The Numbers Behind the Jeremy Lin Contract
This story is now posted on my new site, Stat Dance - a site about sports and statistics, including Jeremy Lin!
This story is now posted on my new site, Stat Dance - a site about sports and statistics, including Jeremy Lin!
Note: this article is now posted on my new website, Stat Dance, a site about sports, statistics, the NBA, sportsbetting, fantasy football, fantasy baseball, etc!
I’ve wanted to look at the NBA draft for a while now - I had lots of questions. I tried to answer a few of them by looking at the last ten NBA drafts (2002-2011) and looking at how their careers turned out relative to their draft positions.
The first thing I had to figure out was how to compare careers. Simple box-score metrics obviously don’t work - looking at points per game would be a very poor single indicator of career success in the NBA. I did some cursory investigating into advanced basketball statistics (APBRmetrics) and found a lot of ideas are out there.
I get the majority of my data from the wonderful Basketball-Reference site, and found that they list Player Efficiency Rating (PER) and Win Shares. Other sites, like the NBA Geek, list Wins Produced. Another metric is adjusted plus/minus, and while I’m sure it has its merits, I’m not really interested in assessing NBA drafts in a world that has Eric Bledsoe as the best per-minute player in the NBA last year. Its not just refusing to accept something that goes against my pre-concieved notions of what happened last year, its that public perception and box-score statistics are how players and drafts are evaluated.
I liked Win Shares and Wins Produced - but they both attempt to gauge a players defensive contributions by looking at how the team did. I don’t want to give a player credit for playing with good defenders, it doesn’t seem fair to me.
The most important metric is minutes played - if you’re good enough to get on the floor and stay on the floor, you’re a contributing member of the team. No other stat can replace that. I decided the best statistic to use for measuring a players quality of contribution is the Player Efficiency Rating. Despite its flaws, it gives a great picture of a player’s ability to contribute. Most importantly, for this exercise, it is relatively consistent with perception. If a GM drafts someone with high PER for his draft position, chances are that pick will be viewed as a “success” when the GM is evaluated.
What I calculated is the PER*Minutes Played - PERMP - for each player drafted since 2002. You can view each photo in full resolution by clicking the gear in the top right corner, or just view the album in full here.
These results were very interesting to me and once I averaged each draft pick’s performance per year, it gave relatively nice curve.
The formula for the percent of the first pick each pick is worth: 318307*e^(-0.06167*Pick)/299270. This gives:
Of course, the numbers at the top are silly - in the 2012 draft, the top pick was probably worth double any other pick - it is expected that Anthony Davis be a superstar, and everyone else would be a longshot for superstar status (see: 2004 Dwight Howard or maybe 2003 LeBron (one pick being significantly better, despite there being a lot of superstars in 2004)).
But, in the 2007 draft, the top pick was only marginally better than the second pick - you were still getting Oden or Durant (which, at the time, was a toss-up). But once you leave the top 5, the pick values are a lot more useful and consistent from draft to draft.
Again, much thanks to basketball-reference.com for all their data. If you have time, check out an analysis posted at 82games.com - he analyzed the drafts from 1980-2003 with a significantly different process and got very similar results.
In the 1983-1984 season, the NBA switched to a playoff system much like the one currently in place. A total of 16 teams make it to the tournament, and every team plays every round. So, every season has 15 series total. From 1984 to 2003, the first round was a best-of-five series. Since then, all playoff series are best-of-seven contests.
While the number of teams and number of series have remained constant, the seeding has gone through several permutations, giving different seeding advantages to division winners. However, the home-court advantage always goes to the team with the best record.
For example, this year the Boston Celtics finished first in the Atlantic Division with a 39-27 record and the Atlanta Hawks finished second in the Southeast Division with a slightly better record, 40-26. As the division champion, the Celtics were guaranteed a top-four seed, despite having finished with the fifth best record in the East. This meant that as the four seed, home-court advantage was given to the five seed. (Note: this had no effect - however, had the Celtics won the division with the eighth best record, they would have still faced the Hawks instead of the #1 seed - the Bulls). In my analysis, I used the NBA’s home-court advantage to determine the “higher seed.”
Every game has its own flavor. From Game 1, with the anticipation of match-ups and rivalry to tense game 7s with seasons on the line. I went through the last 27 years of playoff series and found the winning percentages of the home team and the higher seeded team.
Now, on to the games!
Game 1 is always a home game for the higher seed. The home team has won 76.05% of these games. This nearly matches the overall home winning percentage of the higher seed (75.95%).
Like Game 1, Game 2 is always a home game for the higher seed. Two possible game 2’s exist - the 0-1 game (with the lower seed having won the first game) and the 1-0 game (with the favorite winning the first game).
If the underdog had won the first game, the second game is won by the favorite 79.38% of the time. If the favorite won the first game, the favorite goes up 2-0 73.7% of the time.
This means that favorite more often wins game 2 if they first lost game 1. The combination of the complacency of the underdog, already having snatched home-court advantage back and the desperation of the favorite at the prospect of getting into a two game hole before going into enemy territory leads to a significant increase in home winning percentage.
Overall after game 2 56% of series have seen the favorite up 2-0, 39% tied 1-1, and 5% have the underdog cleaning up in the favorite’s house, up two games to none over the favorite.
For game 3, the home team is always the underdog. In 20 of 405 attempts, the underdog is already up two games to none (5%). In 12 of these 20 games, the underdog takes a 3 game lead on the favorites (winning 60%). This isn’t far from the overall winning percentage of the home team - they win 56.3% of game 3’s overall. However, with such a small sample size, this isn’t very useful information.
When the underdog is down 2-0, they win 58.15% of the time in game 3. If the series is tied, the home team wins 53.16% of the games. One might think that the home team would win more often after having won once on the road, but the opposite is true. The condition of the series (the higher seed not wanting to fall behind in the series) is more indicative of the result of game three than the idea that the teams might be more closely matched.
This could be a general trend, but is more likely an overlap of two different scenarios. The first scenario being that the higher seed is significantly superior to the lower seed, and facing a deficit in the series, really turns it on and dominates game 3. The second scenario being that they are actually closely matched and the home team wins most of the games.
In 5-game series, the favorites swept in 50% of their chances - 43 of 86 attempts. This number is the lowest winning percentage for the home team with at least 50 games played. This is probably a testament to the extremely high numbers of teams that were allowed in the playoffs when the league first switched to a 16-team playoff. In 1984, there were only 23 teams in the league, so 70% of the league made the tournament.
After game 3, of which 405 have been played:
In game 4, the home team is again always the underdog, just like in Game 3. Remarkably, the higher seed has won this game significantly more often than game 3. Boasting a nearly-even 49.58% winning percentage over the past 27 seasons, game 4 has the higher seed overcoming the home-court advantage of the lower seed.
For the 7 games played with the underdog threatening a sweep, only once has the favorite bounced back and took a game (Western Conference Finals, 2005 - the Suns stole game 4 but lost in 5 to the eventual NBA champs, the Spurs). The other 6 times, the underdog got the brooms out.
For the 83.47% of games that start with the series at a 2-1 tally (either the underdogs or the favorites with a one-game lead) the results are very similar, right around a 50% winning percentage. These are cases where neither team has its back against a wall. The previous performance in the series is indicative of the result of this game (although only to a small degree). If the lower seed is up two games to one, they go on to take a 1-3 lead 53.26% of the time. If the higher seed has the 2-1 lead, the lower seed only wins 50.97% of the time. A small, but interesting, difference.
The favorite has threatened to sweep (being up 3 games to none) in 52 of the 253 best-of-seven game series that have been played in the last 27 years. These series obviously represent the games where the favorite is significantly superior to the home team having won both of their home games and their only road game, and represents by far the highest winning percentage of any visiting team, winning 32 of the 52 tries (61.54%). In fact, the next highest away-team winning percentage in a seven game series is game 3 in a tied series, when the favorite wins to take a series lead 49.49% of the time.
Unfortunately, there is no way to compare the winning percentage of the best-of-five series sweeps to best-of-seven sweeps since the close-out game 3 is the first game played at the underdog’s home-court.
While game 5 is usually a home game for the favorite, in the finals game 5 is the third home game in a row for the underdogs.
When the underdog has a 3 games to 1 lead going in to game 5, the higher seed wins 72.73% of the games to bring the series to a 2-3 tally. This is a high winning percentage, but still lower than the overall game 5 favorite winning percentage of 74.53%. This slightly lower winning percentage could be due to some game 5’s being away games for the favorite, or that the lower seed has to be a worthy opponent to have taken a three games to one series lead.
When the favorite is ready to clinch in game 5 with a 3-1 lead, they are almost always playing at home and have a remarkable success rate of 76.74%. This winning percentage is likely dominated by the higher seeds winning against an outmatched opponent that got a win at home in game 3 or 4.
With the series tied at two games apiece heading into game 5, the home team wins 74.32% of the games, to take a series lead. The majority of game 5’s that have been played over the last 27 seasons (55.43%) are of this type, with the series lead in the balance.
Game 6 is usually played at the underdogs home-court (the exception being finals games, of which 6 underdogs have won on the road since 1984). Only two records are possible going in to game 6: 3-2 in favor of the top seed, or 2-3 in favor of the lower seed. Over the past 27 seasons, 66.43% of game 6’s have been 3-2 in favor of the top seed.
When the top seed has a chance to win the series game 6, they are on the road, with two chances to clinch the series, while the underdog has their season on the line at home. In 46.24% of the games, the underdog pulls it out and takes the series to a game 7. Given the gravity of the situation, and that the underdog has already won two games, one might think that this would be more in favor of the lower seed, but in fact it is below the average winning percentage of the lower seed in their home-court (54%).
When the lower seed has won three games going into a game 6, they are relatively dominant - winning 72.34% of their chances to win the series on their home-court. This is easily the highest winning percentage of any other game by the underdog (except for the 6 times the lower seed has swept in the 7 times they had a chance to in game 4 at home).
This large gap in winning percentages in game 6 - in series that has already gone to 6 games - is surprising to me. Only one game of six separates the two teams and there is a 26% difference in winning percentage.
In the 27 seasons that I analyzed since the playoffs switched to a 16-team format, 56 playoff series have gone to a game 7. The top seed has been dominant, winning 82.14% (46 of 56). Considering that the lower seed has already won 3 games against this team, its a very significant edge by the higher seed.
Playoff basketball is all about attitude and talent. The higher seeds usually have the talent, and when their backs are against the wall, the talent perseveres.
The difference in winning percentages depending on the record of the teams in the playoffs is astounding. Whether the difference is a testament to player’s will to win when the pressure is on, or if its an embarrassment that they don’t try hard enough in early games, I’ll leave up to you to decide.
Currently, I’m working on a game-by-game analysis of home-court advantage and seeding in the NBA playoffs. I’ve put a lot of work into the analysis, I hope you find it as informative as I do! It should be up sometime tonight.
Coming soon is a look at the dilution of the NBA and the success of different seeds in the playoffs. This was inspired by a story Peter King talked about in MMQB, an article called Why 2k? by Scott Kacsmar on cnnsi.com.
I’ve got a lot more ideas, mostly about the NFL, but I’m trying to concentrate on the NBA while the season is still going on. If you have any ideas hit me up @MustGetSports or email@example.com.
I analyzed the NBA playoff results from each game of the playoffs for the last 28 years in Excel - not counting the current playoffs. I was hoping I could get a more valuable statistic than the 28 variations of “Being ahead in a series gives you a better chance at winning!” that TNT and ESPN have been telling us. Most of the results are not surprising, but some are.
Watching the game 7 between my Celtics and the 76’ers, I looked at what the historical odds were based on past game sevens.
Since 1984, 56 NBA playoff series have gone 7 games. The home team has won 46 of the 56 - 82% of game seven crowds walk home happy.
In those 56 seven-game series, 392 games have been played - the home team won 73.5% of the games. The higher seed wins 76% of the time at home. The home team playing game 7 has the highest winning percentage of any game situation I looked at.
In the 16-team playoff era (1984-2010) 2,035 playoff games have been played. the home team has an overall winning percentage of 66%. Of course, in a series that goes 7 games, you would expect a higher (73.5% instead of 66%) percentage of the home teams to win.
What might be surprising is that overall, the lower-seeded team has a winning record at home, having won 54% of their home games in the 26-year time span. What doesn’t help their cause is that only 45% of the games played have been at the lower-seed’s court. In the 405 playoff series since 1984, the lower-seeded team has only won 24% of them.
As a proud Celtics fan, I can only hope that 82% holds true!
Since 1984, when the playoffs extended to 16 teams, the home team has a remarkable advantage - they have won 82% of the game 7’s (46/56).
Thanks for checking out the website. My crack team and I are planning on putting some really good things up here to share some ideas about sports!
I’m a big fan of NBA and NFL - so I’ll probably focus on those leagues. I’ll also try to share interesting things I read. That might be more on @MustGetSports but we’ll see what time brings us!