Expanding ‘Points Per Miss’ (PPM)

Yesterday, Jerod wrote a fantastic article on Dirk Nowitzki’s historically efficient night. In his article, he took an idea that was initially launched by Bill Simmons about a stat that measures a player’s efficiency on the offensive side of the ball.

He called the stat Points Per Miss, or PPM.

The stat really speaks for itself. How many points does a player score for every one of his missed shots? Really, it’s determining if a player brings more to the table than he takes from it. Every missed shot is a blown possession for his team while every make is a converted one.

We discovered that Dirk had an outstanding single-game PPM of 16 in Game 1. For every one of his misses, the big fellow scored SIXTEEN points. Simply outstanding.

However, as we thought about the stat more, and took the insightful and analytical contributions of commenters into consideration, we realized a few things.

As one reader pointed out,

“Had Dirk missed one more shot, his PPM would be 12. Had he missed 3 more shots, still a respectable 12-18, his PPM would be 8. Since this stat uses division, the numbers cannot be compared linearly. For example, comparing PPMs of 16 and 12 is not the same comparison as PPMs of 6 and 2, even though the difference between each is 4.”

Another thing we realized was that all shots are not created equal. Should a missed free throw count just as much as a missed field goal? Should missed three pointers count as much or more as a missed two-pointer?

Eventually we came to some conclusions about how PPM could be greatly improved.

First of all, missed threes and twos should count the same. Both misses (unless your team gets an offensive rebound) end up costing your team a possession. That’s one more possession where your team could have scored, but didn’t because you failed to convert.

The other question was about free throws. If you miss the first attempt of a two-shot foul, you haven’t necessarily lost your team a possession. In fact, you still get the opportunity to get your team a point. Really, free throws could be thought of as half of a field goal…since you normally get two of them and each shot is worth half of a field goal.

However, sometimes you only get one free throw because you earned an and-one. Other times, you are fouled on a three point attempt and get three freebies. We decided to use John Hollinger’s formula from his advanced statistic True Shooting Percentage to work out the details. He figured out a free throw attempt is worth 0.44 possessions.

That leads us to our final formula for figuring out Points Per Miss, which is slightly different from yesterday but more precise and useful:

PPM = Points / (Field Goals Missed + (0.44 x Free Throws Missed))

Because Dirk didn’t miss a single free throw, his PPM would still have been an outstanding 16. If he had missed one free throw, it would have dropped to 13.95. If he had missed one more field goal, it would have dropped to 12.
Obviously, with such an outstanding game, the results are likely to change A LOT with just one more make or miss.

However, the benefits of PPM are much more relevant when looking at someone’s season or career as a whole.

We will get to that in a second, but first I’ll address what I’m sure some of you are thinking: Wow…these guys have done nothing significant…this is just a ripoff of Hollinger’s True Shooting Percentage.

Let’s compare the two and discuss a few main points.

• PPM = Points / (Field Goals Missed + (0.44 x Free Throws Missed))
• True Shooting Percentage = Points / (2 x (FGA + (0.44 x FTA)))

The stats are very similar to say the least.

HOWEVER…

I believe they are different enough to both be useful, even together.

Percentage vs. Points

For one thing, Hollinger’s TSP gives you a percentage that the player shot from the floor.  For instance, Dirk had a 61.2% True Shooting Percentage this year and Paul Pierce had a 62% True Shooting Percentage.  With that stat, you get an idea of how well the guy shot from everywhere.

Our stat gives you an idea of how many points that guy scored for every miss.  Dirk scored 2.85 points per miss and Pierce scored 2.79.

That difference is small, but it does give you a different sort of figure to compare the two players.

A More Complete Picture

The BIGGER difference I think is that it tells a more complete picture.

Let’s compare those two guys again.  If you just looked at TSP, you would assume that Pierce is the more efficient scorer than Dirk, but if you really look at the stats that doesn’t make any sense.

• Pierce averaged 18.9 points, shot 86% from the line, 37% from three, and 50% on all Field Goals.
• Dirk averaged 23 points, shot 89% from the line, 39% from three, and 52% on all Field Goals.

So you have a guy who averaged MORE points and shot a better percentage from ALL THREE areas, but somehow he has a WORSE True Shooting Percentage than the other guy. That’s because True Shooting Percentage rewards players that score a higher percentage of their points from the free throw line. Dirk only scored 23% of his points from the foul line whereas Pierce scored 25% of his points from there this season.

Here is a more clear example.

Let’s pretend that two players both scored 30 points on a given night.

• Player A was 10-20 from the floor and also finished 10-12 from the charity stripe.  He missed 12 shots, and ended up with a PPM of 2.757.  However, his True Shooting Percentage was 59%.
• Player B was 14-24 from the floor, but only 2-4 from the foul line.  He also missed 12 shots, and his PPM remains the same – 2.757.  However, HIS True Shooting Percentage dips slightly to 58%.

Just by looking at TSP, the common person would believe that Player A was more efficient.  However, that’s not really the case because while Player B did not shoot as well from the foul line, he actually shot BETTER from the field, which actually saved his team more possessions. Both players were equally effective. PPM shows that, TSP doesn’t.

All of that to say this:

I believe that our stat provides a more accurate picture of true efficiency on the offensive end of the floor than True Shooting Percentage.

It shouldn’t really matter where a player is getting his points. Some players score by getting to the free throw line. Other players score remarkably well without getting to the line. We need a stat that measures overall effectiveness correctly, and I believe that PPM helps us to accomplish that goal a little better.

At the end of the day, Dirk and Pierce are both remarkably efficient, and both deserve lots of credit for that. Like Jerod said yesterday, I had no idea Pierce was so efficient, and he now gets a lot more respect from me. But PPM provides a little more accurate picture of true efficiency.

When I look for efficiency, I am really looking for how many points per possession/shot/miss someone averaged. Percentages may lie; PPM doesn’t.

Below is a quick look at the top fifty scorers from the NBA this season, plus Steve Nash…because I’m always interested to see where he finishes in these types of stats.

What you will notice is that the PPM tends to lean a little more towards a) big men who get their shots around the basket and b) lights out shooters. This doesn’t really tell us anything new though, does it? Big men and great shooters are more efficient scorers than slashers and athletes.

A few interesting players of note: Derrick Rose, Kobe Bryant, and Russell Westbrook all fall out of the top ten and into the mid-30s. Meanwhile, Pau Gasol takes an almost meteoric rise up to #4.

Another player who is not on the list is Chris Paul. He ended up with a 2.444 PPM, putting him higher than all point guards not named Steve Nash and Tony Parker.  However, his playoff PPM of 3.35 was unbelievable.  Anyone who watched him against the Lakers would have said he was remarkably efficient…but good grief!

You can go up and down the list and make your own conclusions. It is fun and, in many cases, quite surprising.

 

	FGM	FGA	FTM	FTA	Total Points	Missed FGA	Missed FTA	PPM
Dwight Howard	619	1044	546	916	1784	425	370	3.03504593399115
Dirk Nowitzki	610	1179	395	443	1681	569	48	2.84857317155833
Paul Pierce	507	1021	386	449	1511	514	63	2.78926382633095
Pau Gasol	593	1120	354	430	1541	527	76	2.74962529441153
Lebron James	758	1485	503	663	2111	727	160	2.64735390017557
Paul Millsap	525	988	256	338	1315	463	82	2.6348481205418
Steve Nash	399	811	227	249	1106	412	22	2.62284196547145
Ray Allen	480	978	193	219	1321	498	26	2.59304334170854
Chauncey Billups	339	794	384	419	1208	455	35	2.56802721088435
Kevin Love	482	1026	424	499	1476	544	75	2.5580589254766
Dwyane Wade	692	1384	494	652	1941	692	158	2.54884966908289
Chris Bosh	524	1056	384	471	1438	532	87	2.5215683523883
Kevin Martin	553	1267	594	669	1876	714	75	2.51137884872825
Tony Parker	555	1069	233	303	1368	514	70	2.51101321585903
Kevin Durant	711	1538	594	675	2161	827	81	2.50510062134842
Amar’e Stoudemire	744	1482	473	597	1971	738	124	2.4868779650752
Stephen Curry	505	1053	212	227	1373	548	15	2.47565813198702
David West	528	1040	264	327	1322	512	63	2.44941821685318
Zach Randolph	598	1188	300	396	1504	590	96	2.37884347716057
David Lee	496	978	210	267	1203	482	57	2.372406720833
LaMarcus Aldridge	707	1415	351	444	1769	708	93	2.36206804465096
Brook Lopez	644	1309	385	489	1673	665	104	2.35381844785863
Blake Griffin	696	1376	446	695	1845	680	249	2.33674451593292
Manu Ginobili	441	1018	357	410	1393	577	53	2.32042910447761
Wesley Matthews	440	979	266	315	1300	539	49	2.31910946196661
Carlos Boozer	431	845	171	244	1033	414	73	2.31552048776114
Carmelo Anthony	684	1503	507	605	1970	819	98	2.28506472416833
Luis Scola	569	1129	214	290	1352	560	76	2.2782421137773
Deron Williams	428	975	348	412	1309	547	64	2.27588844843174
Eric Gordon	427	949	287	348	1247	522	61	2.27206471831499
Rudy Gay	409	869	194	241	1069	460	47	2.22393276192061
Kobe Bryant	740	1639	483	583	2078	899	100	2.20360551431601
Derrick Rose	711	1597	476	555	2026	886	79	2.20035622746427
Al Jefferson	654	1319	220	289	1528	665	69	2.1974229176254
Josh Smith	497	1041	229	316	1274	544	87	2.18795081404135
Russell Westbrook	614	1390	531	631	1793	776	100	2.18658536585366
DeMar DeRozan	539	1154	327	402	1410	615	75	2.17592592592593
Luol Deng	531	1155	253	336	1430	624	83	2.16496093986556
Danny Granger	535	1260	395	466	1622	725	71	2.14482174970909
Andrea Bargnani	525	1173	287	350	1414	648	63	2.09258272657314
Monta Ellis	726	1611	340	431	1929	885	91	2.08531522961169
Nick Young	412	935	186	228	1115	523	42	2.05917116052301
Dorell Wright	485	1146	180	228	1344	661	48	1.97032780155984
Joe Johnson	514	1161	195	243	1312	647	48	1.96371909237861
Michael Beasley	561	1246	219	291	1401	685	72	1.95484735167718
Andray Blatche	426	957	220	283	1076	531	63	1.9258304696449
Stephen Jackson	435	1059	249	305	1240	624	56	1.91169215589541
Antawn Jamison	374	876	171	234	1010	502	63	1.90666767348788
John Wall	398	972	301	393	1131	574	92	1.84058065356073
Tyreke Evans	382	933	205	266	1012	551	61	1.75134985463104
Brandon Jennings	361	926	199	246	1019	565	47	1.73985794290398

 

Three more things of note.

First of all, no stat is perfect. The danger with all new stats is that we think we have figured out something so good that we no longer need to watch the game to decide how good a player is or is not. No one should look at this stat and decide that Derrick Rose, Kobe Bryant, and Russell Westbrook are bad players.  However, it’s not surprising to anyone to see that they really aren’t super efficient on offense.

That’s the thing I love the most about this stat. In my opinion, it really reflects what you see. It’s more of a tangible verification than a new breakthrough. Anyone who has watched the Lakers all year would tell you that Pau is a more efficient scorer than Kobe, but even I didn’t think the difference would be that diverse.

Secondly, I think this stat is still a work in progress as far as what we can learn from it.

I have not had time to find out the league average for PPM yet, but it would be nice to figure that value out so we can really compare players. For instance, if you didn’t know anything about baseball, you would think that someone being successful at the plate only 30% of the time was awful. It isn’t until you realize what everyone is hitting that you understand that hitting .300 is fantastic.

With that said, PPM is still easy to understand because Points Per Miss is about as simplistic as it gets. Everyone who has ever watched basketball can understand that scoring 2.5 points per miss would be outstanding.

The other place this stat could really go is in terms of teamwork. I would be very interested to see how much a player’s presence on the floor affects his teammates’ PPM. Obviously LeBron James made his Cavs teammates more efficient players, but how much so? I believe this could be the next step of PPM.

Finally, I thought this comparison was telling: Reggie Miller’s career PPM was 2.632. Ray Allen’s is a paultry 2.304.

The ball is in your court, SportsGuy.

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Follow me on Twitter @The_Dr_Twitch

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