Is there an advantage to deferring?  Should you try to get the ball first to start the game?  Is it a wash?  That’s the question I try to answer in this post.  All stats are from pfref.com.

My favorite NFL stats site has a great query tool for looking up information, but unfortunately they don’t include an option as to whether the team that won the coin toss elected to take the ball or to defer, so I had to try to come up with a cleverer query in order to select only those drives where the team took the opening kickoff (either by the other team deferring or winning the toss and electing to take the ball).

The query

Using the drive finder query tool at http://pfref.com/tiny/grcC2 I tried to narrow down the drives to only those that meet the following criteria:

  1. It was the team’s first drive of the game.
  2. The ball was acquired via kickoff.
  3. The score was tied.
  4. The drive started in the 1st quarter.
  5. The drive ended in the 1st quarter or 2nd quarter.
  6. Time remaining was 14:45 or greater.

My thinking is

#1 above would narrow it down considerably and speed up the search.

#2 above would exclude drives that started because of any of the following:

Downs, Interception, Punt, Blocked FG, Missed FG, Fumble, Muffed Punt, Blocked Punt, Onside kick, Own kickoff, or Muffed kickoff.

#3 above would narrow the scope of the search.

#4 above would eliminate drives that started with the 3rd quarter opening kickoff.

#5 above would also eliminate 2nd half drives

#6 narrows it down to kickoffs at the beginning of the quarter, but allows for time spent during the kick return or in the event of re-kicking because of a penalty.

Problems with the query

Using that query, we get a total of 4512 games (from 1999-2016) in which the team ended up taking the opening kickoff.  Let’s examine what the results mean before we break it down into wins, losses, and ties.  We only get drives (and hence games) in which the team received the opening kickoff (inferring they would be kicking off in the 2nd half), but what we don’t get are those games where opening kickoff was an onside kick, or where the opening kickoff was muffed or fumbled, or where the kicking team recovered their own kickoff (receiving team failed to field the kickoff or even touch it even though it wasn’t an onside kick).  So, we’re missing some of the games in this type of a query, and problematically, those missing games are those where the team that should have gotten the ball to start the game didn’t get the ball and yet still had to kickoff to start the 2nd half.

Query results

Now that I’ve totally confused you, let’s see how those 4512 games went for those teams taking the 1st quarter kickoff.  Of those 4512 games the team getting the opening kickoff (and not getting tricked with onside kicks or failing to cover the kickoff, or muffing/fumbling it), won 2219, lost 2286, and tied 7.  That makes the record 2219-2286-7 (.493) for teams that take the opening kickoff.  It’s a losing record, but only by 0.7%, which could be within the margin of error.

Margin of error

What do I mean by “margin of error”?  Well, I mean even if you flip a fair coin 5000 times you can’t expect to get *exactly* 2500 heads and 2500 tails.  It can vary from that result and yet still be within a reasonable distance of 50%.  In this case, the result was 49.3% wins, but that doesn’t necessarily mean there is a statistical advantage for always deferring to take the ball in the 2nd half.

The plot thickens

I put together a simple computer simulation in which the computer simulates flipping a count 4505 times (this ignore the 7 ties in the 4512 games, 4512-7 = 4505) to see how often and by what amount the expected result of 4505 / 2 = 2252.5 heads differs from the actual results in those trials.  We would expect 2252.5 wins (+/- 0.5), but we actually got 2219 wins, a difference of 33.5.  How common is a difference of 33.5 or more in 10,000 trials of flipping a coin 4505 times each trial?  Glad you asked, even if you didn’t.  Take a look at the following plot:

deferring plot (10000 trials)

The above plot was produced by simulating the random flipping of a fair coin 4505 times per trial for 10,000 trials.  Each little dot represents the amount by which the number of heads in each trial differed from the expected amount (2252.5).  So, for example, roughly in the middle of the plot at the bottom is an outlier where on that particular trial of 4505 flips we had about 140 fewer heads than would have been expected, but this is the extreme outlier among 10,000 trials.

Recall that the actual difference in the expected number of wins versus the actual number of wins was 33.5, which falls well within the dark band in the middle of the plot between I’m gonna say -35 and +35.

For those interested, the above plot was produced with the following Mathematica 5.1 code:

flip[] := Random[Integer, 1];
doFlips[trials_] := Block[{results = {}, heads = 0},
      
      results = {};
      Do[
        heads = 0;
        Do[
            heads += flip[];
            , {ii, 1, 4505}]
          AppendTo[results, heads - 2252.5];
        , {jj, 1, trials}];
      
      Return[results];
      ];
];

ListPlot[doFlips[10000]]

Conclusion

I’m going to conclude there is no statistical advantage to deferring.  Even though the teams that took the opening kickoff (either didn’t defer or the other team deferred) only won about 49.3% of the time, that falls well within the margin of error for this sample size (4512 games).

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