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Comparing the Different Versions of “Assist Rate”

Posted by Neil Paine on October 1, 2010

In the realm of APBRmetrics, perhaps no stat has as many alternate versions (many under essentially the same confusingly interchangeable name) as "Assist Ratio/Rate". All theoretically attempt to measure passing ability, but each version has its own quirks and biases. Today I want to compare all of the versions I can think of, and show a leaderboard (minimum 500 MP) for each to get a better feel for what each is measuring, starting with...

Assist-to-Turnover Ratio

(Assists / Turnovers)

The granddaddy of all assist-based rate stats, this metric is a mainstay whenever the mainstream media is trying to assess ballhandling and/or passing ability. Obviously it assumes that the positive value of an assist is equal in magnitude to the negative value of a turnover, which isn't necessarily true, and from a functional perspective it rewards turnover avoidance more than passing because as long as you keep the denominator low, even a few cheap assists will give you a decent ATO. While its ease of calculation has made it popular, you can see some of ATO's extreme flaws by looking at the 2009-10 positional leaders:

Pos Player ATO Pos Player ATO Pos Player ATO Pos Player ATO Pos Player ATO
PG Paul 4.29 SG Brewer 2.91 SF Prince 2.68 PF McRoberts 2.32 C Camby 2.04
PG Arroyo 4.17 SG Johnson 2.54 SF Battier 2.56 PF Hayes 1.88 C Tolliver 1.89
PG Calderon 4.08 SG Redick 2.51 SF James 2.49 PF Turiaf 1.84 C Biedrins 1.78
PG Kidd 3.71 SG Vujacic 2.41 SF Turkoglu 2.43 PF Garnett 1.83 C Wallace 1.64
PG Bibby 3.44 SG Ginobili 2.40 SF Posey 2.29 PF Diaw 1.83 C Hilario 1.62
PG Duhon 3.44 SG Evans 2.40 SF Williams 2.28 PF Odom 1.78 C Horford 1.55
PG Williams 3.43 SG Roy 2.36 SF McGrady 2.25 PF Duncan 1.76 C Miller 1.44
PG Rondo 3.23 SG Mason 2.32 SF Garcia 2.14 PF Bonner 1.74 C Hunter 1.23
PG Williams 3.17 SG Green 2.27 SF George 2.13 PF Smith 1.73 C Gasol 1.22
PG Maynor 3.13 SG Carter 2.23 SF Moon 2.13 PF Lee 1.56 C Andersen 1.19
PG Rodriguez 1.86 SG Allen 1.09 SF Wallace 0.90 PF Maxiell 0.57 C Perkins 0.48
PG Alston 1.85 SG Ross 1.09 SF Randolph 0.86 PF Amundson 0.54 C Haywood 0.43
PG Bayless 1.83 SG Hassell 1.06 SF Durant 0.85 PF Hollins 0.54 C Stoudemire 0.38
PG Price 1.80 SG Stackhouse 1.06 SF Young 0.77 PF Brown 0.51 C Jordan 0.28
PG Holiday 1.79 SG Brown 1.05 SF Greene 0.76 PF Landry 0.49 C McGee 0.27
PG Pargo 1.78 SG Ellington 1.00 SF Daye 0.71 PF Humphries 0.48 C Anthony 0.27
PG Farmar 1.76 SG D.-Roberts 0.96 SF Jerebko 0.71 PF Gooden 0.44 C Thabeet 0.26
PG Tinsley 1.71 SG Young 0.86 SF Graham 0.64 PF Hickson 0.43 C Przybilla 0.21
PG Flynn 1.53 SG DeRozan 0.85 SF Young 0.55 PF Gortat 0.37 C Chandler 0.18
PG Beaubois 1.37 SG Pietrus 0.71 SF Graham 0.51 PF Ibaka 0.15 C Lopez 0.17

Hollinger Assist Ratio

(Assists * 100) /  (FGA + (FTA * 0.44) + Assists + Turnovers)

According to John Hollinger's ESPN.com glossary, this is "the percentage of a player's possessions that ends in an assist". In essence, it's not only measuring the player's ability to rack up assists and avoid turnovers, but also his passing tendency relative to his shooting tendency -- in fact, relative to his overall offensive possessions used, since the denominator is the most basic team possession formula. Here were the 2010 positional leaders:

Pos Player JH Pos Player JH Pos Player JH Pos Player JH Pos Player JH
PG Kidd 44.3 SG West 25.0 SF Miller 26.7 PF Oberto 33.9 C Biedrins 24.1
PG Carter 39.5 SG Iguodala 23.6 SF Turkoglu 25.3 PF Turiaf 28.2 C Camby 22.4
PG Nash 39.3 SG Ginobili 23.4 SF McGrady 24.4 PF Hayes 24.3 C Wallace 19.8
PG Duhon 38.5 SG Brewer 22.2 SF James 23.4 PF Diaw 24.2 C Hilario 16.5
PG Rondo 38.4 SG Stevenson 21.2 SF Battier 22.7 PF Odom 21.4 C Miller 16.4
PG Paul 36.6 SG Hughes 21.2 SF Posey 21.3 PF Smith 19.8 C Noah 15.3
PG Calderon 36.2 SG Parker 21.1 SF Wilkins 20.8 PF McRoberts 19.5 C Horford 14.8
PG Blake 36.2 SG Williams 21.0 SF Korver 20.6 PF Garnett 16.0 C Gasol 14.8
PG Williams 35.9 SG Evans 20.7 SF Artest 19.9 PF Gasol 16.0 C Tolliver 13.6
PG Maynor 35.4 SG Iverson 20.5 SF Kirilenko 19.2 PF Hawes 15.8 C Hibbert 13.3
PG Brooks 20.4 SG Morrow 11.1 SF Howard 8.8 PF Jianlian 6.1 C Okafor 5.8
PG Bayless 20.1 SG Richardson 10.9 SF Brown 8.8 PF Speights 6.1 C Haywood 5.8
PG Stuckey 19.6 SG Peterson 10.7 SF Young 8.7 PF Gooden 5.5 C Jordan 5.4
PG Hill 19.3 SG Martin 10.6 SF Gay 8.6 PF Hickson 5.5 C Przybilla 5.1
PG Price 19.2 SG Evans 9.8 SF Daye 8.5 PF Humphries 5.4 C Thabeet 4.9
PG Terry 18.7 SG Thornton 9.8 SF Webster 7.5 PF Cunningham 5.3 C Anthony 4.7
PG Gibson 17.7 SG Ross 8.6 SF Graham 7.4 PF Gortat 5.3 C Stoudemire 4.5
PG Farmar 16.9 SG DeRozan 7.4 SF Young 7.2 PF Villanueva 5.2 C Chandler 4.4
PG Pargo 16.5 SG Pietrus 7.0 SF Jerebko 7.1 PF Landry 5.0 C McGee 3.3
PG Beaubois 16.4 SG Young 6.7 SF Graham 7.0 PF Ibaka 2.0 C Lopez 1.8

Passes per Touch

100 * (AST / 0.17) / Touches

This Bob Chaikin stat isn't specifically named "Assist Rate", but I thought I'd include it anyway because it measures much the same passing tendency as Hollinger's Assist Ratio. Designed to be used in conjunction with Shots, Turnovers, and Fouls Drawn per Touch, Passes/Touch tells you how often a player passes the ball when he gets it in an attacking position on the floor. The only problems are that it's another tendency stat, which doesn't always necessarily capture skill per se, and it also relies on the rather arbitrary (1/0.17) multiplier, which came from Bob watching games and tracking passes but may not always be very accurate, depending on the player. That said, here were the 2010 leaders:

Pos Player P/T Pos Player P/T Pos Player P/T Pos Player P/T Pos Player P/T
PG Kidd 81.7 SG West 64.4 SF Miller 66.8 PF Oberto 73.7 C Biedrins 63.8
PG Carter 79.1 SG Iguodala 62.0 SF Turkoglu 64.5 PF Turiaf 67.0 C Camby 61.1
PG Nash 78.1 SG Ginobili 61.6 SF McGrady 63.4 PF Diaw 64.1 C Wallace 55.6
PG Duhon 77.5 SG Brewer 60.5 SF James 61.5 PF Hayes 63.8 C Miller 50.9
PG Rondo 77.1 SG Parker 59.8 SF Battier 61.4 PF Odom 59.6 C Hilario 50.6
PG Blake 76.4 SG Stevenson 59.5 SF Posey 59.3 PF McRoberts 56.8 C Noah 48.6
PG Williams 76.2 SG Williams 59.5 SF Korver 59.1 PF Smith 56.5 C Horford 48.3
PG Calderon 76.0 SG Hughes 59.0 SF Wilkins 58.2 PF Hawes 51.2 C Gasol 46.9
PG Maynor 75.4 SG Bogans 58.7 SF Artest 57.3 PF Milicic 51.2 C Tolliver 45.7
PG Paul 75.2 SG Sefolosha 58.6 SF Prince 56.7 PF Garnett 50.6 C Hibbert 45.4
PG Brooks 58.2 SG Douglas-Roberts 40.7 SF Durant 34.3 PF Warrick 25.7 C Okafor 23.9
PG Price 56.7 SG Richardson 40.3 SF Daye 33.9 PF Speights 25.5 C Haywood 23.9
PG Stuckey 56.5 SG Peterson 39.4 SF Howard 33.6 PF Hickson 24.1 C Jordan 22.6
PG Bayless 56.2 SG Evans 37.9 SF Gay 33.4 PF Villanueva 23.6 C Przybilla 21.7
PG Hill 56.1 SG Martin 37.6 SF Brown 33.1 PF Gooden 23.6 C Thabeet 20.4
PG Terry 55.3 SG Thornton 37.1 SF Webster 30.4 PF Cunningham 23.3 C Anthony 20.0
PG Gibson 54.6 SG Ross 34.4 SF Graham 30.0 PF Gortat 23.0 C Stoudemire 19.3
PG Farmar 53.0 SG DeRozan 29.9 SF Young 29.3 PF Humphries 22.9 C Chandler 18.6
PG Pargo 52.8 SG Pietrus 29.2 SF Graham 29.1 PF Landry 21.2 C McGee 15.2
PG Beaubois 52.2 SG Young 27.9 SF Jerebko 29.0 PF Ibaka 10.3 C Lopez 8.6

Pomeroy Assist Rate

100 * AST / (((MP / (Tm MP / 5)) * Tm FG) - FG)

This is the official AST% of Basketball-Reference. The metric (developed by Ken Pomeroy) estimates the percentage of teammate baskets a player assisted on while he was on on the court. The big issue here is that teammates can also miss baskets and do other things while on the court besides making buckets, while this just looks at assists relative to teammate made baskets. Here were last year's leaders:

Pos Player KP Pos Player KP Pos Player KP Pos Player KP Pos Player KP
PG Nash 50.9 SG Wade 36.4 SF James 41.8 PF Smith 19.0 C Hibbert 13.5
PG Paul 45.4 SG Ginobili 28.2 SF McGrady 22.6 PF Diaw 18.9 C Camby 12.3
PG Williams 44.5 SG Evans 26.1 SF Turkoglu 19.5 PF Duncan 17.8 C Miller 12.2
PG Rondo 43.7 SG Bryant 23.8 SF Miller 18.5 PF Lee 17.5 C Lopez 11.8
PG Davis 39.6 SG Iguodala 23.7 SF Jackson 17.8 PF Boozer 15.8 C Hilario 11.6
PG Westbrook 38.6 SG Hamilton 23.5 SF Prince 16.9 PF Garnett 15.7 C O'Neal 11.3
PG Kidd 36.4 SG Roy 23.1 SF Ariza 16.7 PF Odom 15.6 C Noah 10.8
PG Arenas 36.3 SG Williams 22.4 SF Anthony 15.9 PF Gasol 15.0 C Horford 10.4
PG Harris 34.6 SG Johnson 22.0 SF Pierce 15.1 PF Turiaf 13.8 C Bogut 10.3
PG Calderon 33.8 SG Ellis 21.2 SF Kirilenko 14.0 PF Blatche 13.8 C Gasol 10.2
PG Price 20.5 SG Wright 7.4 SF Kapono 6.1 PF Humphries 4.5 C Dampier 3.5
PG Alston 20.0 SG Hassell 7.2 SF Brown 6.0 PF Gooden 4.4 C Jordan 2.9
PG Terry 18.8 SG Richardson 7.0 SF Carroll 5.9 PF Maxiell 4.1 C Haywood 2.8
PG Beaubois 18.6 SG Rush 6.9 SF George 5.8 PF Haslem 3.9 C Andersen 2.8
PG Pargo 17.5 SG Peterson 6.3 SF Williams 5.6 PF Hickson 3.9 C McGee 2.4
PG Hill 15.5 SG Young 5.7 SF Jones 5.1 PF Collison 3.7 C Chandler 2.2
PG Watson 14.3 SG Evans 5.5 SF Graham 5.0 PF Amundson 3.7 C Thabeet 1.7
PG Farmar 13.4 SG DeRozan 4.9 SF Webster 5.0 PF Cunningham 3.3 C Przybilla 1.7
PG Fisher 12.9 SG Pietrus 4.7 SF Graham 4.5 PF Gortat 2.4 C Anthony 1.3
PG Gibson 9.8 SG Ross 3.0 SF Jerebko 4.2 PF Ibaka 1.2 C Lopez 1.1

Assists per Team Possession

100 * AST / ((MP / (Tm MP / 5)) * Tm Poss)

Finally, in response to the aforementioned potential shortcoming of Pomeroy Assist Rate, you could tweak the equation to measure assists as a percentage of team possessions while on the floor; this penalizes the player for teammate errors like turnovers & missed baskets (which, admittedly, may or may not actually represent an improvement). Here were the 2010 leaders:

Pos Player A/TP Pos Player A/TP Pos Player A/TP Pos Player A/TP Pos Player A/TP
PG Nash 16.9 SG Wade 9.6 SF James 11.5 PF Smith 6.3 C Camby 4.2
PG Williams 14.6 SG Ginobili 9.0 SF McGrady 7.5 PF Diaw 5.9 C Miller 4.1
PG Paul 14.5 SG Evans 7.9 SF Turkoglu 6.9 PF Odom 5.3 C Hibbert 3.8
PG Rondo 14.0 SG Iguodala 7.8 SF Miller 6.2 PF Duncan 5.3 C Hilario 3.7
PG Kidd 13.0 SG Hamilton 7.1 SF Ariza 5.4 PF Lee 5.0 C Biedrins 3.6
PG Davis 12.3 SG Roy 6.9 SF Prince 5.2 PF Turiaf 4.9 C Horford 3.5
PG Westbrook 12.0 SG West 6.9 SF Jackson 5.0 PF Boozer 4.7 C Noah 3.5
PG Calderon 11.5 SG Iverson 6.8 SF Kirilenko 4.8 PF Garnett 4.7 C Gasol 3.4
PG Maynor 10.8 SG Johnson 6.8 SF Korver 4.8 PF Gasol 4.7 C O'Neal 3.4
PG Collison 10.6 SG Bryant 6.7 SF Pierce 4.7 PF Hawes 4.2 C Lopez 3.2
PG Alston 6.6 SG Morrow 2.5 SF Young 2.0 PF Humphries 1.4 C Okafor 1.2
PG Price 6.1 SG Richardson 2.4 SF Daye 2.0 PF Landry 1.4 C Andersen 1.0
PG Terry 6.0 SG Hassell 2.4 SF George 2.0 PF Maxiell 1.4 C Jordan 1.0
PG Pargo 5.5 SG Peterson 2.2 SF Williams 2.0 PF Amundson 1.3 C Haywood 1.0
PG Beaubois 5.5 SG Rush 2.2 SF Brown 1.9 PF Haslem 1.3 C McGee 0.8
PG Hill 5.2 SG Evans 1.9 SF Jones 1.8 PF Collison 1.3 C Chandler 0.7
PG Watson 4.8 SG Young 1.8 SF Webster 1.7 PF Hickson 1.2 C Przybilla 0.6
PG Fisher 4.7 SG DeRozan 1.6 SF Graham 1.5 PF Cunningham 1.1 C Thabeet 0.6
PG Farmar 4.5 SG Pietrus 1.5 SF Graham 1.5 PF Gortat 0.8 C Anthony 0.5
PG Gibson 3.4 SG Ross 1.1 SF Jerebko 1.4 PF Ibaka 0.4 C Lopez 0.4

So, which Assist Rate is right for you? Well, as always, it depends on what you're trying to capture. If you want to know how much a player passes relative to his other offensive tendencies, Hollinger Assist Ratio or Passes/Touch is the better option. But to measure how active a role the player's passing plays in his team's offense, go with Pomeroy or Assists/Team Possession.

And whatever you do, you should probably avoid ATO.

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11 Responses to “Comparing the Different Versions of “Assist Rate””

  1. DSMok1 Says:

    I prefer the Pomeroy AST Rate, for sure. It seems to me to remove the teammate quality issue more than others--having bad shooting teammates may actually increase the value.

  2. Justin Kubatko Says:

    DSMok1 wrote:

    I prefer the Pomeroy AST Rate, for sure.

    I don't think Neil mentioned this, but that's what I use on the site (I call it "Assist Percentage").

  3. Neil Paine Says:

    I can't believe I forgot to mention that. It's been corrected. And for the record, I think I prefer Pomeroy's version as well. Although to the credit of Ast/TmPoss, being a high assister in a good offense should probably get more credit than in a bad one, since we should theoretically be measuring making one's teammates better.

  4. Greyberger Says:

    Any difference between Pomeroy's AST rate and AST per poss. is going to be minor compared to the difference between them and metrics that don't control for pace. One day I wanted to make the case that, precisely for the reasons above, Pomeroy Assist Rate wasn't sufficiently advanced to replace assists per minute in analysis or data projects... then I actually looked at the difference and found that more than anything it removes pace from the equation and the other differences in evaluation are subtle. Took the air out of my tires a little bit so I'm really glad to see Mr. Paine to take a crack at the subject.

  5. Anon x 2 Says:

    Bryant looks good in the Pomeroy AST rate, so I'll take that one. :D

  6. Joseph Says:

    I don't know how hard it would be to calculate, but maybe comparing a shooter's percentage while the evaluated player is on or off the court would help determine how much the player's assists really mean. If they're on the court and racking up assists left and right, that means the players they're passing to are hitting their shots. If they go down considerably when a bench player comes in, then there's a reason. Perhaps it's the defense who really decides. If the player who racks up assists can create his own shots and is a defensive liability, that makes it more likely that the player who shoots will have less coverage when getting the ball than if there were a reserve player who can't shoot as well.

    I think assists should be tied to shooting percentage, assists per possession, points per assist, and overall point contribution. If a player provides assists to six other shooters and the point total is 30, I think that would be better than assists to seven and a point total of 14. Know what I'm saying?

  7. DSMok1 Says:

    Joseph, I attempted to do what you mention, at least in part, in the following thread:

    http://sonicscentral.com/apbrmetrics/viewtopic.php?t=2532

    I attempted to estimate whose assists were worth the most.

  8. Nick Says:

    Interesting how the Pomeroy metric has Wade and James as the runaway leaders at their positions, James especially. I'd give odds they both go up next year, too. Kinda funny that Wade doesn't even show up on "pass-tendency" lists but dominates the "effective passer" lists at his position. Would the correct conclusion be that Wade only passes when his target is in a good position to score, then?

    Also, why is Tyreke Evans listed as a shooting guard?

  9. Joseph Says:

    DSMok1,

    Thanks for sharing that link. Interesting discussion there as well. Peeling some layers off of that onion quickly!

  10. P Middy Says:

    Neil--

    Without actually begging you to do it, do you think it's possible to weigh and combine these approaches into a single "passing performance" type stat? Or do they measure too differently on too many different criteria?

  11. Dave Says:

    following your kenpom link we get:

    Assist Rate (ARate): This is assists divided by the field goals made by the player’s teammates while he is on the court. [Changed 4/9/06]

    Are you sure that his ARate is an estimate? It reads to me that it is a PbP derived number - and gives a slightly different number to the one your formula gives, your formula is an estimate of this number.
    I only raise this question since his definition is changed 2006 and that is about when we have had reliable PbP data from - at least NBA ...