One more aspect of Brady v Manning

Obviously this is about Peyton Manning and Tom Brady, and the argument about which player is the better quarterback.  I’m not going to reach a conclusion here, but there are two things that are important to consider that as far as I can tell almost everyone ignores.

The first is articulated by Benjamin Morris of FiveThirtyEight in his article here, which is that Peyton Manning was tremendously successful with multiple head coaches and even with two different franchises, whereas Tom Brady has been successful only with Bill Belichick and the Patriots. This isn’t a slight against Brady per se, but it does leave some room for doubt.  Belichick did have Matt Cassel play quarterback for an 11-5 season after all, and had success this year with Brady suspended.  Meanwhile the Colts went 2-14 the season Manning missed with neck surgery.

The second is pretty old hat if you follow baseball and read FanGraphs like I do, but as far as I can tell the media and other internet discussions don’t bring this up as often in football, and with the Super Bowl next week and this article from The Ringer being published yesterday this is a good time to bring it up: players’ value to their team is really their “market value” (if we assume the market is perfect, which it isn’t, but…) minus their actual salary.  Over the course of his career, Manning was paid a lot more money than Brady (see for instance this Forbes article). Therefore, Brady’s teams have had a lot more money to spare to build a team around Brady than Manning’s teams have had to build around Manning.  Even before accounting for Bill Belichick’s team-building ability (which as far as we know is the best in the NFL) this gives Brady better teammates around him, which then improves Brady’s statistics.

Of course, Brady has still had much more team success than Manning has, and their stats are very similar. I certainly wouldn’t be confident in saying that Manning’s career is greater than Brady’s.  I just wouldn’t be confident in saying the reverse, either.

Estimating Trevor Story

Trevor Story, of course, became the first player to homer in each of his first four MLB games.  Obviously this is pretty improbable, so let’s estimate how improbable.

First we need the chance for Story to hit a home run in a given plate appearance.  I’ll use the FanGraphs depth chart projections, so that would be 15 HR in 490 PA, or about 3% per PA.

Story actually got 6, 4, 4, and 5 PAs in his first four games, so I’ll just look at games with 4-6 PAs.

For 4 PAs in one game, there’s an 11.7% chance that Story hits at least 1 HR.  For 5 PAs, 14.4%, and for 6 PAs a 17.0% chance.

For the number of PAs Story actually got, this gives a 1 in about 2984 chance to homer in all of his first four games.  This is somewhat sensitive to the actual PA distribution, but it seems the chance is somewhere in the neighborhood of 1 in 2500 to 1 in 3000 or so, if you get that total number of PAs.  Obviously, very improbable … for any individual player.

It’s a little less astonishing that this happened when you realize that there have been somewhere around 18000 major league baseball players in history.  Using the FanGraphs leaderboards, I get a total of 7417 non-pitchers who have recorded at least 20 PAs since 1900.

It’s … a lot of work to figure out the actual probability of some major league player homering in his first four games of his career.  So I don’t have a good actual estimate for the chance of this happening.  But I think that it’s not terrifically unlikely that some player would have, by this time, homered in his first four major league games. It’s probably reasonably likely after accounting for what I’ve seen called the Wyatt Earp effect; in short, large populations are almost certain to have a few large outliers just by chance.

Still, this is certainly a remarkable start to any individual player’s career.  Congrats to Trevor Story for a resoundingly successful major-league debut; he’s been the fifth-best position player in the majors so far this year, by FanGraphs.

A 2-1 result in a best-of-3 is rarely more likely than a 2-0

This is just a minor thing that bothers me when hearing predictions.  It comes up a lot with League of Legends casters; I hear a fair number of 2-1 predictions for a best of 3 that the casters feel is pretty evenly matched.

In the case of the teams being exactly evenly matched and there being nothing like home-field advantage (or side advantage in League), you get a 2-0 result 50% of the time and a 2-1 result 50% of the time.  Making the teams uneven of course makes a 2-0 result more common.

If there is a home-field/side advantage, such that the team that is more likely to win game 1 is less likely to win game 2, then it is true that with two very closely matched teams a 2-1 is actually very slightly more likely than a 2-0.

Of course what the casters really mean is they just think the teams are close to even.  But you should not be surprised when teams that are evenly matched go 2-0 in a series, unless you have some reason to believe that winning the first game makes you less likely to win the second game.