.5 0.0 1 0.5 0.1 3
Martynas Pocius
7.323943662 7.1 1.9 0.6 0.3 1 0.1 0.0 1

[riverside6]

Jacobs formula is basically what my ACC fantasy league uses for fantasy scoring without dividing by minutes played, and I think it's pretty fair.

That being said, if you want a formula to equate players, check the Efficiency Numbers on my site or Ken Pomeroy's site.

That being said, that formula is a nightmare and you won't see me typing it up here.

[cspan37421]

This is from memory, but here goes.

(points scored + rebounds + assists + steals + blocks + charges taken(if the stat is available) - turnovers - fouls)/minutes played per game. That's it!

Thanks; however, the one I remember was a bit more involved than that. It resulted in a ratio that increased for free-throw percentage over 75% and decreased if under. I think it also took into account 2-pt FG% and later, 3-pt FG% (maybe saying you should make 50% of your 2s and 33% of your 3s). So it didn't just add up points, even per minute played. Thus, someone who goes 6-22 from the field (let's say all 2s) and 10-18 from the line would not have as high ratio as someone who went 6-11 from the field and 10-13 from the line.

Maybe I'll have to re-create it. But the numerator more or less translated in to points. So a rebound or steal might be worth 1 point (b/c you get your team another shot at the basket, which should roughly be 50% from a 2 or 33% from a 3. [BTW I am aware that 50% for a 2 is generous these days - but that's about how it worked]. I can recall what assists were worth, though.

Anyway I guess everyone can make their own. I had hoped to find this one particular formula - I thought it captured things pretty well. Also, in light of the recent discussions on Laettner, I wanted to compare him with Bill Bradley.

Some stats aren't readily available on Bradley but just using points, rebounds, and assists, all per minute played, Laettner comes out ahead, 0.74 to 0.62 by my calcs. Both had one all-star appearance. Both were excellent free throw shooters (adv. Bradley) and accurate jump shooters (adv. Laettner). Bradley played on 2 NBA championship teams, and that seems to be the difference. Bradley got in the NBA hall of fame in his first year of eligibility. Laettner - well, I've never heard it suggested he belongs there - though posters here point out that had he not been injured, ....

[The Gordog]

That formula would be decent for comparing players at the same position. However it skews things in favor of bigs and should not be used to compare a post player to a perimeter player.



I'm not sure why you would say it favors bigs. Would elaborate on that?

[g_olaf]

Similarly, the NBA gives efficiency ratings as:

Points+Rebounds+steals+blocks-Turnovers - FT missed - FG missed.

This works pretty well, as it punishes low shooting percentages.

[johnb]

I didn't remember the formula, but I really liked Jacobs' use of it.

And it reveals the team that K seemed to think he had. In other words, Josh was the best player, but all of the starters and semi-starters had remarkably similar scores. Marty and Lance--while guys with great potential and presumably sparkling personalities--didn't deserve as much time as the rest of the gang (but there is always next year).

[-jk]

I pulled my '87 Barry Jacobs Fan's Guide, with Amaker, Bogues, Hammonds and Smith (recently of the World Games) on the cover. In short shorts.

Barry credited Tech coach Dwane Morrison, "among others", for the formula.

The specifics include (using season totals, not averages):

Plus one point for each of blocked shots, rebounds, assists, and steals.

Minus one point for each of personal fouls and turnovers.

Field Goal points were calculated by (FGs Made)/0.5 - (FG Attempts)
*Presumably three's would be (3s made)/0.333 - (3s Attempts)

Free Throw points were calculated by (FTs Made)/0.75 - (FT Attempts)

Jacobs also added the player's scoring average to those total points, then divided the new total number of points by total minutes played to get a "rating". Pretty much anyone with a positive rating was an asset.

Horace Grant, with a rating of .333, was the best returning player in the conference in '87. Here's some context:

Tommy Amaker .183
Danny Ferry .128
Billy King .076
The original "Marty doesn't foul" Nessley -.100, but in fewer than 200 minutes.

Joe Wolf .228
Kenny Smith .202

Chas Shackleford .142

Muggsy Bogues .209

Duane Ferrell .212
Bruce Dalrymple .186
Tom Hammonds .199

-jk

[ACCBBallFan]

I'm not sure why you would say it favors bigs. Would elaborate on that?

Since equal weight is given to all categories, the formula favors bigs since it is much more common for a big to grab more than 5 rebounds than it is for a guard to dole out more than 5 assists.

Since fouls max out a 5 per game that is not a big differentiator, and does not vary all that much by position anyway.

Bigs tend to have a worse assist to turnover ratio, but since guards handle the ball more, the number of turnovers is usually pretty close.

Though Zoubek scored high on the formula, K chooses not to play him, perhaps because the formula does not take into account matador defense; fouls yes, but back doors with no one close no.

If you apply the formula to Duke totals

Duke totals 18.70333988 203.6 71.1 31.9 13.2 15.4 7.3 4.7 17.6

and the only players who score above the average are McRoberts, Nelson and Zoubek.

The UNC bigs also score higher:

NAME NAME MIN PTS REB AST TO STL BLK PF
Tyler Hansbrough 33.04347826 29.9 18.4 7.9 1.2 1.9 1.1 0.4 2.4
Brandan Wright 31.53284672 27.4 14.7 6.2 1.0 1.6 1.0 1.8 1.5
Reyshawn Terry 26.23255814 21.5 9.7 5.4 1.7 1.8 0.7 0.6 2.2
Wayne Ellington 25.10460251 23.9 11.7 2.9 2.1 1.2 0.8 0.0 1.3
Ty Lawson 24.43579767 25.7 10.2 2.9 5.6 2.2 1.5 0.1 2.4
Danny Green 24.11764706 13.6 5.2 2.8 1.1 0.8 0.6 0.7 1.4
Alex Stepheson 21.875 6.4 2.1 2.2 0.1 0.4 0.0 0.3 0.8
UNC totals 20.5334728 382.4 147.5 64.5 23.8 28.3 13.9 8.4 33.5
Deon Thompson 18.38709677 12.4 4.7 2.4 0.4 0.9 0.5 0.4 1.8
Marcus Ginyard 17.75147929 16.9 4.1 3.2 1.5 1.1 1.1 0.1 1.4
Bobby Frasor 14.25742574 10.1 2.4 0.7 1.6 0.8 0.5 0.0 0.8
Wes Miller 12.45283019 10.6 2.5 0.5 1.1 0.4 0.3 0.0 0.7

[-jk]

I would submit the game of basketball, prima facie, favors Bigs.

Hence the adage, "You can't coach height", our lust for Patrick Patterson, etc. (cf. 1F on Throatybeard's reference (http://www.duke.edu/~bct1/images/DBRHPR7.1asPDF.pdf)).

;)

-jk

[cspan37421]

-jk: THANK YOU! That's the one.

I had 3 Fans' guides over the years. IIRC Laettner shared the cover on one of them, wearing road royal blue. I forget who else was on there. Kenny Anderson maybe? And one of my favorites had a picture of Jacobs' head that made it look disembodied, and almost like a basketball on a court. Funny.

[darthur]

I would submit the game of basketball, prima facie, favors Bigs.

Can a team with 5 big men actually do well? Hint: No. Can a team with 0 big men actually do well? Hint: Yes (exhibit: Golden State). And so, how can you say big men are "better" than guards?

I also hate these systems, particularly with regards to the rebounds. A very average big man will pull down around 8 rebounds a game just because he is parked under the basket. Meanwhile, the point guard who never crashes the offensive boards because he is staying back to defend the fast break gets penalized. When someone truly excels for their position (eg DeMarcus Nelson), that's really good, but you shouldn't get huge bonus points just because you are the designated under-the-basket guy for your team (eg Josh McRoberts).

The penalty for fouls is also stupid IMO. Fouls on defense are often very good - they come from a help defender stopping an easy layup.

Anyway, even sophisticated versions of these stats suck. Just look at the PER ratings that the ESPN NBA page keeps touting. Steve Nash is going to just miss threepeating as MVP this season, and he is something like the 30th best player in the NBA? Riiiight...

[BobbyFan]

Anyway, even sophisticated versions of these stats suck. Just look at the PER ratings that the ESPN NBA page keeps touting. Steve Nash is going to just miss threepeating as MVP this season, and he is something like the 30th best player in the NBA? Riiiight...

Player efficiency ratings are an excellent tool; they hardly "suck". It has it's limitations, which are accepted.

And Nash doesn't have the 30th best PER in the league - it is much higher than that. He also doesn't have a top 5 PER either, probably because he isn't a top 5 player. He isn't as good as his MVP awards would suggest.

[cspan37421]

Anyway, even sophisticated versions of these stats suck.

So if you were a GM, what non-statistical tool would you use to evaluate players? Looks? Skin color? Do tell.

[darthur]

So if you were a GM, what non-statistical tool would you use to evaluate players? Looks? Skin color? Do tell.

Yes, yes, "suck" was too strong a word. However, I would *never* use a player effeciency rating in the way ESPN does (e.g., deciding whether the league's best point guard is better than the league's best power forward).

Even if I was a GM forced to make a personnel decision, I'd be very leery of these stats. Much more interesting would be the simple ones: points per minute, rebounds per minute, etc. I know exactly what those mean, and I can decide for myself on a case-by-case basis what role I need, and how much I care about each stat. After all, why does, say, an assist count for +1 instead of +2 like it sometimes does in fantasy leagues? Changing that would make a big difference.

I never said I had a problem with stats in general - just with meta-stats that try to rank the overall goodness of all players.

[darthur]

Player efficiency ratings are an excellent tool; they hardly "suck". It has it's limitations, which are accepted.

And Nash doesn't have the 30th best PER in the league - it is much higher than that. He also doesn't have a top 5 PER either, probably because he isn't a top 5 player. He isn't as good as his MVP awards would suggest.

See my last post about the "suck" comment.

As for PER and Steve Nash: I am not an Insider so I do not know what his current PER ranking is, but I am pretty sure it was around 30 the last time I saw it displayed on ESPN. As for his "real" ranking, you are entitled to your opinion, but I (and apparently most journalists) strongly disagree with you. Nash is by far the top in assists in the league, his shooting efficiency is unreal for a guard, and somehow his acquisition transformed Phoenix from a middling team to a powerhouse. And coincidentally, while he was injured this year, Phoenix reverted to a middling team.

[BobbyFan]

Even if I was a GM forced to make a personnel decision, I'd be very leery of these stats. Much more interesting would be the simple ones: points per minute, rebounds per minute, etc. I know exactly what those mean, and I can decide for myself on a case-by-case basis what role I need, and how much I care about each stat.

Points per minute doesn't account for pace or shooting efficiency. Rebounds per minute also doesn't take into account pace nor the number of rebounds available. TS%, rebound rate do take these factors into account and these stats are factored into PER. Simply put, PER is by far the single best statistical measure available to evaluate an individual player. Sure you can deal with basic stats on a case-by-case basis, but you will inevitably create inconsistencies which will diminish the value of your end result.


As for PER and Steve Nash: I am not an Insider so I do not know what his current PER ranking is, but I am pretty sure it was around 30 the last time I saw it displayed on ESPN.

Nash's PER has consistently been around 10-15 for this season, not including the first few weeks when were obviously higher variations.


As for his "real" ranking, you are entitled to your opinion, but I (and apparently most journalists) strongly disagree with you. Nash is by far the top in assists in the league, his shooting efficiency is unreal for a guard, and somehow his acquisition transformed Phoenix from a middling team to a powerhouse.

It wasn't just Nash's acquisition that transformed Phoenix. It was also the addition of Richardson, continued improvement of a young Amare (and Amare not missing extensive time due to injury which occured the year before Nash arrived), and the lack of a need to rely on players like Voskhul and Penny for significant minutes. By the same line of reasoning, what does it say that Dallas became a better team after letting Nash go?

I agree that Nash is the league's best passer and that his efficiency is terrific. But he is also a larger liability on the defensive end than any of the other league's superstars.

And I could care less what journalists think; I've read their material and I've heard their opinions and it's obvious that many don't watch games on a regular basis. It's a shame that some of them are allowed to vote on significant awards. Dedicated message boards like this one provide much better material.

[darthur]

Points per minute doesn't account for pace or shooting efficiency. Rebounds per minute also doesn't take into account pace nor the number of rebounds available. TS%, rebound rate do take these factors into account and these stats are factored into PER. Simply put, PER is by far the single best statistical measure available to evaluate an individual player. Sure you can deal with basic stats on a case-by-case basis, but you will inevitably create inconsistencies which will diminish the value of your end result.

Let's just agree to disagree on Nash since that was never the main point anyway.

As for PER, I agree that it's one of the most sophisticated statistical measures for evaluating an individual player. However, I do not take it as a given that this makes it the best - having worked in AI and stats, I know for a fact that accounting for more things is never a guaranteed improvement. More importantly, and this was my original point, I think it is unreasonable to look for a *single* stat to evaluate player performance. And the main reason continues to be different players have very different roles. Who is John Hollinger to say that the role of rebounding is worth X goodness points, the role of scoring is worth Y goodness points, and the role of staying back to defend the fast break is worth Z goodness points? In reality, the importance of these roles (a) is impossible to just guess, and (b) varies from team to team.

You are telling me PER is the best single stat for evaluating all players, and all you are doing is reinforcing my belief that it is impossible to come up with a good single stat to evaluate all players.

[cspan37421]

While "per minute" formulas may not account for the pace of the game, they're the best we've got in terms of evaluating someone like JJ Redick, whose per-game totals are meager but that's largely due to meager playing time.

[The Gordog]

I don't understand this part:

"Field Goal points were calculated by (FGs Made)/0.5 - (FG Attempts)"

If player X made 6 ot of 10 shots per game he would have

6 / .5 - 10 = 3 - 10 = -7 ???

[cspan37421]

Divide by 0.5, don't multiply. In your example, if player X went 6-for-10 from 2-pt range, you get:

6 / 0.5 - 10 = 12 - 10 = +2.

So you get positive numbers when you shoot over 50%. These days, 50% from 2-pt range is maybe setting the bar a little high - I doubt the average 2-pt percentage is that high. Probably about 45% I would guess. In that case you could argue that you divide 2-pt shots made by 0.45 and then subtract attempts, to see if the player is contributing or detracting w/r/t their shooting.

Note that with 3-pointers you divide by 0.333. So JJ, who shot 0.388 for 3-pointers in his rookie season, was a plus with respect to 3-pt shooting. IIRC Laettner did not shoot over 33% from downtown so his 3-pt shooting (in the NBA) was not a plus for his overall game.

[mepanchin]

Tempo-free stats are the best kind of stats to use in evaluating a player or team, but combining all stats into one super stat like player efficiency is misleading because every statistician weighs stats differently. The better way to evaluate players is to look at stats like eFG% (field goal percentage giving greater weight to 3 pointers made since they are worth 50% more points), TO% (percentage of possessions they turn the ball over), OR% and DR% (percentage of rebounds pulled down while on the floor), FT Rate (number of free throws made per field goal attempt). There is an amalgamated stat called offensive rating which is the amount of points a player is projected to score in 100 possessions, which takes into account eFG%, TO%, and FT Rate.

[cspan37421]

That may be true but possession stats are not as easy to come by. If you're the team statistician, yes you might do a Stats, Inc. level analysis, either analyzing every possession and crunching the numbers yourself, or paying a subscription fee. For some that is overkill. Per-minute played stats are a nice middle ground for looking beyond pure averages and having intelligent to say about a player's ability when called upon.

Don't NHL teams keep +1 and -1 type stats on players that are on the ice when one team scores? I don't know much about it but I get the impression that it provides a kind of stat that indicates whether the team plays better or worse when they're in. Maybe it wouldn't work for basketball - or would be redundant b/c of stats like turnovers and so forth.

[ikiru36]

That may be true but possession stats are not as easy to come by. If you're the team statistician, yes you might do a Stats, Inc. level analysis, either analyzing every possession and crunching the numbers yourself, or paying a subscription fee. For some that is overkill. Per-minute played stats are a nice middle ground for looking beyond pure averages and having intelligent to say about a player's ability when called upon.

Don't NHL teams keep +1 and -1 type stats on players that are on the ice when one team scores? I don't know much about it but I get the impression that it provides a kind of stat that indicates whether the team plays better or worse when they're in. Maybe it wouldn't work for basketball - or would be redundant b/c of stats like turnovers and so forth.

This stat actually is compiled for NBA players, at least over the past few years at the following site: 82games.com (http://www.82games.com/index.htm)

It is also used to look at which 5/4/3/2 player units are specifically most effective together. Interesting stuff.

As for going back and tabulating such information for, say, Duke, I imagine it would require nothing more than the play-by-play game logs (so long as it includes substitutions, which they typically do) a big spreadsheet and a LOT of free time. I wouldn't be surprised if some teams kept such stats in-house to aide in evaluating their player/line-up efficiencies.

And one could look not only at pt. +/- but also at differential rebounds, turnovers, shot %...etc. ("Fun!" says my geeky streak)

Go Duke!!!!!!!!!! Go Devils!!!!!!!!!!!!!! GTHCGTH!!!!!!!!!!!!!!

[pfrduke]

As for going back and tabulating such information for, say, Duke, I imagine it would require nothing more than the play-by-play game logs (so long as it includes substitutions, which they typically do) a big spreadsheet and a LOT of free time. I wouldn't be surprised if some teams kept such stats in-house to aide in evaluating their player/line-up efficiencies.

And one could look not only at pt. +/- but also at differential rebounds, turnovers, shot %...etc. ("Fun!" says my geeky streak)

It does require nothing more than the play-by-play game logs, several spreadsheets, and the willingness to devote a chunk of time to it. I've been doing it for the past two years at my website Blue Devil Hoops (http://dbdhoops.blogspot.com). The game logs don't always have substitution data, which is frustrating, although can be fixed by watching the games and tracking substitutions (assuming the game logs have accurate play-by-play data, which is also not always the case). This past year, the stats reflect how the team performs with a particular player on the court (see the "Duke Team Stats by Player" link on the right side of my main page). Next year, I'm thinking of going to a +/- form at least for points, and trying to set up something that's more lineup-based, rather than player-based (so more like the 82games setup).

Sorry for the shameless self-promotion, but just wanted to let you know that data like this is out there in the ether. Another place to feed the geeky streak...

[pfrduke]

That may be true but possession stats are not as easy to come by. If you're the team statistician, yes you might do a Stats, Inc. level analysis, either analyzing every possession and crunching the numbers yourself, or paying a subscription fee. For some that is overkill. Per-minute played stats are a nice middle ground for looking beyond pure averages and having intelligent to say about a player's ability when called upon.

There's actually a convenient way to estimate possession data. You can figure out the number of offensive possessions for a team with the following formula:

Poss. = FGA - ORB + TO + FTA*0.475.

Then, you can multiply the total possessions by the following:

Min. Played/40

to get the estimated number of possessions the player was on the court for.

This accounts for differences in pace. For example, scoring 10 pts in 20 minutes for UNC last year would not have been as impressive as scoring 10 pts in 20 minutes for Duke, because UNC played more possessions in those 20 minutes. The per/minute stat would be the same, but the per/possession stat would be different (and significantly so - about 10-15%).

This certainly doesn't give you the availability to do a +/- though - for that, you need to be able to track possessions. But it doesn't really take much more than 30-60 minutes for each game. I live on the West Coast, so I usually do the statistical inputting during commercial breaks/halftime while I watch the tape of the game.