Due to storm damage at our data provider's ISP, it is unlikely that Basketball-Reference.com will be updated tomorrow morning with the results from opening night. We will try to get these results up as soon as possible. Our apologies for the inconvenience.

Update: It turns out the update was not delayed. The site should now be updated with the results from last night. Please let us know if you find any bugs.

WARNING: Math post.

PFR user Brad emailed over the weekend with an interesting question:

"Wondering if you've ever tracked or how it would be possible to find records vs. records statistics....for instance a 3-4 team vs. a 5-2 team...which record wins how often? but for every record matchup in every week."

That's a cool concept, and one that I could answer historically with a query when I get the time. But in the meantime, here's what I believe is a valid way to estimate that probability...

1. Add eleven games of .500 ball to the team's current record (at any point in the season). So if a team is 3-4, their "true" wpct talent is (3 + 5.5) / (7 + 11) = .472. If their opponent is 5-2, it would be (5 + 5.5) / (7 + 11) = .583.
2. Use the following equation to estimate the probability of Team A beating Team B at a neutral site:
   

   p(Team A Win) = Team A true_win% *(1 - Team B true_win%)/(Team A true_win% * (1 - Team B true_win%) + (1 - Team A true_win%) * Team B true_win%)

3. You can even factor in home-field advantage like so:
   

   p(Team A Win) = ((Team A true_win%) * (1 - Team B true_win%) * HFA)/((Team A true_win%) * (1 - Team B true_win%) * HFA +(1 - Team A true_win%) * (Team B true_win%) * (1 - HFA))

   In the NFL, home teams win roughly 57% of the time, so HFA = 0.57.

This means in Brad's hypothetical matchup of a 5-2 team vs. a 3-4 team, we would expect the 5-2 team to win .583 *(1 - .472)/(.583 * (1 - .472) + (1 - .583) * .472) = 61% of the time at a neutral site.

Really Technical Stuff:

Now, you may be wondering where I came up with the "add 11 games of .500 ball" part. That comes from this Tangotiger post about true talent levels for sports leagues.

Since the NFL expanded to 32 teams in 2002, the yearly standard deviation of team winning percentage is, on average, 0.195. This means var(observed) = 0.195^2 = 0.038. The random standard deviation of NFL records in a 16-game season would be sqrt(0.5*0.5/16) = 0.125, meaning var(random) = 0.125^2 = 0.016.

var(true) = var(observed) - var(random), so in this case var(true) = 0.038 - 0.016 = 0.022. The square root of 0.022 is 0.15, so 0.15 is stdev(true), the standard deviation of true winning percentage talent in the current NFL.

Armed with that number, we can calculate the number of games a season would need to contain in order for var(true) to equal var(random) using:

0.25/stdev(true)^2

In the NFL, that number is 11 (more accurately, it's 11.1583, but it's easier to just use 11). So when you want to regress an NFL team's W-L record to the mean, at any point during the season, take eleven games of .500 ball (5.5-5.5), and add them to the actual record. This will give you the best estimate of the team's "true" winning percentage talent going forward.

That's why you use the "true" wpct number to plug into Bill James' log5 formula (see step 2 above), instead of the teams' actual winning percentages. Even a 16-0 team doesn't have a 100% probability of winning going forward -- instead, their expected true wpct talent is something like (16 + 5.5) / (16 + 11) = .796.

(For more info, see this post, and for a proof of this method, read what Phil Birnbaum wrote in 2011.)

Due to hurricane-related issues with our data provider, stats for the Monday night NFL game are incomplete. We will update them as soon as we have the data, but until that point the player pages for 49ers and Cardinals players will be missing yesterday's game stats.

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PI Player Game Finder

PI School Game Finder

With the Dream Team documentary and book coming out this summer, I've gotten asked several times to provide the roster for the '92 U.S. Select Team that famously defeated the Dream Team before they went to Barcelona for the Olympics. For posterity, here was the roster of that team, which was made up of the top college players of the day:

1992 United States Development Team

Head Coach: George Raveling (University of Southern California)
Assistant Coach: Roy Williams (University of Kansas)
Athletic Trainer: Ron Linfonte (St. John's-NY)
Manager: Dennis Johnson (University of Southern California)

Roster

(Source: USA Basketball)

PI Team Pitching Streak Finder

Probably yes.
Read the rest of this entry

If you've spent a lot of time at Baseball-Reference, you've probably seen the "SHARE" command in red text above a table of stats... but maybe you don't know what that does, or have forgotten how to use it. No worries -- here's a quick rundown of the features you can access by clicking "SHARE":

• Customize rows & columns - Sharing lets you delete certain rows/columns that you don't want to include in your table. Just click the round 'x' button to delete a specific row/column, or the arrow 'x' to get rid of everything to the right (columns) or directly below (rows) the row/column in question.
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Happy sharing!