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Alphabet Soup: AIPTOS, OBP, PPA

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What's up with the Twins wearing red caps every so often? Hey, Pohlad: your team looks lame with those stupid caps. And -- my God -- Carlos Baerga is still in the majors? Shouldn't he be playing for the Cancun Lobstermen?

One of the recurring themes in the Moneyball era is the importance of plate discipline. In my previous article I talked about the relationship between patience at the plate and the ability to hit for power.

Another commonly cited reason for GMs to assemble a collection of patient hitters is to make the opposing pitcher work. In particular, if you force a pitcher to throw a lot of pitches - whether it be by drawing walks, fouling off tough pitches, or simply working deep into the count before striking out - then the opposing manager is forced to dip into his relief corp earlier in the game. I don't know about you, but I would get freaked out every time I had to see Jim Brower, Cliff Politte, Felix Rodriguez, or any number of journeyman failed starters called in to maintain a lead (or, God forbid, maintain a tie game).

How do we estimate how long starting pitchers last against teams? Without looking up the exact number, which would require a thorough analysis of box score data, we can estimate the average innings pitched of a team's opposing starter (AIPTOS).

Let's say that a typical pitcher is effective for 100 pitches. Then, X pitches/PA translates to 100/X PAs. Out of the 100/X PAs, (1 - team OBP)x100% will be outs. (For now, let's limit the discussion to aggregate lineups and ignore the variance in OBP/SLG as a function of pitches in the plate appearance.)

Translating the number of outs into the number of innings, we have:

AIPTOS = (100/X) x (1-OBP)/3

The name AIPTOS is misleading, since it is not a measure of the average innings pitched by opposing starters as much as it is a measure of how quickly a team wears an opposing pitcher down. If you're the Red Sox or Yankees, your team might put up a five spot in the third inning and have the opposing starter out after 80 pitches and 3 1/3 inning. Understand what we're looking for here and use your intuition. Here's plot:

AIPTOS plot

What's that? Pictures are for sissies? Time for some manly numbers? Onto the tables!

TEAM P/PA OBP AIPTOS
Boston 3.86 0.358 5.54
Philadelphia 3.81 0.347 5.71
Oakland 3.86 0.336 5.73
Cincinnati 3.84 0.338 5.75
NY Yankees 3.71 0.355 5.80
Milwaukee 3.83 0.332 5.81
Florida 3.75 0.344 5.83
Arizona 3.79 0.335 5.85
Texas 3.8 0.331 5.87
San Diego 3.79 0.332 5.88
LA Dodgers 3.80 0.330 5.88
Cleveland 3.79 0.327 5.92
St. Louis 3.69 0.340 5.96
Chicago Sox 3.76 0.327 5.97
Colorado 3.73 0.331 5.98
Toronto 3.70 0.336 5.98
NY Mets 3.76 0.321 6.02
Minnesota 3.68 0.330 6.07
Atlanta 3.67 0.329 6.09
Detroit 3.67 0.329 6.09
Seattle 3.73 0.318 6.09
Washington 3.69 0.323 6.12
Tampa Bay 3.64 0.331 6.13
Baltimore 3.63 0.332 6.13
Houston 3.67 0.321 6.17
Chicago Cubs 3.61 0.328 6.20
Kansas City 3.65 0.319 6.22
Pittsburgh 3.65 0.319 6.22
LA Angels 3.64 0.320 6.23
San Francisco 3.54 0.327 6.34
AVG 3.72 0.332 5.99

*Stats are for 2005 season up to 28 Jul 2005

Notice that the top five teams in this table are all in the top third of major league offenses. Polished hitters in New York, Boston, and Philadelphia usually run the pitch count of opposing starters to 100 before the end of the sixth inning. When your opponents, on average, ask for 10 outs from their bullpen, there is a good possibility of getting into the underbelly of shallow bullpens.

Low-scoring teams like San Francisco, Kansas City, and Pittsburgh combine low OBPs with an impatient approach to allow opposing starters to pitch almost a 6 1/3 innings per start. These teams' opponents need only 8 outs from their bullpens. Note the anamolous Angels - they are a middle-of-the-pack offense and yet allow starters to go deep into games. I've played around with various models of offensive production and Angels teams are usually blips in the data. That's the case here, as well. Mike Sciosa, why do you torture me so? With the Angels moving runners around the bases without the use of actual hits (SB, sac bunts, Darin Erstad reaching on a CI), it would appear that they need fewer pitches to put some runs on the board.

I know what you're thinking: "The difference between the best and worst team in terms of wearing out starting pitchers is a lousy two bullpen outs?" Well, consider this: ever since OBP became fashionable in the early aughts, low payroll teams have been priced out of the on-base market. Guys like Jason Giambi started becoming compensated as much for their eye at the plate as for their home run power. A team can regain the competetive advantage of wearing a pitcher out by signing cheaper guys that work the count, foul off tough pitches, and make contact with the ball.

Imagine two teams, both who see an MLB-average 3.72 P/PA. Team A has the league's worst OBP at .320, while Team B has the league's best OBP at .360. Team A has an AIPTOS of 6.09, whereas Team B has an AIPTOS of 5.73. Team A realizes that starters are taking advantage of them but are unable to obtain OBP on the open market. Over the offseason, they obtain hitters that can work the count, but not necessarily ge on base. The upgrade from a league average P/PA of 3.72 to a league-best 3.85, but their OBP remains a sub-par .325. Their AIPTOS jumps to 5.84, much closer to the high-OBP Team B.

This is an extreme and simplistic example, as P/PA and OBP are correlated. But it shows that an organization can find ways to retain competetive advantages on offense even when the market for one skill or set of skills explodes. I'll be totally honest with you here, my favorite team is the Athletics, and I sense that their GM, Billy Beane, has collected a set of patient, pesky hitters that have solid (if not eye-popping) OBPs. The Athletics share the lead for most P/PA this year, by the way.

You're still thinking: "The difference between the best and worst team in terms of wearing out starting pitchers is a lousy two bullpen outs?" If you are playing a closely matched team in critical games that may be decided late, would you rather ask for 10 outs from your bullpen or 8? When would such a situation occur? How about a short playoff series...

Mad props to my homies on AthleticsNation for inspiration for this article, especially Donner and Fabulous G.