NFL Wild Card Weekend: Day 2

Note: This post was originally posted here.

San Diego Chargers – Cincinnati Bengals

Defense-adjusted Value over Average (DVOA) suggests that San Diego “should have” scored 29.3 points per game and allowed 27.9 points per game. Cincinnati should have scored 23.6 points per game and allowed 20.2 points per game. This highlights a difference between the two teams, with San Diego playing higher scoring games than Cincinnati. Thus, we would expect a score of Bengals 25.75, Chargers 24.25. To correct for home field, we add half of the difference between home and road performance for home team and subtract it for the road team. San Diego scores 0.3 points more per game on the road and allows 4.3 points per game more, so we take away (4.3-0.3)/2, or 2 points from the Chargers total. Cincinnati scores 15 more points per game at home and allows 4.6 points less per game, so we add (15+4.3)/2, or 9.65 points to the Bengals. Rounded, this puts the totals at 35 for the Bengals and 22 for the Chargers.

A factor that has been key in the playoffs so far is turnovers, and Cincinnati has the edge in that area. The Bengals have a +0.9 turnover differential per game at home this season, and +0.7 in the last three games. The Chargers have a -0.6 turnover differential on the road this season, and a -0.3 differential the last three games. Yet, the Bengals have recovered 58 percent of fumbles this season compared to 34 percent for San Diego, indicating that luck could explain the difference in turnovers. However, in the Bengals’ favor is that both teams that won on Saturday rushed on much lower percentage of plays than their respective opponents, meaning that passing team may be better in the playoffs. The Bengals rushed on 43 percent of plays compared to the Chargers’ 45 percent, and the Chargers have averaged nearly 80 passing yards less than the Bengals in the past three games. San Diego converts 88 percent of field goals on the road, identical to the rate Cincinnati converts at home, and both team have converted all field goals in the last three games. However, the Chargers were a better passing offense throughout the entire season.

Prediction:  A season’s worth of data suggests that the Bengals are the better team, and they are in the top-5 both offensively and defensively at home. However, San Diego has recovered from some bad luck to improve its play at the end of the season and pull out some wins over elite opponents. This game will be close, but the Bengals will prevail. Bengals 24, Chargers 20.

San Francisco 49ers – Green Bay Packers

Based on the DVOA, the 49ers should have scored 25.9 points per game while allowing 16.8 points per game. The Packers should have scored 25.7 points while allowing 29.1 points per game. We would expect the 49ers to score 27.5 points, while the Packers score 21.25 points. To correct for home field advantage, we factor in each team’s home-away performance. The 49ers scored 2.8 more points per game on the road and allowed 1.6 points less per game, so we add a total of (2.8+1.6)/2, or 2.2 points to their total. The Packers scored 1.4 more points per game on the road, and allowed 8.3 less points. So we add (8.3+1.4)/2, or 4.85 points. Our location adjusted, rounded score is 30 for the 49ers and 26 for the Packers.

A key factor could be turnovers, with the 49ers having a positive turnover margin per game for the season overall, on the road, and for the past three games. Green Bay is negative on the year and even at home. San Francisco has thrown no interceptions in the last three games, while Green Bay has thrown interceptions on 3.42 percent of pass attempts. Both teams have had good luck with fumbles: Green Bay has recovered 62 percent at home (56 percent overall for the year) and San Francisco 58 percent on the road (53 percent overall for the year). Green Bay has the advantage in regards to penalties, while field goal kicking is nearly identical for both teams.

There is a real difference in styles, with the 49ers rushing on nearly 10 percent of their snaps than Green Bay (53 percent vs 43 percent), and the 49ers lead the league in that category. San Francisco is 30th in passing yards, while Green Bay is 6th.

Prediction: The San Francisco has been the better team through the larger sample size of the entire season, Green Bay has a great home field and is dangerous through the air with Aaron Rodgers’ return. It’ll come down to the wire, but the 49ers will prevail in the final minutes. 49ers 27, Packers 24.

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Previewing Saturday’s NFL Wild Card Games

Note: This post was originally posted on the UC Irvine Sports Analysis Collective blog, but is posted here as well.

With the NFL playoffs kicking off on Saturday, it’s going to be an exciting weekend. Let’s break down the two Saturday games.

Kansas City Chiefs- Indianapolis Colts

The Chiefs scored an average of 26.9 points per game and allowed 19.1 points per game during the regular season. However, using Football Outsider’s Defensive Value Over Average metric for both offense and defense and fitting a regression model (download data here), the Chiefs “truly should” have scored 24.2 points per game and allowed 21.7 points per game. The Colts scored an average of 24.4 points per game and allowed 21.0 points per game during the regular season. By DVOA, the Colts should have scored 24.6 points per game and allowed 23.7 points per game.

To obtain the predicted points for each team, I averaged the amount the offense scored with the amount the opposing defense allowed. On a neutral field, we would expect the Chiefs to score 23.95 points and the Colts to score 23.15 points. Kansas City scores 7.5 more points per game on the road and allows 3.5 points less, while Indianapolis Colts score 0.9 points more per game at home and allow 0.2 points per game less at home. To correct for this, we’ll take (7.5 + 3.5)/2, so add 5.5 points to the Chiefs. We’ll add a total of (0.9 + 0.2)/2, or .55, points to the Colts. That totals 29.45 for the Chiefs and 23.7 for the Colts.

However, there are other things that need to be taken into account, factors that could indicate a team will “regress” to a truer form than we have seen. Teams on average recover 50 percent of fumbles over large sample sizes, and a deviation from there indicates that a team is either lucky or unlucky. The Chiefs have recovered over 68 percent of fumbles on the road this season, while the Colts have recovered 51 percent of fumbles at home. The Chiefs recovery rate is unsustainable, and indicates that they may not be as good as their record indicates. The Chiefs also have averaged 2.4 less turnovers than their opponents per game while on the road, and have thrown interceptions on only 0.77 percent of pass attempts on the road, both incredibly better than the league average. Indianapolis is  +0.8 turnovers per game at home, better than the league average, and interceptions on 2.41 percent of pass attempts, about the league average.

On special teams, Kansas City makes 82 percent of field goal attempts on the road, but only 33 percent in the last three games. Indianapolis makes 87 percent and has made 90 percent in the last three games. Indianapolis attempts 2.5 field goals to Kansas City’s 1.7 per game.  In addition, the Colts average only 4.1 penalties per game (3.0 in the last three games) compared to 6.3 for the Chiefs (5.3 in the last three).

Prediction: Using DVOA alone to determine true ability, these teams are even. The Chiefs are better on the road than at home, which seems to give them a slight edge. However, field goals and penalties may be key in this indoor game, and both edges go to the Colts. The Chiefs are not likely to keep up the turnover rate, and will struggle to win the turnover battle on the road. Colts 28, Chiefs 24.

New Orleans Saints – Philadelphia Eagles

I used the same regression model as mentioned above to figure out expected points scored and allowed. New Orleans scored 25.9 points per game and allowed 19.0 points per game, but “should have” scored 27.6 points per game and allowed 21.9 points per game. Philadelphia scored 27.6 points per game and allowed 23.9 points per game, but should have scored 29.4 points per game and allowed 24.7 points per game. Averaging it out, we would expect 26.15 for New Orleans and 25.65 for Philadelphia. New Orleans scores 16.2 points less and allows 6.8 points more on the road. So, to correct, we take away (16.2 + 6.8)/2, or 11.5 points from the Saints. Philadelphia scores 7.2 less points at home than on the road, but allows 8 points less at home. Thus we’ll add a total of (8 – 7.2)/2, or 0.4 points to the Eagles. That puts the totals at 14.65 for the Saints and 26.05 for the Eagles.

For other factors, the Eagles have won the turnover battle by one turnover per game over their last three games, and are at +0.8 per game on the season. The Saints are even on the season, but have lost the turnover battle by one turnover a game over their past three games. The Eagles have recovered only 43 percent of fumbles on the season, but 52 percent at home. They have recovered only 28 percent in the past three games, a sign of being unlucky to end the season. The Saints have recovered an even 50 percent on the road this season, but none in their last three games, a sign of unluckiness as well. New Orleans has thrown interceptions on 2.65 percent of pass attempts on the road this season, but on 3.03 percent of passes in the last three games. Philadelphia has thrown interceptions on 3.1 percent of pass attempts at home, but only 1 percent in the last three games. Both teams averaged 5.9 penalties per game this season, but New Orleans has averaged 7 per game in the last three games compared to 5.7 for Philadelphia.

In terms of play style, Philadelphia is run-heavy team, rushing on 47 percent of plays for the season and 49 percent of plays at home. New Orleans has rushed on only 36 percent of plays for the season, and 33 percent on the road. The Eagles lead the league in rushing while the Saints are 25th. Both teams have converted field goals at a rate in the mid-70 percent range for the season, but Philadelphia has not missed a field goal in the last three games while New Orleans has only converted 60 percent in that span. Both of these aspects will be critical with the harsh conditions.

Prediction: Both teams are evenly matched in terms of ability, but New Orleans is greatly diminished away from home. With rough weather, the ability of the Eagles to run the ball effectively will play a large role. This will reduce turnovers and penalties, which are in Philadelphia’s favor. Philadelphia 27, New Orleans 20.

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Do Steroids Boost Hitter Performance?

With Biogenesis, A-Rod, and steroids all over the news lately, it brings up the age old question: what is the effect of steroids on athlete performance? David Schoenfield, in this article, argues that steroids usage didn’t drive performance in the early 2000’s. Simply, today’s hitters just aren’t making enough contact to put up big numbers. He claims that hitters are hitting home runs at a similar rate when accounting for the increased strikeout rate and bigger strike zones called in today’s game. I was skeptical, and I decided to put the numbers to the test.

Schoenfield’s argument rests on the fact that home run rate per contact, the percentage of balls put in play that result in a home run, has stayed nearly constant from 1993 to 2013. He cites a home run per contact rate of 3.13% in 1993, a peak of 4.19% in 2000, and a rate of 3.68% in 2013. A deviation of about one percentage over an entire season, nothing to see here right?

But wait, Schoenfield doesn’t include the sample size that this deviation occurred over. Using Baseball Almanac’s season-by-season league batting averages, league home run totals, and league strikeout totals, I reconstructed his statistics and decided to compare the home run rate in 2000, the height of the Steroid Era, versus the home run rate in 2012, accepted to be past the end of the Steroid Era. Using the fact that an entire year of at-bats as an independent sample and home run as a nominal/binary outcome, I set up a two sample z-test for proportions to see if there was a statistically significant difference in these rates.

Our default, or null, hypothesis is that these rates do not differ, while the alternative is that they do.  First, let’s look at all at-bats. Home runs were hit on 3.04% of all at-bats in 2000 and on 2.98% of all at-bats in 2012, and we can reject our null hypothesis and conclude these rates are statistically significant. Home runs were hit at a higher rate in 2000 than in 2012, lending credit to the effects of the Steroid Era. But what if we do what Schoenfield suggests and remove strike outs? Removing strike outs drops the sample size of at-bats from 167,290 to 135,934 in 2000 and from 165,251 to 128,825 in 2012. Yet, home runs were hit on 4.19% of balls put in play in 2000 versus 3.83% of balls put in play in 2012. This, these rates are statistically significant as well, disproving the strike outs theory.

Yes, strike outs rose from 19% of at-bats in 2000 to 22% in 2012, but this doesn’t explain the change in home run rate that occurred in the Steroid Era.  Steroids may not teach you how to hit a baseball, but they sure can help you hit it farther.

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NBA Eastern Conference Playoffs

With the NBA playoffs starting today, I wanted to use the hazard rates model described in this great post and apply it to the NBA Playoffs. Instead of finding the rate of losing and subtracting that rate from one, I used the probability of a team winning directly. To calculate the odds of a team advancing, I used a binomial probability distribution function. In a binomial distribution, the result of every trial is either 1 or 0, in this case a win or a loss. When a successful trial is a win for the given team.

In essence, the probability of a team advancing is the probability that it can win four games. I used the team’s regular season winning percentage squared as the probability parameter. I squared the winning percentage because the playoff teams have similar winning percentages, and a non-squared parameter seemed to overstate the probability of upsets for the seven and eight seeds. These calculations assume independence of each game and round, discarding factors such as momentum and slumps for the sake of a simpler analysis.

I calculated the odds of four “successes” out of four games. Then I added the odds of four successes out of five, plus four out of six and four out of seven. Let that number be the odds that Team A wins four games. I used the same methodology to get Team B’s odds of winning four games. Let the combined probability of Team W winning four games be TeamA4. The probability of a team advancing is as follows:

Pr(TeamA Wins) = TeamA4 / (TeamA4 + TeamB4)

With that, I calculated the odds of a team advancing in the first round. For the second and third rounds, the math gets trickier. To calculate the probability that a team wins in round two, let’s assume that Team A can only play Team C or Team D in Round 2 (R2). Pr(TeamA Wins in Round2) is equal to, by Bayes Theorm:

Pr(TeamA beats TeamB)*Pr(TeamB makes R2)+Pr(TeamA beats TeamC)Pr(TeamC makes R2)

Take this value and multiply by Team A’s probability of getting to the second round, and this is the probabiliy that a Team A wins in round 2. Do this for all parts of the bracket to get every team’s odds of winning in Round 2. Assume that in Round 3, Team A can only play Team E, F, G or H, so sum the probability that each team reaches Round 3 (winning in R2) times the probability that A beats that team (using the same probability function created for Round 1).  For Team A winning in Round 3: 

Pr(Team A wins R2)*Σ(Team A beats Team X)*(Team X wins R2 )

From that, we get a spreadsheet of of probabilities.


I also graphed the probabilities.


 As you can see, the odds of advancing in each round decrease. By the conjunction fallacy, a team cannot have a higher probability of winning two series than one. This model will always predict the higher seed winning, so it is no surprise that it picks the 1-4 seeds to advance in Round 1, the 1 and 2 seeds to advance in Round 2, and 1 seed Miami to win the conference. Only Miami and New York have over a 50 percent chance of making the conference finals. Miami is the clear favorite to make it to the finals, having a 55% chance of winning the Eastern Conference.


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Does speed matter for wide receivers?

Does speed matter for wide receivers?

40 Yard Dash vs. NFL Receiving Yards for 2002 WR Class

Data Sources:

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First Post

New post is on the way, glad to get this blog started.

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