How Many Runs Makes a Win?

I'm sort of gearing up to do some historical work on the Reds (I hope!).  One of the questions I wanted to answer was how many runs equals a win.  We did something like this in SABR 101x, but something about the algebra didn't seem right at the time, and the estimates we were finding seemed low.

In any case, I decided to instead generate this estimate in a fairly inelegant way called the "+1 method" (mentioned here by Patriot, though in a different context).  The approach is:

1. For each year in baseball history, find the average PythagenPat record based on average runs scored and runs allowed per team.  This will, obviously, be a 0.500 record, unless there is a clerical error.
2. For each year, find the expected PythagenPat record if you add 1 run scored to the average team.  This will be, barely, a 0.500+ record.
3. Figure the expected number of wins each year based on those two records.  This will vary depending on the number of games, and, of course, the expected record.
4. Calculate the difference between the "0.500 record" wins and the ".500 record +1 run" wins.  This gives you the wins per run.
5. Take the reciprocal of wins per run.  This is runs per win.

I actually added 0.1 runs instead of 1 run, just to avoid changing the run environment.  It probably doesn't matter.  I also tried it using +1 run allowed or -1 run scored, and it really didn't change the estimates.

Here are the results!

In addition to my run per win estimate (the blue line), I've also added straight-up total runs scored per game (i.e. runs scored + runs allowed for each game).  In the past, I've advocated just using total runs scored per game as a shorthand for the runs per win estimate.  You can see that it tracks pretty well (although it consistently underestimates the correct number over most of baseball history.

To get away from the noise of the 1800's, let's just look at the live ball era:

Ok, so from this you can see that runs per win (again, focus on the blue line) tracks between 9 and 10 runs pretty consistently.  But it definitely does vary with run environment.  As runs per game increases (orange line), so too does the number of runs you need to score to win a game.  That makes sense.

When I was working on my player value series, and as the WAR frameworks at FanGraphs and Baseball Reference were being developed in the mid-2000's, you often heard people say that 10 runs = 1 win.  That was pretty much true from 1993-2009.  But as the run environment has plummeted over the past several years (the strikeout era?), the runs needed per win has decreased as well.  In 2013, I have it at 9.07 runs per game.  It's a small thing, but something to keep in mind as we look at different eras over baseball history.

Also, different leagues unquestionably differ in runs per win.  The AL should always require more runs per win than the NL, at least since the debut of the designated hitter.  But I just wanted a blanket per-year conversion, so...

I'm sure these numbers are available elsewhere, but for those interested I'm posting a spreadsheet with these data on google docs.  If you use those data for a project that is published somewhere, please link back to this post.  All data pulled from the Lahman Database.

Reds History, Graphically

I had a fun idea for a graphic that summarized the Reds' regular season winning percentages, playoff appearances, and top players over their history.  Here is the result:

You can click it to make it larger.

Some Takeaways:

Winning Teams

Based on a five-year moving average, the Reds have had six collections of winning teams: the late 1890's, the late 1910's-1920's, the late-30's-early-40's, the teams of the 60's and 70's, the 1990's, and the current 2010+ teams.  All but one of these winning stretches have at least produced one playoff appearance.  The playoffs weren't a thing in the 1800's, although the Reds never finished in first place in the National League until 1919.  Of the successful stretches of Reds teams during times when the World Series was an annual event, only the current incarnation has not won a World Series.

The highest winning percentage in Reds' history is not the Big Red Machine's peak in 1975, but rather the 1919 Reds team that won the World Series in the Black Sox scandal.  They went 96-44 (.686 WPct in 140 games).  That was a brilliant team, and the fact that their victory was tainted by what happened with the Black Sox just make that episode all the more irritating.  There's no reason to think that they couldn't have won that series anyway.

For the stat-minded Big Red machine fan, though, fear not: the 1975 Reds have the best PythagenPat winning percentage in Reds history (their mark of .662 just edged out the 1919 team's .654 PythagenPat).  The best PythagenPat winning percentage for the current Reds' squad was last year, 2013, at .576 (2010: .567; 2012: .558).

Losing Teams

The Reds have also have really only gone through four extended stretches as losing teams.  These include the 1900's, the 1930's, the mid-40's/early 50's, and then Jim Bowden-era from the late 1990's through the 2000's.

Great Players

I listed the top-26 players by rWAR (courtesey of Baseball Gauge).  I would have included more, but I ran out of space (sorry, Frank McCormick!).  Not surprisingly, the 1960's and 1970's, the most successful stretch in Reds history, were home to a lot of the great players from the Reds' past.  But I was surprised at how many of the great Reds players appeared not just during the peaks in the 20's and late 30's (as would be expected), but also during the big swoon in the early 30's.  That said, when you look at it, most of those greats were either finishing up their careers, or just starting out during that time...and many of them were responsible for the successes of 1938-1944.  I'm looking forward to digging into those teams a bit more.

The Cost of the Strikes

In 1981, because of a player strike, MLB played a shortened season.  And for some reason, the justification for which seems lost to history, they opted to take the winners of the first half and the second half as the teams that made the playoffs.  Meanwhile, the Reds, who had the best record in their division overall, went home in October.

In 1994, the Reds were in first place when the season ended, again due to a player strike.  That team would repeat their success and go to the playoffs in 1995, but it's hard not to wonder what might have been.

I tend to side with players over owners most of the time these days when it comes to financial disputes. I might not like that players make bazillions of times more money than people who do more important work outside the entiertainment industry.  But society has made its choices on how it spends its money, and I'd much rather the players share in those profits than it stay in the pockets of owners.  That all said, the strikes have come at awful times for the Reds.

Afterthought: I have no memory of writing it, but I found this somewhat similar post from 2009 after writing this article.  Funny when that happens!

Chapman abandons change (mostly)

So, less than two weeks ago, I wrote about how Aroldis Chapman's improvement this year can arguably be traced to the debut of his change-up.  Well, as Jeff Sullivan noted, almost coinciding with when I wrote that, Chapman now seems to be moving away from using his change-up.  In fact, he's thrown the pitch in only 1 of the last 5 games, and 2 of the last 8:

The reason appears to be that he has a hard time throwing the change-up for strikes.

The good news was that while he was not throwing it for strikes, he was usually missing down (assuming he was even trying to get it in the zone).  Nevertheless, it does look like the pitch has fallen out of favor.  So much for my last piece on him! :)

I personally hope that he can continue to work it in, even as a show-me pitch.  Hitters can catch up to his fastball if they know that it is coming.  The slider is a fantastic pitch, and I'm sure he can be quite successful as a fastball/slider reliever.  But a third pitch against right-handers, at least, would be one additional thing that hitters need to keep in their minds as they step in to face him.